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Index

Symbols

.mnf suffix, 325 2-D to 3-D analysis

benefits, 155 initial-state-based analysis, 161 introduction to, 155

key commands, 158

map solution variables, 161 performing, 159 requirements, 155 restrictions, 161

selecting a region for remeshing, 160 starting, 160

substep at which to initiate, 159 supported analyses, 155 understanding the process, 157

A

ADAMS (see ANSYS-ADAMS Interface) ADAMS.MAC macro, 325

adaptive meshing

activating custom subroutines, 82

ADAPT macro: customizing (via UADAPT.MAC), 83 custom loads (via ADAPTBC.MAC), 82

custom meshing (via ADAPTMSH.MAC), 81 custom solution (via ADAPTSOL.MAC), 82 element types for, 79

example problems: finding, 84 hints, 83

modifying the basic process, 80 overview of, 79

prerequisites for, 79 process involved, 79 selective adaptivity, 80

user subroutines: employing, 81 aeroelastic analysis, 375 ANSYS-ADAMS Interface

ADAMS simulation: running, 321 ADAMS.MAC macro, 325

batch mode

exporting to ADAMS, 320 importing loads, 324

example analysis, 326 exporting to ADAMS, 318 interface points: modeling, 317 introduction, 315

loads

transferring from ADAMS to ANSYS, 321 methodology employed by, 325

modal neutral file, 318, 325 model: building, 316 overview of, 315 rigid-body dynamics, 315

verifying results following export to ADAMS, 320 weak springs, 323, 325-326

automatic rezoning, 135

B

birth and death of elements applying loads and solving, 333 building the model, 333 constraint equations, 332 controlled by analysis results, 335 example problems, 335

first load step: defining, 333 in linear models, 332

initial strain, 332-333

material properties: changing, 333 multiple load steps, 332 Newton-Raphson option, 332 nodal constraints and loads, 333 overview of, 331

reviewing results, 334 sample input, 334-335

status of an element: determining, 332 strain, 331

subsequent load steps: defining, 334 supported elements, 331

usage guidelines, 332 using in an analysis, 333

C

Campbell diagram, 225 CDB generic mesh file, 101

CMS (see component mode synthesis) component mode synthesis

database: saving copy during generation pass, 287 definition of, 285

example analysis, 290

example:expanding a superelement in a transformed location, 305

expanding superelements in transformed locations, 290

expansion pass, 289 generation pass, 287 introduction to, 285

lumped mass approximation, 287 master DOFs, 287

methods supported, 285

mode shapes: plotting or printing, 290 offsets: applying to node and element IDs, 290

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process (passes) involved, 287 solvers and files used, 286

specifying CMS results files for postprocessing, 290 superelement: creating, 287

understanding, 285 use pass, 289

constraint equations

in a cyclic symmetry analysis, 172 Coriolis effect, 223

cut boundary displacement method (see submodeling) cyclic symmetry analysis

ANCYC command, 196 automated, 163 availability, 163

basic sector, 165 buckling, 183

commands affected by non-cyclic loading, 176 constraint equations for non-cyclically symmetric loading, 173

coupling and constraint equations (CEs), 172 CYCLIC command, 166

database: saving after solution, 192 definition of cyclic symmetry, 163 deleting a sector load, 173

Duplicate Sector solution method, 171 edge component pairs, 166

edge node patterns: identical vs. dissimilar, 169 example: buckling, 203

example: modal, 198 EXPAND command, 196 expanding the solution, 196 geometric nonlinearity, 181

graphical picking of non-cyclic boundary conditions, 176

harmonic index, 178 inconsistent constraints, 173 introduction to, 163

large-deflection prestressed modal, 181 linear buckling, 183

meshing the cyclic sector, 169 modal, 178

model only one sector, 163

model verification during preprocessing, 171 model verification during solution, 192 modeling, 164

most common commands, 164

naming convention for lowand high-edge component pairs, 166

nodal diameter, 178 non-cyclic loading, 176

non-cyclically symmetric loading, 173

phase sweep of repeated eigenvector shapes, 197

plotting and listing non-cyclic BCs, 176 postprocessing, 193

prestressed modal, 180

real and imaginary solution components:understanding, 195

sector angle, 166

SECTOR primary variable, 173 solution architecture, 171 solving, 171

static (linear and large-deflection nonlinear), 176 stress-free modal, 179

traveling wave animation, 196 understanding, 163

unmatched nodes on edge-component pairs, 170 vt accelerator, 178, 181

D

damping substructuring, 266

diffracted wave, 381

E

elements

birth and death of, 331 expansion pass

substructuring, 275

F

files

.mnf, 325 Jobname.LOOP, 3 Jobname.NODE, 249 Jobname.PDS, 3

probabilistic design analysis file, 9 sename.sub, 266

fixed-interface CMS method, 285

flexible body dynamics (see rotating structure analysis) free-interface CMS method, 285

H

hydrodynamic analysis, 381

J

Jobname

in a submodeling analysis, 247 in a substructure analysis, 265

L

loads

substructuring, 266

 

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M

macros ADAMS.MAC, 325

manual rezoning, 87 material properties

changing to deactivate or reactivate elements, 333 mesh nonlinear adaptivity, 135

meshing adaptive, 79

modal neutral file, 325 model generation

adaptive meshing, 79

N

natural frequencies, 230 Newton-Raphson

birth and death analysis, 332 nonstandard uses of ANSYS, 339

O

ocean loading, 381 offsets

to node and element IDs in a CMS analysis, 290

P

PDS (see probabilistic design) pile analysis, 347 probabilistic design

algorithms available, 24, 51 analysis file

creating, 9 specifying, 13

analysis flow, 3

analysis results: reviewing, 41

and traditional analysis methods: comparison of, 2 correlations between random variables, 20 cumulative distribution function: plotting, 42 definition of, 1

employing, 8 example analysis, 69 example problem, 10

histogram: plotting, 42 HTML report: generating, 67

inverse probabilities: requesting, 42 loops: executing, 25

Monte Carlo Simulation method, 51 parallel execution, 27

parameters: establishing, 12 PDS database

clearing, 69 description of, 3 saving, 68

postprocessing, 59

print correlation matrix, 43

Probabilistic Method Determination Wizard, 24 probability value: printing, 42

process involved, 8 random input variables

declaring, 14 visualizing, 20

random output parameters: specifying, 23 report options, 43

response surface analysis: sampling methods, 55 response surfaces: fitting and using, 38 restarting an analysis, 68

results data: reviewing, 41 results report: creating, 44 sample history: plotting, 42 scatter plot, 43 sensitivities, 43

serial execution, 27 statistics: viewing, 42 techniques available, 51 terminology

analysis file, 3 loop file, 3 looping, 3

random input variables (RVs), 3 random output parameters (RPs), 3 response surface set, 3

simulation, 3 simulation loop, 3 solution set, 3

trends: viewing, 43 understanding, 1 using, 8

variables: guidelines for defining, 44 when to use, 3

Probabilistic Design System (PDS) (see probabilistic design)

Probabilistic Method Determination Wizard (see probabilistic design)

R

residual-flexible free-interface CMS method, 285 rezoning

automatic (see mesh nonlinear adaptivity) balancing residual forces, 118

benefits, 87

contract boundaries, 116

convergence difficulties during mapping operation, 120

example, 124, 127

file structures for repeated rezonings, 121

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forces and isolated applied displacements, 116 horizontal rezoning, 101

introduction to, 87 key commands, 96 limitations, 89

mapping variables, 118 mesh control during, 114 multiframe restart after, 120

multiple regions remeshed at the same substep,101 nodal temperatures, 116

postprocessing results, 121

pressure and contiguous displacements, 116 remeshing, 99

repeating as needed, 120 requirements, 90 restrictions, 123

selecting a region for remeshing, 98 starting, 98

substep at which to initiate, 97 supported analyses, 90 understanding the process, 92

using a generic (third-party) mesh, 101 using manual mesh splitting, 105 variable mapping, 118

rigid-body dynamics, 315 rotating structure analysis Campbell diagram, 225

Campbell diagram analysis example, 231 choosing the appropriate reference frame option, 230

Coriolis analysis example, 234 flexible body dynamics, 228

harmonic analysis for unbalance forces example,236 introduction to, 223

natural frequencies, 230 rotating reference frame, 228 rotordynamics, 224

stationary reference frame, 224 understanding, 223

rotordynamics (see rotating structure analysis)

S

soil data description, 357 soil-pile-structure analysis, 347

soil data description, 357 solid modeling

adaptive meshing, 79 mesh density, 79

State-Space Matrices Export of, 341

submodeling, 245

analyzing the submodel, 250

coarse model: creating and analyzing, 247 creating the submodel, 248

cut-boundary interpolation: performing, 249 distance between cut boundaries and stress concentration: verifying, 252

example input, 253 example problems, 261 introduction, 245 shell-to-solid, 259 understanding, 245

Submodeling

process involved, 246 substructuring

applying loads, 266 benefits of, 263 bottom-up, 278 damping, 266

example problems, 283 expansion pass, 275 generation pass, 264 introduction to, 263 nested superelements, 282 prestressed, 282

process (passes) involved, 263 sample input, 278

top-down, 279 use pass, 270

superelements

and substructuring, 263

expanding in transformed locations, 290 generating automatically, 281

T

traveling wave animation, 196

U

UPFs (see user-programmable features) user-programmable features

available types, 338 overview of, 337 process involved, 337

V

Variational Technology, 75

W

wind turbine analysis, 375 sequentially coupled, 375

 

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ANSYS WORKBENCH

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2010

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.........................................................................................................................................

5

1. ..........................................................................................

7

1.1. .................................................................................................................................

7

1.2. ........................................................................................................

8

1.3. ......................................

12

1.4. .......................................................................

14

1.5. . .................................

16

1.6. ....................................................................................................

20

1.7. ..............................................................................................

22

1.8. ...............................................................................

24

1.9. ..............

32

1.10. ...........................................

42

1.10.1. .........................

49

1.10.2. ............................

51

1.10.3. ...........................

53

1.11. ANSYS ...................................................................................

57

..............................................................

60

2. ANSYS WORKBENCH.........................................................................

61

2.1. Workbench ..................................................................................

62

2.2. Workbench..........................................................................................

67

..............................................................

73

3. ..............................................................................

74

3.1. Design Modeler..............................................................

75

3.2. ..........................................................................

81

3.2.1. .............................................................................................

86

3.2.2. ........................................................................

88

3.2.3. ....................................................

92

3.2.4. ......................................................................

95

3.3. ..............................................................................................

99

3.3.1. .....................................................................

99

3.3.2. ...........................................................................

110

3.3.3. .....................................................

123

3.4. ................................................................

130

3.5. ........................................................................

132

............................................................

136

3

 

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4. ..................................................

138

4.1. ..........................................

138

4.2. ..........................................................................................

144

4.3. ...........................................................................

147

4.4. .........................................................................

157

4.4.1. ..............................................................

162

4.5. ....................................................................

164

...........................................................

170

5. ..............................................................

171

5.1. ............................................................................................................

171

5.2. .................................................................................

174

5.3. Mesh Control .............................................................................................

181

5.3.1. .....................................................................................

181

5.3.2. .....................................................................................

189

5.3.3. ..................................................................

195

5.3.4. Refinement ..................................................................................................

195

5.3.5. ...............................................................

198

5.3.6. ....................................................................

201

5.4. .............................................................................

202

5.5. ...........................................................................................

204

5.6. ...................................................................................

204

5.7. Mechanical ANSYS ..

208

...........................................................

209

6. . .............................

211

6.1. ......................................................................

213

6.1.1. .............................................................................................

218

6.1.2. .....................................................................................

221

6.2. ...........................................................................................................

234

6.3. ..........................................................................................

241

6.3.1. .........................................................................................

243

6.3.2. .............................................................................................

245

6.3.3. .......................................................................

247

6.3.4. .........................................................................

249

6.3.5. ...............................................................................

249

6.3.6. ......................................................................

252

...........................................................

252

.................................................................................................................................

255

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– .

( ) , -

.

– -

(21), (22) .

.

-

. -

.

1.6.

(18),

,

, , -

( ).

,

, K , -

, –

U . -

(21) , ,

, . -

T .

20

(18) (21) K :

, , , . [2].

: [1, 2, 5, 6].

(« ») -

, -

. -

: , -

, , , -

.

, -

.

, -

.

, ,

,

.

(20) -

(22) -

[5]. -

.

,

.

.

, -

– , , -

.

.

-

21

vk.com/club152685050 | vk.com/id446425943

( , ,

.) .

,

-

. -

[5]. -

-

, . -

, -

.

1.7.

-

U -

U e . -

.

U e

(14) F e , -

, . -

,

,

.

-

-

, ,

. -

-

. -

22

. -

. , -

-

, , . -

[8, 9].

(18), , . -

,

:

N

 

Ps Ksquq Psg Psq .

(23)

q 1

( , , -

) .

, -

, ,

. -

.

-

,

.

-

. -

. -

.

23

vk.com/club152685050 | vk.com/id446425943

1.8.

-

, .

, -

. -

, , , -

.

, n m ,

( . 1.3). -

; -

, .

y

ujy

j

 

ujx

 

 

 

e

h

 

 

Piy

 

 

i

Pix

x

a

b

a

. 1.3

-

. ,

– . -

, .

( ) . 1.4.

( ) x, y .

) x, y -

i.

24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

u

j

 

 

 

 

 

 

 

 

 

 

 

 

ujy

 

 

 

x

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

j

 

 

 

y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ujx

 

 

 

 

 

 

 

 

 

l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

y

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

 

 

 

Fiy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fi

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

i

 

Fix

 

 

 

 

x

 

 

 

 

 

 

 

 

 

. 1.4

, -

:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

u

i

 

 

 

F

 

 

 

 

 

 

 

 

 

 

U

 

 

 

, F

 

i

.

(24)

 

 

 

 

 

 

 

 

 

 

 

 

e

 

u

j e

 

 

e

Fj e

 

, -

, , -

.

 

 

uix

 

 

 

 

Fix

 

 

 

 

 

u

iy

 

 

 

 

 

F

 

 

 

Ui

 

 

 

 

 

F i

 

iy

 

 

U

 

 

 

 

,

F

 

 

 

 

(25)

 

 

 

.

e

Uj e

 

u

 

 

 

e

Fj e

 

F

 

 

 

 

 

 

 

jx

 

 

 

 

 

 

jx

 

 

 

 

u jy

e

 

 

 

Fjy

e

 

:

25

vk.com/club152685050 | vk.com/id446425943

 

 

 

 

 

 

 

 

 

U1

P1

 

 

 

 

 

 

 

 

 

 

 

 

....

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

....

 

 

 

 

 

 

 

 

U Ui

 

, P P i

,

(26)

 

 

 

 

 

 

 

 

 

 

....

 

....

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Un

P

 

 

 

 

 

 

 

 

 

 

 

 

 

 

n

 

 

U

 

U

 

uix

, P

 

 

P

Pix .

 

 

 

i

 

i

u

i

 

i

 

P

 

 

 

 

 

 

 

iy

 

 

 

 

 

 

iy

 

 

U P (26) -

. -

-

.

: «ix»

« 2i 1», «iy» « 2i ».

, -

,

u1

u1

 

P1

Pi

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

u

 

 

 

u

 

 

P

 

P

 

(27)

U

 

2i 1

 

 

 

q 1

,

P

2i 1

 

s 1

,

 

u

2i

 

 

u

q

 

 

P

 

 

P

 

 

 

 

 

 

2i

s

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

u2n

uN

 

 

P2n

PN

 

q, s – -

; N -

.

( ). -

x :

u

(

x

) 1 2

x

.

(28)

(28) i, j:

26

ui 1 2

xi ,

u

j 1 2

x

j .

(29)

1, 2 (29) (28),

u

(x) N (

x

) e U

e Ni , N j e U

e ,

(30)

Ni (x j x ) / l, N j (x xi ) / l -

( . . 1.4); l – .

Ni , N j

-

:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ni N j 1, Ni (

x

j ) N j (

xi ) 0, Ni (

xi ) N j (

x

j ) 1.

(31)

 

(30),

 

 

 

 

 

du

(x)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B

e U e .

(32)

 

d

x

 

B e :

 

 

 

 

B

 

1

,

1

.

(33)

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

 

 

 

 

l

l

 

 

E E B e

 

e ,

(34)

U

E .

:

 

 

 

 

 

 

Fi

S , Fj S ,

(35)

S .

(34) (35)

 

 

 

1

1

 

 

 

 

 

 

 

 

B e

U

.

 

F S

1

 

ES

1

 

(36)

 

 

e

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

 

 

 

 

 

(36)

 

 

e

 

e

 

e ,

(37)

K

U

F

27

 

 

 

vk.com/club152685050 | vk.com/id446425943

K e

, 2 2:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K ii

K ij

 

ES

1 1

 

 

 

K

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.

(38)

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

K

ji

K

jj e

 

l

1 1

 

 

(37) . -

 

x

:

 

 

 

 

1 (x j xi ) / l, 2 ( y j yi ) / l ,

(39)

xi , x j , yi , y j

i,

j .

 

x

,

 

 

 

 

ui uix 1 uiy 2 ,

u

j

u jx 1 u jy 2 .

(40)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

e U e ,

 

(41)

 

 

 

 

 

 

 

 

 

U

 

1 2

0

0

 

 

 

 

 

 

 

 

 

 

 

 

 

e 0

0

 

 

 

.

 

 

 

1

2

e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T

 

U Te F e .

 

(42)

 

 

 

 

 

U

F

 

 

 

 

 

 

 

 

 

 

 

 

e

 

e

 

 

 

 

 

 

 

(41) (42),

 

 

 

 

 

 

 

 

 

 

 

U Te eT

 

e U Te F e ,

 

(43)

 

 

 

 

F

 

, U e

, -

 

 

F e

Te

 

e .

 

(44)

 

 

F

 

(37) (41),

 

 

F

 

 

T

 

 

 

 

 

U

 

(45)

 

K

 

e ,

 

e

 

e

e

 

 

 

e

 

 

 

 

 

 

28

 

 

 

 

 

 

 

 

, (37):

K e U e F e , (46)

K e

4 4:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T

 

 

 

 

 

 

 

K

ii

K

ij

 

 

 

 

K ij

K ij

 

 

 

 

 

K

 

 

 

 

 

 

 

 

 

K

 

 

 

 

 

 

 

 

 

 

, K

 

 

 

 

1

1

 

1 2

 

. (47)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

ij

 

 

K ij

K ij

 

 

 

 

e

 

e e

 

 

e

 

K ji

K jj

e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

1

2 2

 

, (47)

.

, -

P .

( . 1.5), N=2n

:

m F

 

 

P

 

 

 

 

 

 

 

ix

 

 

ix

0,

i 1, 2,..., n .

(48)

F

P

e 1 iy

e

 

iy

 

 

 

 

 

 

2

Fiy

2

 

Fiy3

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

y

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fix3

 

 

 

Fix1 Fix1 i

Piy Fix4

Fix4

 

 

 

x

 

 

 

 

 

 

 

 

 

 

 

Fiy3

 

Fix3 Pix

 

 

4

 

1

 

 

 

 

 

 

 

Fiy2

. 1.5

 

(46)

 

K U P ,

(49)

K ( ) .

-

,

:

29

vk.com/club152685050 | vk.com/id446425943

 

m

 

 

 

 

 

(50)

Kij

Kij

e , i, j 1, 2,..., n .

 

e 1

 

 

 

 

i, j -

Kij e

m .

 

-

, K -

. -

K e

-

N N.

-

K -

(Ksq )e

m

 

Ksq (Ksq )e , s, q 1,2,..., N .

(51)

e 1

(Ksq )e

q, s m .

(49)

U . -

– .

. 1.5.

U , (49),

.

(49), . -

-

N

 

Ps Ksquq .

(52)

q 1

30

U -

U e (41) -

U e . ( ) -

l u j ui , (32), (34) (35)

, .

, -

,

. -

x, y, z -

-

. (41)-(47) -

( -

):

e

1

2

3

0 0 0

 

 

0

0

0

 

 

 

 

,

(53)

 

 

 

 

1

2 3

 

 

 

1 (xJ xi ) / l, 2 ( y j yi ) / l,

3 (z j

zi ) / l .

 

, , -

,

.

. i -

3 : uix , uiy , uiz . -

n 3n

, ,

N=3n.

31

vk.com/club152685050 | vk.com/id446425943

1.9.

h, -

, -

( . 1.6).

,

x, y.

x , y , xy ,

z

yz

 

zx 0 .

x

, y , xy

z

 

 

 

x y ,

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.

 

 

 

 

 

 

 

 

 

 

 

 

 

y

 

 

 

j

 

 

qy

q

 

 

 

 

 

 

Psy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

qx

 

 

 

 

 

 

 

 

 

gy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

gx

 

 

 

 

 

 

 

s

 

 

 

 

 

 

 

 

i

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Psx

uky

 

e

 

 

 

 

 

 

 

 

 

 

 

 

k

 

 

 

ukx

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

. 1.6

-

, , , .

m ,

n ( .

. 1.6). , -

32

, -

qx , qy

, q qx , -

 

e

qy e

g x , g y

, g gx .

 

e

g y e

-

. ( ) -

Pi :

 

 

 

 

 

 

P1

 

 

 

 

 

...

 

 

 

Pix

 

 

 

 

Pi

 

P Pi

 

, Pi

P .

(54)

...

 

 

 

iy

 

 

 

 

 

 

 

Pn

, ( )

 

U1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

U

...

 

,

U

 

U

 

uix .

(55)

U

 

 

 

 

 

 

i

 

 

 

i

 

i

u

 

 

...

 

 

 

 

 

 

iy

 

 

 

 

 

 

 

 

 

 

 

 

Un

-

.

. 1.7. x, y.

33

vk.com/club152685050 | vk.com/id446425943

 

Fjy

y

 

 

ujy

 

 

 

ujx

Fjx

 

 

j

 

 

 

 

 

x

Ve

 

qy

 

 

 

 

 

 

 

qx

Fiy

 

gy

 

 

uiy

 

 

 

 

 

Fky

 

gx

 

 

 

 

i

uix

Fix

uky

 

 

 

 

k

ukx Fkx

. 1.7

:

 

Ui

 

 

 

Fi

 

 

 

j

F

j

(56)

U

U

,

 

 

F

,

e

U

 

 

 

 

e

F

 

 

 

 

k e

 

 

 

k e

 

U

j

U

u jx

, F

 

 

F

 

Fjx .

 

j

 

j

 

 

j

 

 

 

 

u jy

 

 

 

 

 

Fjy

x, y -

:

ux x, y

 

U (x, y) uy x, y

.

(57)

 

 

 

-

ux x, y 1 2 x 3 y, uy x, y 4 5 x 6 y .

(58)

34

(58) -

, 6 :

uix 1 2 xi 3 yi ,

 

 

4 5 xi 6 yi ,

 

uiy

(59)

..................................

 

 

 

 

4 5 xk 6 yk .

 

uky

 

(59) 1 6 . -

(58), , -

-

:

 

 

 

U (x, y) e N(x, y) e U e ,

 

 

(60)

 

 

 

 

 

 

 

 

;

N (x, y) e INi IN j

INk e

 

 

1

0

 

 

 

1

 

 

 

I I

 

 

; Ni

 

 

 

(ai bi x ci y) -

2 e

 

 

0

1

 

 

 

 

 

 

; ai x j yk xk y j ,

 

 

 

 

 

 

 

 

 

 

 

1

 

1

xi

yi

 

b y

j

y

,

c x

x

j

,

 

 

 

 

1

x

 

y

 

 

e

 

j

j

i

k

 

i k

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

x

 

y

k

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

k

 

 

i jk . N j , Nk -

, -

i, j, k . Ni (x, y)

i ,

N j (x, y) Nk (x, y). -

, -

.

-

(60) :

35

vk.com/club152685050 | vk.com/id446425943

 

x

 

 

ux / x

 

 

 

 

 

 

uy / y

 

(61)

y

 

 

.

e

 

 

 

/ y uy

 

 

 

xy e

ux

/ x

 

(61) (60),

 

 

 

 

e B e U e ,

 

(62)

B e , :

 

1

 

bi

0 | bj

0 | bk

0

 

1

 

 

 

 

B

 

 

0

ci

|

0

c j

|

0

ck

 

 

 

Bi B j Bk

 

. (63)

2

 

 

 

2

 

e

 

 

 

|

c

 

b

 

|

c

b

 

 

 

 

 

 

 

e c b

j

j

 

 

 

e

 

 

 

 

 

 

i

i

 

 

 

 

 

k

k

 

 

 

 

 

 

 

:

x

e y D e e D e B e U e , (64)

xy e

D e :

 

E

1

 

0

 

 

 

D

 

1

0

 

,

(65)

 

 

e

1 2

 

 

 

 

 

 

 

 

 

1

 

 

 

 

0

0

 

 

 

 

 

 

 

2

 

 

 

 

 

 

e

 

 

E – ; – .

-

-

. , D e B e -

. ,

.

-

, [1, 7], -

-

36

,

, ,

.

-

– ,

, -

, :

 

 

U1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

U

 

...

 

 

,

U

 

U

 

 

uix .

(66)

 

U

i

 

i

i

 

 

 

 

 

 

 

 

 

 

 

 

 

...

 

 

 

 

 

 

 

 

uiy

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Un

:

 

U

i

 

 

ui, j,k x

 

 

 

 

,

(67)

U Uj

Ui,j,k Ui, j ,k

.

e

 

 

 

 

ui, j ,k y

 

 

Uk e

 

 

 

 

-

-

:

U (x, y) e N(x, y) e U e .

(68)

(62) :

 

x

 

 

 

 

y

 

B U

.

(69)

e

 

 

e

e

 

 

xy e

 

 

 

,

, [1]:

37

vk.com/club152685050 | vk.com/id446425943

T

m

T

m

T

g e dV

U P

e e

dV U (x, y) e

 

e 1 V

 

e 1 V

 

(70)

 

e

 

e

 

 

 

 

 

m

U (x, y) Te q e dS 0,

e 1 Se

Ve eh ,

e ; Se , -

,

.

V

Ve . -

, -

, -

,

.

(70) –

,

, -

, – -

– -

.

(64)-(69) (70)

T

U P

m

U

e 1

m

U

e 1

 

m

 

 

T

 

T

 

 

 

 

 

 

 

 

 

U

 

 

B

D

e

B

e

dV

U

 

 

 

e

 

e

 

 

 

e

 

e 1

 

 

 

Ve

 

 

 

 

 

 

T

 

 

 

 

T

 

 

 

 

 

 

 

 

 

 

N (x, y)

g dV

 

 

 

 

e

 

 

 

e

 

e

 

 

 

 

 

 

Ve

 

 

 

 

 

 

 

 

 

 

 

 

 

T

 

 

 

 

T

 

 

 

 

 

 

 

 

 

 

N (x, y)

q dS 0.

 

 

 

e

 

 

 

e

 

e

 

 

 

 

 

 

 

Se

 

 

 

 

 

 

 

 

 

 

 

 

 

(71)

(71)

38

K e

B Te D e B e dV ,

(72)

 

 

Ve

 

 

U T K

e

U

-

e

 

e

 

.

-

B e ,

K e B Te D e B e Ve .

(73)

(71) -

, -

, :

P eg N (x, y) Te g e dV .

(74)

Ve

 

(74)

g e Ve ( . . 1.7)

 

 

P g

 

 

 

 

g

x

 

 

 

 

 

ix

 

 

 

 

g

 

 

 

 

P g

 

 

y

 

 

 

 

iy

 

 

 

 

 

 

 

 

Pg

 

 

 

 

 

 

 

Pjx g

 

 

1

 

gx

 

 

g

i g

 

 

 

 

 

 

P

Pj

 

P g

 

 

 

Ve

g y

.

(75)

3

e

P g

 

 

 

 

 

 

 

jy

 

 

 

 

 

 

k e

 

 

 

 

 

 

 

 

P g

 

 

 

 

gx

 

 

 

 

 

kx

 

 

 

 

 

 

 

 

 

 

 

P g

 

 

 

 

g

y

 

 

 

 

 

ky

e

 

 

 

 

 

 

-

.

(71) -

, -

,

Se:

39

vk.com/club152685050 | vk.com/id446425943

P eq N (x, y) Te q e ds .

(76)

Se

 

(76) q e

i j Sij -

:

 

 

 

Pix q

 

 

 

 

qx

 

 

 

 

 

 

P q

 

 

 

 

q

y

 

 

 

 

 

 

iy

 

 

 

 

 

 

 

 

Pi q

 

 

 

 

 

 

 

q

 

 

1

 

qx

 

 

q

 

q

 

Pjx

 

 

 

 

 

P

Pj

 

P q

 

 

 

Sij

q

 

.

(77)

2

 

e

P q

 

 

 

 

 

 

 

 

jy

 

 

 

y

 

 

 

k e

 

 

 

 

 

 

 

 

 

P q

 

 

 

 

0

 

 

 

 

 

 

kx

 

 

 

 

 

 

 

 

 

 

 

 

P q

 

 

 

 

0

 

 

 

 

 

 

ky

e

 

 

 

 

 

 

(71),

,

 

 

T

P

P

g

P

q

 

 

 

 

0 .

(78)

U

 

K U

 

 

 

 

 

 

 

 

 

 

 

 

 

u1x , u1 y ,......, uny -

, (78) -

,

N=2n

 

K U P P g P q ,

(79)

K -

.

K -

(72)

 

,

 

m

 

Ksq (Ksq )e , s, q 1, 2,...., N ,

(80)

e 1

 

(72)

40

,

 

m

 

 

 

 

, i, j 1, 2,....,n .

(81)

Kij

Kij e

 

e 1

 

 

, P g ,

, P . -

P eg ,

(76), –

m

 

Psg (Psg )e , s 1, 2,...., N ,

(82)

e 1

 

P g

,

e

 

 

 

 

m

 

 

Pi g Pi eg , i 1, 2,....,n .

(83)

e 1

 

 

,

-

P q , –

 

 

m

 

 

Ps q

(Psq )e ,

s 1, 2,....., N ;

(84)

 

 

e 1

 

 

 

 

m

 

 

Pi

q

Pi eq ,

i 1, 2,...., n .

(85)

e 1

U , P , K -

q, s -

. 1.2.

(79) . -

-

F e ( . . 1.7).

T

 

F

 

 

g

q

 

T

 

U 0 .

(86)

U

e

P

 

P U

K

e

e

 

 

e

 

e

 

e

e

 

 

 

 

 

 

 

 

41

 

 

 

 

 

vk.com/club152685050 | vk.com/id446425943

,

 

 

(79),

 

:

 

 

 

 

 

 

 

 

 

 

K

e

U

e

F

e

P

g

P

q .

(87)

 

 

 

 

e

 

e

 

n ,

P F e ,

F e (87), (79).

, K -

-

. ( -

) K P ,

. 1.5. -

.

(79)

U .

(62) (64) . -

, us 0 , Ps ,

s (79), -

:

2n

 

Ps Ksquq Psg Psq .

(88)

q 1

1.10.

-

, -

.

, .

x, y, z [4, 9]

42

K

 

2T

K

 

2T

K

 

2T

w c

T

,

(89)

xx x2

yy y2

zz z2

 

 

 

 

 

t

 

T T x, y, z,t ; Kxx , Kyy , Kzz -

x, y, z ; w w x, y, z,t ; – -

; c – .

(89) -

. -

, .

S1 -

Ts1 :

Ts T x, y, z,t , x, y, z S1 .

(90)

1

 

S2 -

q:

Kxx

T

x K yy

T

y

Kzz

T

z q ,

(91)

 

y

 

 

x

 

 

z

 

x , y , z -

S2, , .

S2 , q 0 .

S3

:

Kxx

T

x Kyy

T

y Kzz

T

z h Ts Tb ,

(92)

 

y

 

 

x

 

z

 

Ts S3, Tb – -

, h – , qh h Ts Tb -

, .

– -

t0:

T0 T x, y, z, t0 .

(93)

43

 

vk.com/club152685050 | vk.com/id446425943

(89)-(93) : -

(89) (92), (93)

[4, 9]

 

 

1

T 2

 

T 2

T 2

 

 

T

 

 

 

Kxx

 

 

 

 

 

K yy

 

 

Kzz

 

 

2

w c

 

T dV

 

 

 

 

 

 

 

t

 

 

V

2

 

 

x

 

 

y

 

z

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(94)

 

 

 

 

 

h

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

qT dS

T Tb dS .

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

S

2

 

 

S

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(94) -

.

m , n . -

. ( ) -

( ) T T T1 Tn .

-

( . 1.8). jkp

q, ijp -

qh,

w. -

, T Te Ti Tj

Tk Tp e

. -

Q Te Qi

Qj Qk Qp e .

Z

P

Q

 

 

Q

 

 

 

 

TI

 

K

 

QK

I

 

J

X

Y

 

. 1.8

 

44

-

T x, y, z 1 2 x 3 y 4 z .

(95)

-

, 4 ,

-

1,..., 4 .

(95), :

T (x, y, z) N (x, y, z) e T e .

(96)

N(x, y, z) e 4-

Ni (x, y, z),..., N p (x, y, z), -

x, y, z :

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N (x, y, z) e

 

 

 

;

 

Ni

1

(ai bi x ci y di z),

(97)

 

 

 

Ni

N j Nk N p e

 

6Ve

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

xj

y j

z j

 

 

 

1

y j

z j

 

 

 

 

xj

1

z j

 

 

 

 

 

 

 

 

 

ai det

xk

yk

zk

; bi det

 

1

yk

zk

 

 

; ci det

 

xk

1

zk

 

;

 

 

xp

yp

zp

 

 

 

1

yp

zp

 

 

 

 

xp

1

zp

 

 

 

xj

y j

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

di det

xk

yk

1

 

; Ve

.

 

 

 

 

 

 

 

 

 

 

xp

yp

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N j , Nk , Np -

,

i, j, k, p .

:

 

Kxx

0

0

 

 

 

D

 

0

K yy

0

 

;

(98)

e

 

0

0

K

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

zz e

 

 

45

vk.com/club152685050 | vk.com/id446425943

 

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

x

 

 

 

 

g

T

 

B T ,

(99)

 

e

y

 

e

e

 

T

z e

 

1

bi

bj

bk

bp

 

B

ci

c j

ck

cp

.

6V

e

 

 

d

 

d

 

d

 

 

 

e d

i

j

k

 

 

 

 

 

 

 

 

p e

e, (96) ,

 

 

 

 

 

 

 

 

T

 

N (x, y, z)

 

 

 

 

T .

 

(100)

 

 

 

 

 

 

 

 

t

e t

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

(94) , (96)-

(100)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m

 

 

 

m

 

 

 

1

 

 

 

 

T

 

 

 

 

T

 

 

 

 

 

 

 

 

 

 

e

 

 

T

 

B e

D e B e T dV

 

2

 

 

 

 

e 1

 

 

e 1

Ve

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

c

 

N

T

N

 

t

 

T dV

 

 

 

w

 

N

T dV

 

 

Ve

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ve

 

 

 

 

 

 

(101)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

h

 

 

 

 

 

 

 

 

 

 

 

q N e T dS

T T N Te N e T dS

2

 

e 1

S2 e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

S3e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b

 

 

 

 

 

h

 

b

 

 

 

 

 

 

 

 

 

 

 

S3e

 

hT

 

N T dS

S3e

2

T 2dS.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(101)

T ,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

m

 

 

m

 

e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

0 .

(102)

 

 

 

 

 

 

T

 

 

 

 

 

 

 

T

 

 

 

 

 

 

 

 

T e 1

 

 

e 1

 

 

(102)

-

:

46

 

T

 

 

e

 

 

 

e

t

e

 

 

 

e e

 

e

e

 

e

 

 

e

 

 

 

Q

 

 

C

 

 

T

 

 

K

T

 

Q

q

Q g

Q

h ,

(103)

 

 

 

 

 

 

 

 

« » :

 

 

 

 

 

 

 

 

 

K e B Te D e B e dV

h N Te N e dS ,

 

 

 

(104)

 

 

 

 

 

 

Ve

 

 

 

 

 

 

 

S3 e

 

 

 

 

 

 

 

 

« » :

 

 

 

 

 

 

 

 

 

 

 

 

 

C e c N Te N e dV ,

 

 

 

 

 

(105)

 

 

 

 

 

 

 

 

 

 

 

Ve

 

 

 

 

 

 

 

 

 

 

 

 

, -

q, w, -

:

 

Q eq

q N Te dS ;

 

 

 

 

(106)

 

 

S2 e

 

 

 

 

 

 

Q eg w N Te dV ;

 

 

 

 

(107)

 

 

Ve

 

 

 

 

 

 

Q eh

hTb N Te dS .

 

 

 

 

(108)

 

 

S3e

 

 

 

 

 

(102) , -

:

 

 

 

 

 

 

q

g

 

h

 

 

C t

 

 

 

 

T K T Q Q

 

Q

,

 

(109)

K ( ) ; C

) ; Q q

, -

, Q g , -

,

Q h ,

.

.

47

vk.com/club152685050 | vk.com/id446425943

, (109),

-

:

m

Kij Kij e , i, j 1,..., n ; (110)

e 1

m

Cij Cij e , i, j 1,..., n ; (111)

e 1

 

 

m

eq ,

 

 

Qi

q Qi

i 1,..., n ;

(112)

 

 

e 1

 

 

 

 

 

m

eg ,

 

 

Qi

g

Qi

i 1,..., n ;

(113)

 

 

e 1

 

 

 

 

 

m

eh ,

 

 

Qi

h Qi

i 1,..., n .

(114)

e 1

(109) -

.

C

T K T

Q

,

(115)

t

 

 

 

 

Q Q q Q g Q h .

t t1 t0

T

 

T

1

 

T T

.

(116)

t

t

 

1

0

 

-

-

:

T

1

T 1 T

0 ;

(117)

2

 

 

 

 

 

Q

 

1

Q 1 Q

0 .

(118)

 

2

 

 

 

 

 

 

 

 

48

 

 

(116)-(118)

(115),

 

 

2

 

 

2

 

 

 

 

.

(119)

 

 

C T 1

 

 

K

T 0

K

 

t

C

 

2 Q

 

 

 

t

 

 

 

 

 

 

 

 

 

, -

(119)

. K , C , Q q -

(119), ( -

, ,

) . -

,

.

, (119)

.

, -

, (119)

, -, .

(91) – -

(92) –

(101).

(93) -

,

.

1.10.1.

. .

,

A ( . 1.9). i

q, j – -

qh.

49

vk.com/club152685050 | vk.com/id446425943

Ti

Tj

q

i

j

qh

x

 

 

L

 

 

. 1.9

( ) -

T Te Ti

Tj .

:

 

 

 

 

 

 

 

 

 

 

T x N e T e

Ni

N j e T e ,

(120)

Ni

x j

x

N j

 

 

 

 

x x

 

 

 

 

 

 

 

 

 

 

 

 

 

;

 

 

 

 

 

i

.

 

 

 

 

 

 

 

 

 

 

 

x j

 

 

x j

 

 

 

 

 

 

 

 

 

 

 

 

 

x j

 

 

 

 

xj

 

 

 

 

 

 

 

 

 

 

 

-

:

 

 

 

 

 

 

 

 

 

 

e

xx

 

 

 

e

 

1

 

 

 

(121)

 

 

 

 

 

 

 

 

 

D

K

 

,

 

B

 

 

L

 

1

1 .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(« ») :

 

 

 

K e B Te D e B e dV h N Te N e dS

 

 

 

 

 

 

Ve

 

 

 

 

 

 

 

 

 

 

S j

 

 

 

(122)

 

 

 

AKxx

 

1

1

 

 

 

0

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ah

 

 

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L

 

1

1

 

 

 

0

1

 

 

 

 

(« ») :

C e c N Te

Ve

 

cAL

2

1

 

 

 

 

.

6

 

 

1

2

 

x j x

 

 

 

 

x

 

 

 

 

x j

x

 

 

j

x j

xi

N e dV c x

x

 

 

 

 

 

x

 

x

xi

 

 

i

 

 

j

i

 

 

 

 

 

x j

xi

 

 

 

 

x x

 

 

i

dx

 

 

 

x j xi

(123)

 

 

50

,

q :

Qeq q N

Si

Qeh hTb N

S j

T 1

e dS qA ,

0

0

 

Te dS A hTb .

1

 

(124)

(125)

,

w:

g

 

T

wA x j x j

x

wAL

 

Q e

w N

e dV

 

x

x dx

 

.

(126)

L

2

 

V

 

 

x

i

 

 

 

 

e

 

 

i

 

 

 

 

i , q 0

: Qq 0 . e 0

1.10.2.

-

. -

.

( . 1.10). jk – -

q, ij – -

qh. .

y k

q

 

W(x,y)

i

j

qh

x

 

. 1.10

51

vk.com/club152685050 | vk.com/id446425943

 

 

( ) -

,

 

 

 

 

 

 

 

T

Ti

 

Tj

 

 

Tk .

q jk -

T e

 

 

 

ij, :

 

 

 

 

 

 

 

 

 

 

 

:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

qL

 

 

0

 

 

 

 

 

 

 

 

 

 

 

hT L

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

T x N T e

Ni

 

 

N j

 

Nk

T e ,

 

(127)

 

 

q N T dS

jk

 

 

 

 

 

 

 

hT N

T dS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Qq

 

 

1

, Qh

 

 

b ij

1 . (131)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

 

 

 

 

e

e

2

 

 

 

 

 

e

 

 

 

b

 

e

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

x

y

 

 

Si

 

 

 

 

 

 

 

S j

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

0

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

i

 

i

 

,

 

Ni

 

 

(ai

 

bi x ci y) ,

 

e

 

det

1

x j

y j

 

 

 

 

 

 

 

 

 

 

 

 

2 e

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

1

x

y

k

 

w:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

k

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

ijk;

ai

 

x j yk

xk y j ,

bi

y j

yk , ci

xk

x j .

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

w

 

 

 

 

 

 

 

 

 

 

g

w N Te dV

e

 

 

 

 

 

 

Nj, Nk , -

 

 

 

Q e

 

1 .

 

 

(132)

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

Ve

 

 

 

 

 

 

 

 

 

 

 

 

 

i, j, k.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

-

:

 

 

 

 

 

 

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ti

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

bi

 

bj

 

bk

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Kxx

 

 

 

 

o

 

 

 

 

 

 

 

 

 

 

bi

 

bj

bk

 

 

 

 

 

 

g

 

 

x

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

D

 

 

 

 

 

 

B

 

 

1

 

 

 

(128)

 

 

 

T

 

 

 

 

 

 

ci

 

c j

 

ck

Tj

.

(133)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,

 

 

 

 

 

 

 

 

 

 

 

.

 

 

 

e

 

 

 

 

 

 

e

 

 

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

o K yy

 

 

 

e

 

 

 

2 e ci

 

c j

ck

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

y e

 

 

 

 

 

 

 

 

 

 

 

k

 

 

K e B Te D e B edV h N Te N e dS

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.10.3.

 

 

 

 

 

 

 

 

 

Ve

 

 

 

 

 

 

 

 

 

 

 

 

S j

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ni Ni

 

 

Ni N j

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

B T

D

 

 

B

 

 

h

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(129)

 

e

 

 

 

 

 

N

 

N

 

 

 

N

 

 

N

 

 

0 dS

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

e e

 

 

 

j

 

 

i

 

 

 

j

 

j

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

, . 1.11. L 0, 2 ,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Sij

 

0

 

 

 

 

 

0

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

A 1 10 3 2. – , -

 

 

 

 

 

 

bibi

 

bibj

 

bibik

 

 

 

 

 

 

 

ci ci

ci c j

 

ci cik

 

 

 

 

 

2 1 0

 

 

 

Kxx

 

 

 

 

 

K yy

 

 

hLij

 

 

Kxx

50 . : -

 

 

 

b b b

 

b

 

 

b

b

 

c

 

c c

 

c

 

 

c c

 

 

 

1 2 0

.,

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

j

j

 

 

j

j

j

 

k

 

 

 

 

T1 = 100 , -

 

4

 

 

 

j

i

 

 

 

 

j

 

k

 

 

4

 

 

 

i

 

 

 

 

 

j

 

6

 

 

 

 

 

 

 

 

 

e

b b b b

j

b b

 

 

 

 

 

 

e

c c c c

j

 

c c

k

 

 

 

 

 

0 0 0

 

 

q 1 10

4

 

 

 

 

2

,

Lij

k

i

 

k

 

 

k

 

k

 

 

 

 

 

 

 

k

 

i

 

k

 

 

 

k

 

 

 

 

 

 

 

 

 

 

 

 

i, j.

 

 

 

 

 

 

 

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(« ») :

T1

L

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

1

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e

 

 

 

 

 

T

 

e

 

c e

 

 

 

 

1

2

3

C

 

c

N

e

 

 

1

2

1

 

(130)

 

 

 

 

 

 

 

N

 

dV

12

 

 

 

 

 

 

 

 

Ve

 

 

 

 

 

 

 

1 1 2

L1

L2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. 1.11

 

52

53

vk.com/club152685050 | vk.com/id446425943

L1= 0,1 , L2= 0,1 .

T T T1 T2

 

T3 , T2 , T3 .

 

-

, (120)-(125):

 

 

 

 

 

 

K

1

 

 

 

 

 

AKxx

1 1 1 10 3 50 1 1

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K

 

 

L 1

1

1

0,1 1

1

 

 

 

 

 

 

 

 

 

 

 

(134)

 

 

 

 

 

1

1

 

 

 

 

 

 

 

50 10 2

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

1

 

 

 

 

 

 

 

 

q

 

0

1

104 1 10 3

0

 

 

0

(135)

Q

qA

 

 

 

10

.

2

 

1

 

 

 

 

 

 

 

1

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

-

(110)-(112):

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

1

0

 

 

 

 

0

 

K 50 10 2

1

2

1 , Q 10

 

(136)

0 .

 

 

 

 

 

 

 

0

 

1

1

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(109)

 

 

 

 

 

 

 

 

 

 

 

1 1 0 T

0

 

 

 

50 10

2

1

 

2

 

 

 

1

 

 

0

 

 

(137)

 

 

 

 

1

T2

 

.

 

 

 

 

 

 

0

 

1

1

 

 

 

 

 

10

 

 

 

 

 

 

 

 

 

 

 

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

T1 = 100 -

 

 

1

0

 

0 T

 

 

100

 

 

 

 

, :

 

0

 

2

 

 

1

 

 

 

 

 

 

 

 

 

 

 

1

T2

100

.

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

20

 

 

 

 

 

 

 

0

 

1

T

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3

 

 

 

 

 

 

-

: T1= 100 C, T2= 80 C, T3= 60 C.

-

, . 1.11. L 0, 2

, A 1 10 3 2. – ,

54

Kxx 50 , c

=500 , = 8000 3. : -

T1 = 100 ,

q 1 102 T 2, .

: T0 = 0 t0 = 0.

 

 

 

 

 

 

 

tn t0

1000 ,

 

n = 2.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L1= 0,1 , L2= 0,1 .

T T T1

 

 

T2

 

 

 

T3 , T2 , T3 .

 

-

, (120)-(125):

 

 

 

 

 

 

 

 

 

 

 

 

K

1

 

 

 

 

 

 

 

 

 

AKxx

1 1 1 10 3 50 1 1

 

 

 

 

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

K

 

 

 

L 1

1

 

1

0,1

 

1

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(138)

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

50 10 2

 

 

 

 

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

q

qA

0

 

 

 

 

 

0

 

0

.

 

(139)

 

 

Q

 

 

1 104 1 10 3 10

 

 

 

 

 

 

 

2

 

 

 

 

 

 

 

1

 

 

 

 

 

1

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

2

 

 

cAL 2

1

 

8000 500 1 10 3 0,1 2

1

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

C

 

C

 

 

 

 

 

 

 

6

 

 

1

2

 

 

 

6

 

 

 

1

2

 

(140)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

 

 

1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

66, 667

 

 

 

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:

Q

q

q

 

T

A

 

0 1 102 T 1

10 3 0

0,1T

0 .

(141)

2

 

 

 

 

 

 

3

 

 

 

 

 

3

 

 

 

 

 

3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1

 

 

 

 

 

 

1

 

 

 

 

1

 

 

-

(110) (112):

55

vk.com/club152685050 | vk.com/id446425943

 

1

1

 

 

0

 

 

K 50 10 2 1

2

 

1

,

(142)

 

 

1

 

 

1

 

 

 

 

0

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2

1

0

 

 

 

 

 

 

4

1

 

,

 

 

(143)

66,67 1

 

 

 

 

0

1

2

 

 

 

 

 

 

 

 

 

 

 

 

 

0

Q 0,1T3 0 . (144)1

t = 500 .

(119), :

KC

K

2

 

 

 

 

t

CK

2

C

t

 

 

 

 

C

 

1,0333

0, 2333

0

 

 

 

0,2333

2,0667

0, 2333

, (145)

 

 

 

0

0, 2333

1,0333

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0,0333

0,7667

0

 

 

K

 

 

 

0,0667

0,7667

 

(146)

 

0,7667

.

 

 

 

 

0

0,7667

0,0333

 

 

 

 

 

 

 

 

 

 

(119)

,

:

 

 

0

 

 

0

 

 

Q

Q

 

 

 

 

0

 

(147)

0 0,1 0

 

 

0,1

.

 

 

 

 

 

 

 

 

 

 

 

T3

0

T30

 

 

 

 

 

 

 

 

 

 

(119),

T1 = 100 -

, :

2,0667

0, 2333 T

 

 

100

 

0,0667

0,7667

T

 

 

 

0, 2333

1,0333

 

2

 

0,2T

 

 

0,7667

0,0333

 

2

.

(148)

 

T

 

 

30

 

T

0

 

 

 

 

3

 

 

 

 

3

 

. 1.1.

56

1.1

 

1

2

 

3

 

,

 

 

 

 

 

500

100

49,7

 

11,2

 

 

 

 

 

 

 

1000

100

59,6

 

48,5

 

 

 

 

 

 

 

1.11. ANSYS

ANSYS -

, -

, -

, , , -. . -

-

.

(Batch) -

(Interactive) .

-

APDL (ANSYS Parametric Design Language)

ANSYS. , ,

ANSYS .

, -

, , « – » .

-

(GUI) ANSYS,

Workbench.

.

, -

. -

– , -

-

.

57

vk.com/club152685050 | vk.com/id446425943

-

ANSYS . -

( )

. -

:

1.( -

, , .), -

.

2.-

.

.

3.-

. -

ANSYS.

( , ,

.), .

4..

ANSYS

PREP7. Workbench Design Modeler. -

CAD-

.

5..

.

6.-, .

– :

1.– , ( ) .

2.( , , -

.).

(

, .).

58

3. , -

. ,

( -

, .).

( ) – . -

( , ,

, .)

ANSYS , , , . -

.

-

ANSYS ,

.

.

(Help) ANSYS

.

, -

.

ANSYS, Inc. -

– Workbench, -

. Workbench

, , -

, , -

, , . Workbench CAD CAE,

. ,

Workbench

ANSYS , -

, . -

ANSYS, Inc. Workbench -

,

.

Workbench .

59

vk.com/club152685050 | vk.com/id446425943

1.?

2., ?

3.?

4..

?

5..

6.?

7.?

8.-

.

9.?

10..

11.( )?

12.?

13..

14.?

?

16.?

17.-

?

18..

19.-

.

20. -

?

21. ANSYS?

60

2. ANSYS WORKBENCH

ANSYS Workbench -

, -

, -

, .

, -

. ,

– , -

. -

:

( ). -

,

, , -

. -

, ;

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.

.

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,

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-

. Workbench -

, , -

-,

.

2.1. WORKBENCH

ANSYS Workbench

/ANSYS 12/Workbench. -

, -

. ( . 2.1).

. 2.1

,

Windows. -

.

62

Project Schematic -

,

Workbench

. 2.2).

( ) -

. -

.

. 2.2

Toolbox – -

 

, Project Schematic. -

, -

( . 2.3). : Analysis Systems – ,

, ANSYS.

.

Component Systems – ,

-

, :

, -

.

Custom Systems -

-

, -

-

. 2.3

. -

, -

. Design Exploration -

,

.

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Properties – , -

-

Project Schematic -.

,

-

,

,

. 2.4 . . 2.4

Geometry.

,

, -

.

Messages,

,

( . 2.5). -

, Messages

, ANSYS -

, .

Hide/Show Messages, -

Workbench.

. 2.5

Workbench -

. , -

.

64

Reset Window Layout View.

-

( . 2.6).

, -

-

( -

) -

Workbench

. 2.6

CAD/CAE- .

Refresh Project

, Update Project

-

. Compact Mode -

Workbench,

( . 2.7).

. 2.7

Workbench

Tools/Options. . 2.8 -

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.

Restore Defaults .

. 2.8

Units , -

( . 2.9).

-

. , , -

.

ANSYS Workbench

Help

. -

-

F1,

-

, -

. 2.9 , . -

.

66

2.2.WORKBENCH

, ANSYS -

; -

Toolbox, ( . 2.10).

:

Static Structural – ;

Transient Structural – ;

Steady-State Thermal – ;

Transient Thermal – ;

Modal – ;

Harmonic Response – ;

Linear Buckling – ;

Explicit Dynamics – .

-

, , -

-

. . 2.10,

-

: ANSYS, Samcef, MBD

.

-

. 2.11.

Workbench -

. Workbench 2.0

,

 

. 2.10

67

 

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, -

( . . 2.11). -

-

,

.

. 2.11

:

Toolbox Project Schematic.

-. . -

( ) ;

-

Toolbox.

( ) .

Project Schematic

( . 2.12) :

(Update), (Duplicate),

(Replace With),

68

(Clear Generated Data), (Delete),

(Rename),

(Properties).

,

( . 2.13).

,

,

. 2.12

(Edit), (Update),

(Transfer Data From New) .

,

.

,

Engineering Data, .

( . . 2.11). -

,

( .

Setup . 2.11).

,

( .

Solution Results

. 2.11),

. 2.13

,

.

Workbench

. ,

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, -

.

,

,

.

.

. 2.14

Workbench ,

:

(Transfer Data) (Share).

.

,

.

,

.

. 2.14 -

.

70

(Engineering Data), (Geometry),

(Model) ,

Share.

,

Solution Steady-State Thermal Setup Static Structural .

.

Toolbox, -

, -

. , Geometry, -

, Engineering Data Geometry. , Model, -

, Engineering Data, Geometry Model. ,

, ,

( . 2.15).

. 2.15

. -

( . 2.16) Transfer Data To New Transfer Data From New -

. -

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,

. -

-. -

.

Workbench.

.wbpj

. 2.16

. -

.

dp0. -

, ,

dpN,

N .

:

(.agdb) (.mechdb);

(.mechdb);

(file.rst);

ANSYS, Workbench (ds.dat);

(file.err);

(solve.out).

, , -

, ,

user_files.

72

1.ANSYS Workbench. :

Workbench?

Project Schematic Toolbox?

Static Structural,

Transient Structural, Steady-State Thermal Modal?

?

Import ?

Refresh Project Update Project -

?

2. -

. « ». -

« ». :

Geometry,

Model, Results?

?

?

?

, ?

« »,

« »?

3. : -

. -

. -

:

? -

?

, ?

?

, ?

4.Workbench?

5.?

6.file.rst?

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3.

Geometry. Design Modeler,

. -

Design Modeler -

,

ANSYS, .

-

,

Geometry, -

, -

Properties . 3.1).

Basic Geometry Options -

-

, , , -

,

, -

,

Advanced Geometry Options -

:

(

3D -

),

CAD- ,

-

.

, ,

. 3.1

.

74

3.1. DESIGN MODELER

, -

.

,

Geometry, -

,

New Geometry . 3.2). Workbench -

Design Modeler; -

-

, . 3.3.

. 3.2

Design ModelerCAD-

, , Import Geometry. ANSYS

, : Parasolid (.x_b, .x_t), IGES (.iges,

.igs), SolidWorks (.SLDPRT, .SLDASM), Unigraphics NX (.prt), Inventor (.ipt, .iam), Pro/Engineer (.prt, .asm), ACIS (.sat) . -

, Design Modeler,

.agdb. -

, Reset

. . 3.2).

Design Modeler

:

.

.

;

(Tree Outline).

;

(Details View).

;

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(Graphics). -

.

. 3.3

:

File -

;

Create

;

Concept – -

;

Tools – -

,

;

View – -

;

Help – Design Modeler.

76

(Tree Outline) -

-

-

-

( . 3.4).

, -

. -

-

, -

.

 

. 3.4

 

, -

.

,

. 3.6).

. 3.4.

. 3.5

(Details View)

, ( .

. 3.6). -

, ,

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. -

,

.

(Graphics) -

-

,

, -

. -

.

-

. 3.7. -

, -

.

-

. 3.6

.

:

– . -

-

. -

Ctrl, . -

Ctrl.

-

. .

– .

. Ctrl, -

78

, Shift, -

. ,

, – ,

( . . 3.7).

– .

.

,

. , -

.

. 3.7

-

, -

. -

Esc.

, , -

: , , . Design Modeler -

, -

. -

: . -

,

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, .

-

( . 3.8).

. 3.8

, -

-

.

(« »),

Extend to Adjacent

. Extend to Limits -

, ; -

, .

-

Flood Blends. ,

, -

Flood Area.

-

, , -

. Design Modeler

, ,

,

( . 3.9).

80

-

-

-

.

,

-

.

. 3.9

3.2.

.

, ,

.

-

. -

Design Modeler

: -

(Sketching) –

,

(Modeling) –

-

.

-

-

. 3.10

( . 3.10).

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Design Modeler

Oxyz,

: x – , y – , z – .

, -

,

. ,

. -

: Oxy (XYPlane), Oxz (ZXPlane), Oyz (YZPlane). , -

Create New Plane -

.

Details View. ( Plane)

( . 3.11):

From Plane – ;

From Face – ;

From Point and Edge – ;

From Point and Normal – , -

;

From Three Points – ;

From Coordinates – , -

.

, , -

– (Base Plane),

(Base Face), (Base Point, Base Edge) . -

, :

(Axes) – -

, , ;

(Offset) –

;

(Rotate) – -

.

82

. 3.11

-

Transform ,

. -

: -

Move Transform Up – -

Move Transform Down

. -

Remove Transform.

-

, , Generate

. Design Modeler

. , -

Generate -

; ,

.

,

.

-

.

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Sketch1, -

, .

,

: (Hide Sketch), -

(Look at), -

(Show Dependencies),

(Rename) (Delete) . -

(Look at)

, Sketching.

(Tree Outline)

(Sketching Toolboxes),

( . 3.12):

Draw – ;

Modify – ;

Dimensions – ;

Constraints – -

;

Settings – .

 

-

 

:

 

 

 

, -

 

.

 

-

 

Modify -

 

-

 

Constraints

 

.

 

,

 

-

 

 

. 3.12

Generate.

 

84

, -

, .

, -

. -

,

.

Settings -Sketching Toolboxes. :

(Grid). : Show in 2D Snap

;

(Major Grid Spacing).

. -

;

(Minor-Steps per Major). -

. -

, , -

; , ,

;

(Snaps per Minor). -

-

, .

, ,

,

. , , -

.

Draw, Modify, Dimensions, Constraints. -

-

. , -

ANSYS Design Modeler.

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3.2.1.

Design Modeler

. -

Draw :

(Line).

;

, (Tangent Line). -

-. -

, ;

, (Line by 2 Tangents).

;

(Polyline). .

-

,

Open End. ,

Closed End;

(Polygon).

. -

n;

(Rectangle). ,

. -

Rectangle by 3 Points;

(Oval). , -

-

.

;

(Circle). ,

. ,

, Circle by 3 Tangents;

(Arc by Tangent). ,

86

.

,

.

(Arc by 3 Points)

(Arc by Center);

(Ellipse). ,

;

(Spline). , -

. -

Polyline. -

: -

(Open End),

(Open End with Points), (Closed End), -

(Closed End with Points);

(Construction Point).

. ,

,

Construction Point at Intersection, -

.

-

(Sketching Toolboxes). Esc.

, ,

Undo . -

Redo.

. -

, , -

. -

.

,

, Back.

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-

,

Details View. . 3.13 -

.

-

( Full Circle).

. 3.13 -

, , ,

.

3.2.2.

-

. Modify -

:

(Fillet). , -

. , -

Radius. -

.

, :

(Trim Both), (Trim 1st, Trim 2nd),

(Trim None), (Full Circle);

(Chamfer). .

Length. -

, . -

-

;

(Corner). -

. -

,

;

88

(Trim).

; -

, . -

.

, -

Ignore Axis;

(Extend).

. -

Ignore Axis;

(Split). . -

: Split at Select , -

, Split Edges at Point – ,

; Split Edges at All Points -

; Split Edge into n Equal Segments n ;

(Drag).

. ,

, .

. -

, ,

, ;

(Cut). -

.

« » (Paste Handle) , -

.

. ,

, . -

( )

: End/Set Paste Handle – -

, End/Use Plane Origin as Handle – -

-

, End/Use Default Paste Handle –

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-

. Clear Selection

. -

, -

. (Paste),

: (r)

(f)

. -

( . 3.14),

.

. , -

, .

End.

Esc.

, , -

;

. 3.14

(Copy).

. ,

Cut, ; -

.

(Move). . -

,

90

;

(Replicate). .

,

;

(Duplicate). -

.

( . 3.15),

-

, .

;

. 3.15

(Offset). , -

. -

. -

,

End Selection/Place Offset.

, , -

. , -

, ;

(Spline Edit). -

, Spline. -

.

, -

, , . -

,

.

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3.2.3.

, -

-

, -

.

,

. -

, -

. Constraints, -

, :

(Fixed). -

. -

( -

).

Fixed Endpoints – -

.

;

(Horizontal). -

( -

X). , X

;

(Vertical). -

( Y).

, Y ;

(Perpendicular).

-

. , -

-

. , ,

-

;

(Tangent). -

. -

92

, , -

;

(Coincident). -, -

. ;

(Midpoint). -

.

;

(Symmetry).

. ,

, ( , ).

. -

( Select new symmetry axis);

(Parallel). -

.

, -

. ,

, -

( Select multiple). -

.;

(Concentric). -, . -

, ,

;

(Equal Radius).

. -

, , -

;

(Equal Length).

. , -

, -

;

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(Equal Distance).

. -

.

-

(1-2 2-3, 2-3 3-4 .).

Design Modeler

, : -

, , , -

. -

. 3.16.

. 3.16

Auto Constraints -

. : Cursors Global. Cursors -

, -

, -

. Global -

.

Design Modeler -

. -

,

, ,

. -

. -

,

94

, Design Modeler

.

AutoConstraints.

3.2.4.

-

,

, , , -

. -

, , , , Design Modeler . -

, , , , -

.

,

: ,

,

. -

. -

. Design Modeler -

,

,

(over-constrained) .

Dimensions.

Semi-Automatic. Design Modeler -

; , -

. ,

, Details View. -

: Skip

; Exit

; Continue

.

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. -

Dimension;

, , , , . -

.

-

, -

. -

. Design Modeler

, -

, ,

.

 

,

 

 

. ,

.

 

.

 

 

(Horizontal). -

 

 

( X).

Details View

 

, , -

. 3.17). -

 

, -

( -

 

;

 

. 3.17

(Vertical).

), (Value).

 

( Y). -

, -

;

, Reference Only; -

(Length/Distance). -

.

. -

Edit.

 

,

 

;

Move. ,

(Radius). -

, -

, .

.

 

(RMX) (RMN),

-

;

Animate, -

(Diameter). -

. -

. ;

, .

(Angle).

( ) -

.

Cycles.

 

: -

 

. -

. -

( Alternate Angle);

.

(General). -

Display Values. Values

96

97

 

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, Names – . -

, .

-

-. Design Modeler -

. -

Sketch Instance,

-

. 3.18

,

. -

Details View ( . 3.18) :

Base Sketch – , ( ).

-

. , ,

;

Base X, Base Y – -

. ;

Instance X, Instance Y

;

Rotate Angle

(Instance X, Instance Y);

Scale – .

Generate. Design Modeler

. -

, , .

-

.

.

98

3.3.

-

, .

,

Modelling .

-

.

, Details View,

Generate.

:

,

;

,

;

.

3.3.1.

:

, , , -

, .

(Extrude)

-

.

. 3.19 :

Base Object – , -.

;

Operation – , -

. Add Material,

.

, Cut Material , Imprint Faces – « » ,

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. Add Frozen -

( . . 110);

Direction Vector – , .

-

, . None (Normal), ;

Direction – .

: Normal – -

, Reversed – , Both Symmetric -

, Both Asymmetric .

Extent Type – . Fixed

,

Through All – , To Next -

, To Face – -

, To Surface

-

( . 3.20);

Depth – , -

. .

. 3.19

100

. 3.20

, (Line Body), -

– (Surface Body).

(Revolve) -

( . 3.21). Base Object, Operation Direction Extrude. Axis

– , -

. Angle .

101

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.

-

, -. -

,

. As Thin/Surface? Yes,

.

(Sweep)

-

. 3.21

. :

Profile – ;

Path – ;

Alignment

. Path Tangent – -

. Global Axis -

;

Scale – .

;

Twist Specification – ,

.

(No Twist)

Turns

Pitch – ,

. Turns Pitch

.

Sweep . 3.22.

,

. -

102

( ), -. ,

.

. 3.22

(Skin/Loft). ,

-

, . Profiles

, .

,

, -

Ctrl. . 3.23.

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. 3.23

Design Modeler -

, -

(guide line). ,

Fix Guide Line.

. Continue Sketch Selection -

.

,

, .

( . . 3.23). -

.

Details View. -

,

Profiles -

( . 3.24):

104

Move to Top

;

Move Up – -

;

Move Down

;

Move to Bottom – -

. 3.24

.

 

, Delete.

,

 

 

, -

 

( . 3.25).

 

:

 

 

Line Body

, -

 

 

( ).

. 3.25

,

, Lines From Points, Lines From Edges, Lines From Sketches ( . . 126);

Surface Body – , .

, ,

( Thickness). -

, , -

Surface from Edges, Surface from Sketches, Surfaces from Faces ( . . 128);

Solid – , . -

, , , Primitives ( . . 109).

(Parts) -

Form New Part .

-

.

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-

 

.

 

 

 

.

Fixed Radius Blend. -

 

Extrude, Rotate, Sweep, Skin/Loft -

 

Geometry -

 

As Thin/Surface?, .

,

-

 

( No). (

, Radius -

 

Yes), : Inward Thickness

.

 

, , Outward Thickness

 

 

 

 

, .

,

-

. 3.26

-

Variable Radius

 

. , Solid

Blend. Transitions -

.

: Smooth – ,

 

Linear – . Start Radius, End Radius -

Thin/Surface.

. -

Selection Type -

-

:

.

Faces to Remove – ;

. 3.26. .

Faces to Keep c , -

 

 

;

( . 3.27) -

 

Bodies Only

Chamfer. -

 

.

Geometry -

 

Geometry

 

 

.

 

 

Selection Type. Direction -

,

 

 

: Inward

.

 

z, Outward -

Type -

 

, Mid-Plane

: Left-Right

 

 

.

 

. 3.27

,

,

 

. Design Mod-

, Left-Angle (Right-Angle) – -

eler ,

-

.

.

 

 

( . Freeze

(Line Body)

Body . 110).

(Sufrace Body) Vertex Blend.

106

 

 

 

 

107

 

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( Verticies) -

.

, ,

.

, , -

Points. -

: Construction Point – -

, Spot Weld – , -

« », Point Load

. (

Base Faces) ( Guide Edges), -

( Definition):

Single – , :

(Sigma),

(Edge Offset), -

(Face Offset);

Sequence By Delta – , -

:

(Sigma), (Edge Offset)

(Delta),

(Face Offset);

Sequence By N – , -

:

(Sigma), (Edge Offset),

(N) -

(Omega),

(Face Offset);

From Coordinates File – ,

;

Manual Input – .

Points . 3.28.

108

. 3.28

Design Modeler

: , , , -

, , , . -

Create Primitives ( . 3.29). -

,

(Base Plane), (Origin Definitions), , -

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. Operation Add Material, Cut Material -

, .

-

As Thin/Surface?, -

. -

Design Modeler.

. 3.29

. , -, , -

. , Design Modeler -

, -

, , -

.

, ,

, .

, , -

,

. Design Modeler Freeze – ( ) -

.

.

( . 3.30).

110

. 3.30

Freeze

, .

Unfreeze. Freeze Unfreeze

Tools ,

. ,

Generate .

-

, .

Orientation Add Frozen.

-

(Pattern), Create. -

-

. Geometry .

Pattern Type :

Linear – . -

(Direction), (Offset) (Copies);

Circular – . -

, -

(Axis), (Angle)

(Copies). Angle Evenly Spaced

;

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Rectangular – .

-

.

Pattern -

Pattern Type . 3.31. -

,

, « »

.

. 3.31

-

Body Operation. -

112

, , , -

, . -

Create -

, -

. Bodies , -

. Type

; .

Mirror – ( . 3.32).

Mirror Plane , -

.

No Preserve Bodies?;

. 3.32

Move – .

: (Source Plane) (Destination Plane).

. No Preserve Bodies?, ,

.

. 3.33;

Delete – .

Body Operation

.

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. 3.33

Scale – .

,

Scaling Origin): World Origin

, Body Centroids – , Point

. (Scaling Factor) -

0,001 1000.

Simplify – . -

Design Modeler . -

Simplify Geometry ( -

Yes). , , -

Simplify Topology;

Sew – ( ). -

(Surface Body),

. -, , -

Tolerance, : Normal – , Loose – , User Define – . -

.

, Yes

Create Solids. Sew -

. 3.34. (0,5 )

, User Tolerance (1 ), -

;

114

. 3.34

Translate – .

, ( Direction Definition): Selection

, Coordinates – -

.

Distance, – -

X Offset, Y Offset, Z offset. Preserve Bodies?

;

Rotate – . -

, ( Axis Definition): Selection – , Components

. -

Angle. Preserve Bodies? -

;

Cut Material – .

Body Operation -

(Extrude, Rotate .)

. -

, ( ) .

( Preserve Bodies?

No). Body Operation -

Cut Material . 3.35.

115

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. 3.35

Imprint Faces – -

. Body Operation « -

» . -

-

Operation, Imprint Faces.

-

( . 3.36). (

Preserve Bodies? No);

. 3.36

Slice Material – .

, , -

, . .

( Preserve Bodies?

Yes). Body Operation

. 3.37.

116

. 3.37

, -

Boolean.

(Solids), (Surface Body). (Line Body)

. -

Create.

Operation :

Unite – . Tool Bodies

;

Subtract – . Target Bodies -

, Tool Bodies . Preserve Tool Bodies? -

;

Intersect – . Tool Bodies

, Intersect Result – -

: Intersection of All Bodies

, Union of All Intersection -

. -

Preserve Tool Bodies? , Yes/No, -

Yes, Sliced, -

(Frozen) .

117

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Boolean

. 3.38.

. 3.38

Slice.

Create , ,

, ( , -

Freeze). Slice Type

:

Slice by Plane – . -

(Base Plane). -

, Slice Targets ( -

All Bodies) Selected Bodies

. Slice Slice by Plane

. 3.39. -

;

118

. 3.39

Slice By Surface – .

( Target Face) -

(Slice Targets=Select Bodies).

, Slice Targets=All Bodies. Bounded Surface? -

-

( No). Slice

Slice by Surface . 3.40.

Target Face -

Slice By Surface

, .

Bounded Surface?;

Slice Off Faces – .

, -

. Faces. Design Modeler ,

.

Slice Slice Off Faces . 3.41;

119

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. 3.40

. 3.41

120

Slice Off Edges – . -

Slice Off Faces -

(Line body). -

(Cross Section). Edges.

Slice . 3.42.

. 3.42

-

Face Delete, Create.

Faces , Healing Method « »

( Automatic). -

Edge Delete,

. Face Delete Edge Delete

. Face Delete

. 3.43. . 3.44

Edge Delete -

Healing Method. -

,

, No Healing Healing Method -

.

121

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. 3.43

. 3.44

122

-

. -

Sketch Projection, -

. -

, , . -

, ,

-

.

Geometry . -

Generate. -

,

, . -

, , Sketch Instance, ,

.

3.3.3.

, Design Modeler -

, . -

-

, -

,

.

Named Selection,

Tools .

( ), -

, ,

, , .

, ,

123

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. -

, «-».

(Surface body)

Mid-Surface. -

Face Pairs, ,

. -

,

,

. 3.45).

.

. 3.45

-

, -, . , -

,

.

Symmetry Tools. Number of Plains

( 1 3). ,

, -

Mechanical ,

. -

.

-

Symmetry . 3.46.

124

. 3.46

Fill -

. Tools.

( Extraction Type): By Cavity

, By Caps

. -

Faces.

(Surface Body).

( Preserve Capping Bodies Preserve Solids). Fill

. 3.47. -

-

, . -

1 2 3, -

(Surface Body). Extraction Type By Caps Fill, ,

2 3 .

(Line Body)

(Surface Body) -

Concept. :

125

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. 3.47

Lines From Points – .

Point Segments -

, -

, Points. -

( Point Pairs) , -

( Point Chains).

, -

; -

(Remove Last Segment) (Clear All Segments). -

Operation,

Add Material, Add Frozen -

;

Lines From Sketches

. Base Object ,

, (Plane from Face), -

. Operation ;

126

Lines From Edges -

. Edges Faces -

;

. , -

. Operation .

3D Curve

. ,

, Points. -

Definition -

: Point Selection – , From Coordinates File

. Operation

. -

,

-

: Open End – , , Closed End , , Clear All Points – , Delete Point

– .

Split Edges. Edges , -

, Definition

:

Fractional – .

Fraction , -

0,5 ;

Split by Delta – : Sigma – , Delta – ;

Split by N N . -

: Sigma – -

, Omega – -

, N – .

127

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, -

. -

Surface From Edges ( . ), -

. -

, .

(Surface Body) -

:

Surface From Edges – -

. Edges

, , -

.

Flip Surface Normal?) ( -

Thickness);

Surface From Sketches

, . Base Object

. Operation

( Add Material)

Add Frozen) .

-

Orient With Plane Normal? ( Yes – -

). Thickness ;

Surface From Faces

. Faces

, Operation .

, -

, Holes Repair Method ( -

No Healing) Natural Healing.

128

-

Design Modeler -

-

. -

-

Concept Cross Section. . 3.48, -

, -

-

. ,

User Integrated,

. 3.48

, -

, ,

. User Defined

.

-

.

Cross Section Details View . 3.49). -

-

( Offset Type).

. 3.49

129

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,

. ,

-

. ,

,

, -

,

. ,

.

:

Edit Selection – .

, Details View;

Insert – . ,

,

. . 3.5 . 77);

Rename – .

. , -

, -

, -

, ;

Delete – ;

Generate – .

-

; Generate

;

Always Show Sketch

, .

Show Sketch;

130

Hide Sketch – -

. . -

-

Show Sketch;

Look at – -

. -

;

Suppress – .

,

. Suppress & All Below, -

;

Unsuppress Suppress. -

.

Unsuppress & All Below, -

;

Show Dependencies – .

, -

, . Parents

( ) , Children

. ,

, -

, ;

Suppress Body – -

. ,

(Line Body, Surface Body, Solid), -

Mechanical.

Unsuppress Body;

.

. 3.50.

131

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. 3.50

-

, -

, , . -

, , Depth

Extrude, Angle Revolve . -

,

. , , ,

, -

.

,

,

.

, -

, , -

. -

. -

,

-

ANSYS.

-

, -

132

. -

, -

. , -

-, . -

Workbench -

, , , . -

.

.

Parameter Manager,

Tools Parameters. -

.

Details View . 3.51). Design Modeler

,

. Parameter Manager, .

. 3.51

. 3.52

:

Design Parameters – -

;

133

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Parameter/Dimension Assignments – -

;

Check

;

Close – .

. 3.52

,

Parameter Manager.

-

, Parameter/Dimension Assignments.

-

. -

@.

:

– abs(x), sin(x), cos(x), tan(x), -

ln(x), exp(x), – sqrt(x). -

Generate.

:

ZXPlane.L1 = @ZXPlane.L1

ZXPlane.L1 -

@ZXPlane.L1;

134

ZXPlane.L2 = 2*@ZXPlane.L1 + @ZXPlane.L3 – -

ZXPlane.L2

: @ZXPlane.L1 @ZXPlane.L3;

Extrude1.FD1 = dist

Extrude1.FD1 dist,

;

Extrude1.FD1 = sqrt(x_dist*x_dist+y_dist*y_dist)

Extrude1.FD1

x_dist, y_dist, .

Check Design Modeler -

( . 3.53). -

, -

. Close Parameter Manager.

. 3.53

-

.

Parameters Parameter Set

. 3.54).

, , -

. Parameter Set

135

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.

. 3.54

1.ANSYS Workbench, -

Static Structural. Design Modeler. -

:

Tree Outline Details View?

?

Graphics ?

2.. -

Draw

. Dimensions

.

136

3.(XYPIane, ZXPIane, ZYPIane), 50

X 45 .

. .

. Move

.

5., -

. – . – -

.

6.-

.

Extrude . ,

, . .

7.3 .

5 .

8.. -

.

Revolve 90° .

9.Revolve ,

.

10.Body Operation -

. , -

.

11..

.

. .

(Surface Body).

13.-

. .

14.10R, R

. -

. -

.

137

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4.

. Workbench

,

Engineering Data. -

, . -

.

-

Engineering Data ,

.

.

-

.

4.1.

-

, ,

, ,

-

. -

Engineering Data, -

( . 4.1).

,

. 4.1

Engineering Data -

 

 

138

Edit ( . 4.2).

, ,

,

.

Engineering Data

 

 

 

,

 

-

 

.

 

-

 

-

 

.

 

 

. 4.2

-

. View -

. . 4.3 -

.

. 4.3

-

. 4.1.

139

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4.1

 

 

 

 

 

 

 

 

 

Toolbox

,

A

 

 

)

 

 

 

 

 

 

 

 

 

 

 

 

Outline Filter

 

B

, -

)

 

 

 

 

 

 

 

 

 

 

Outline Pane

-

C

 

)

 

(Outline Filter)

 

 

 

 

 

 

 

 

Properties Pane

 

D

-

)

 

(Outline Pane)

 

 

 

 

 

 

 

 

Table Pane

 

E

 

 

 

)

 

(Properties Pane)

 

 

 

 

 

 

 

 

Chart Pane

,

F

 

 

 

)

 

(Properties Pane)

 

 

 

 

 

 

 

 

 

,

, , -

. 2.1. -

,

, .

( ).

(Toolbox) -

.

,

, . , . 4.3 ( ) – (Structural Steel).

140

. 4.4,

.

Toolbox

:

;

-

,

;

.

. 4.4

(Outline

 

Filter) -

, .

( Engineering Data), , -

, .

Favorites, -

.

Outline Filter :

;

;

;

;

.

(Outline Pane)

Outline Filter

. 4.5). ,

. , . 4.5 Outline of General Materials ,

General Materials.

.

141

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. 4.5

(Properties Pane) ,

( . 4.6).

:

,

( );

;

;

;

.

(Property) , -

. -

.

.

142

. 4.6

(Table Pane)

, ( . 4.7). -

( ,

) -

-

,

, -

-

. -

*,

. -

. 4.7

.

(Chart Pane) -

( . 4.8). -

, -

Edit Properties

Properties of Chart ( . 4.9).

, -

, , -

.

143

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. 4.8

. 4.9

4.2.

. , -

:

, .

,

. -

. -

, -

Outline Pane. -

.

144

.

, -

. , -

Outline Filter.

Add Outline Pane.

ANSYS\v120\Addins\EngineeringData\Language\<lang>\Samples. -

:

General Materials -

. , -

;

General Nonlinear Materials -

;

Explicit Materials

;

Hyperelastic Materials

, -

. -

;

Magnetic B-H Curves ,

B-H , .

File Import, Import

.

Engineering Data File *.xml, *.engd. ,

, ,

.

( Favorites).

,

XML- .

145

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-

. -

Location Outline Filter. -

Ok.

-

, , -

:

, -

ANSYS 9.0 11.0;

MatML 3.1 Schema;

, AUTODYN.

, -

. -

. -

Outline Pane, *. -

-

. Outline Pane

Outline Filter,

. -

,

.

.

(Location) -

( ). ,

, .

,

, , ( ).

« » ( Favorites) , -

. -

146

,

Add To Favorites). Favorites -

( . . 4.3).

4.3.

Outline Pane. -

:

;

;

;

(Suppress);

;

;

.

,

. -

. -

:

, , ;

, , -

.

(Suppression) -

.

, ,

. , -

.

(Add)

, -

, . -

147

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,

Favorites.

().

, ( ). -

– -

Engineering Data.

, , -, -

. -

, Outline Filters

– « » (Favorites).

Source

. ,

, . -

-

:

;

;

-

.

, -, ( View Linked Source),

( Refresh From Linked Source)

( Break Link To Source).

(Description) -, .

, .

, ,

.

,

, Outline Filter ,

Outline Pane

148

« » ( Add to Favorites).

Outline Filter , Favorites,

, , -

Default Solid Material ( -

), Default Fluid/Field Material (

). -

(Structural Steel),

– (Air).

,

. -

, (

) , -

.

-

, . -

.

, Toolbox

Properties.

,

.

( Value)

( Unit) Properties Pane. -

. , -

.

, , -

,

Tabular. , -

Table Pane. -

,

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. -

, *. -

, -

. -

,

. -

, .

:

;

;

, , -

;

, -, .

-

Display Validation Failure

( . 4.10).

.

.

Suppression, . -

.

.

Parametrize

.

. -

, -

.

Parameters

. . 135). -

Parametrize, -

.

150

. 4.10

.

-

.

. -

:

= * + .

1,0 0,0 -

.

. 4.2 , -

.

.

151

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4.2

 

 

 

 

 

 

 

1.

 

Engineering Data

 

Edit….

 

1.

 

 

Outline Filter Pane.

 

 

2. Edit Library

 

.

 

 

3.

File Import Engineering Data….

 

4.

.

 

1.

 

 

.

 

 

 

2.

.

 

 

1.

 

 

.

 

2.

File Export Engineering Data….

 

3.

,

 

 

.

 

 

 

 

 

1.

 

 

.

 

 

2.

-

Outline Pane.

 

 

 

3.

File Export Engineering Data….

 

 

4.

,

 

.

 

 

1.

-

 

, .

 

 

2.

Edit Library

 

 

 

.

 

 

3.

.

 

 

4. -

 

 

 

, -

 

.

 

 

5.

-

 

.

 

 

6.

Save ( )

 

.

 

 

 

152

 

. 4.3 , -

.

:

;

Outline Filter Pane;

,

.

 

 

4.3

 

 

 

 

1.

Outline Pane

 

, Click here to add a

new material.

 

2.

-

 

 

Enter.

 

1.

,

-

.

 

2. ,

 

Toolbox.

 

1.

, -

 

, .

 

2. Properties

 

Pane.

 

3.

,

 

Delete.

 

1.

,

 

.

 

2.

Properties Pane.

 

3.

:

 

– , ,

 

 

;

 

 

 

– , , -

 

-

 

Table Pane.

 

1.

,

 

.

2. -

 

Parametrize. , ,

 

 

.

 

1.

,

-

.

 

2.

 

 

Suppression.

 

 

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.4.3

 

 

 

 

 

 

 

1.

,

 

.

 

2.

 

 

Add to Favorites.

 

3.

Favorites Outline Filter.

4.

,

 

, -

 

 

Default Solid Material ( -

 

), Default

 

Fluid/Field Material ( -

 

) .

, -

Toolbox.

), ,

. , -

, ANSYS.

, ,

, .

( Suppression)

-

. ,

(Bilinear Isotropic Hardening) -

(Multilinear Isotropic Hardening) -

. -

, , -

, . -

. 4.4.

, ,

x, y, z,

( )

). -

. -

154

. -

– ,

x, y, z (2D- x, y).

4.4

(Isotropic Elasticity);

(Orthotropic Elasticity);

(Mooney-Rivlin);

(Neo-Hookean);

(Polynomial);

(Yeoh);

(Ogden)

(Bilinear Isotropic Hardening);

(Multilinear Isotropic Hardening);

(Bilinear Kinematic Hardening);

(Multilinear Kinematic Hardening)

(Thermal Conductivity Isotropic);

(Thermal Conductivity Orthotropic)

(Isotropic Resistivity);

(Orthotropic Resistivity)

, ( f(T)

),

. -

. -

, -

,

.

-

. ANSYS

, -

.

:

155

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( – );

( – );

( – );

.

-

:

(Mooney-Rivlin);

(Neo-Hookean);

(Polynomial);

(Yeoh);

(Ogden).

, -

-

-

.

CAD- -

.

.

(Material Properties) Properties Pane. , CAD-

, . -

CAD-

MatML 3.1, . -

, . -

CAD- .

,

.

(Material Properties) , CAD-

, -

.

156

4.4.

– -

. -

-

, ,

( . 4.11).

 

 

 

 

 

 

 

,

 

-

 

. -

 

 

 

-

 

.

 

. 4.11

 

 

 

. -

,

( ) ,

, -

.

, -

.

, -

:

.

(149)

-

:

1 , ln 1 ,

(150)

.

157

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, -

:

(

);

-

.

– » ( . . 4.11). -

. -

, -

.

,

:

– ;

– .

, -

,

-

. -

( -

) :

e

 

1

 

1

2 2

 

2 3 2

3

1

2

,

(151)

 

 

2

 

 

 

 

 

 

 

 

 

 

1, 2 , 3 .

.

1 2 3 . ,

, . ,

( 1 2 3 ), .

158

( . 4.12) -

.

-

. , -

. -

.

“ e -

. 4.12

ANSYS ,

:

.

( . 4.13);

.

( . 4.14).

. 4.13

. 4.14

159

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, -

, ,

-

. « – »

( . 4.17).

. 4.15.

 

. 4.15

-

, -

.

, -

-

. -

, -

.

,

2 y ,

. . 4.15). .

 

-

 

 

 

.

 

-

 

-

 

 

. 4.16

( . 4.16).

 

160

. 4.17

ANSYS « – -

»: ( . 4.18). -

, ,

. -

. -

.

.

. 4.18

161

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.

.

. -

, .

Toolbox Plasticity -

. , . 4.19 -

-. -

Include Property,

Bilinear Isotropic Hardening

Properties Pane.

. 4.19

-

(Yield Strength)

(Tangent Modulus) . 4.20). -

(Chart) -

( . 4.21).

. 4.20

162

. 4.21

, -

(Multilinear Isotropic Hardening) (Multilinear Kinematic Hardening) ( . 4.22).

. 4.22

163

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-

 

;

, ( . 4.23).

 

.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. 4.23

, -

, -

( . 4.24).

-

-

:

;

;

( );

;

164

. 4.24

-

. -

( , -

1 E ). -

, . -

, -

-

.

. 4.5

. -

, 0,5. , -

. -

( 0,5)

:

;

;

.

165

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4.5

 

 

1

2

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. -

« – »

. 4.25. ,

,

. ,

(Mullin). ( -) (

) -

.

1,8

1,6

1,4

1,2

1

0,8

0,6

0,4

0,2

0

-0,5

0

0,5

1

1,5

2

2,5

. 4.25

166

.

Toolbox Experimental Stress Strain Data, , -

.

, , Uniaxial Test Data – ,

Include Property,

( . 4.26). , -

.

. 4.26

:

,

Ctrl + C, ;

Table of Properties, Ctrl + V.

-

( A) ( B).

– »

( . 4.27).

-

Toolbox, -

( . 4.28).

167

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. 4.27

.

, -

( . 4.29).

. 4.28

168

. 4.29

Curve Fitting

Solve Curve Fit. -

,

. -

Chart Pane « – »

( . 4.30).

. 4.30

Error Norm for Fit ( . 4.31)

.

169

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(Normalized Error) ,

(Absolute Error)

. , -

. ,

,

.

. 4.31

1.ANSYS Workbench, -

Static Structural. .

:

Outline Filter Outline Pane?

?

Table Chart?

2.«NewMat1».

( ).

3.«NewMat1», -

. .

4.Aluminium Alloy General Materials .

.

5.Aluminium Alloy ,

.

6.?

7.-

?

8.ANSYS? -

?

9.Curve Fitting -

?

170

5.

-

.

Mechanical.

, -

.

5.1.

-

-. :

. -

( review) ,

;

.

.

:

1. ( , .),

. 5.1. -

, , -

FLUENT, CFX .

2. -

( , , .).

.

3. , ,

.

. -

.

171

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4.. -

.

2 3.

-

-

.

-

.

(Surface

. 5.1

bodies) -

. (Line bodies) (Beam).

-

.

DesignModeler -

– , -

(Multibody Part). -. , , -

. DesignModeler

,

. -

.

.

ANSYS Workbench

172

.

-

. -

-. , -

. -

.

. 5.2 .

(Mesh) -

.

Mesh , -

.

,

Mesh.

. 5.2

173

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-

Preview Surface Mesh

Mesh ( . 5.3). -

Mesh . 5.4).

-

. 5.4.

. 5.3

. 5.4

5.2.

Defaults (Details of Mesh)

( . 5.5):

, -

(Physics Preference);

(Relevance).

. , (Structural)

, .

174

. 5.5

,

, .

-(Relevance),

100 +100 ( . 5.6).

, -

.

Preview Surface Mesh.

. 5.7.

. 5.6

Relevance -100

Relevance 0

Relevance 100

426

986

2766

212

492

1382

 

. 5.7

 

Statistics -

. . 5.6

.

175

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.

,

( , .) -

.

, .

.

.

(Relevance) -

(Relevance Center)

(Sizing).

. 5.8, . 5.9.

. 5.8

. 5.9

176

(Element Size) -

( . 5.10). -

, .

(Use Advanced Size Function):

,

(Relevance) (Initial Size Seed).

.

. 5.10

(Initial Size Seed) -

,

.

(Smoothing) -

(Use Advanced Size Function). -

.

. -

( . 5.11).

177

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(Transition)

( . 5.12). Transition -

(Use Advanced Size Function).

Fast.

. 5.11

. 5.12

Span Angle Center ( ) -

.

, -

. :

Coarse ( ) – 91 60 ;

Medium ) – 75 24 ;

Fine ( ) – 36 12 .

Span Angle Center . 5.13 5.14.

. 5.13

178

. 5.14

ANSYS Workbench -

:

1.(Use Advanced Size Function) .

:

2.1.(Element Size)

. -

( , ).

Element Size ( . 5.15).

2.2.(Proximity and Curvature) -

( . . 5.16).

100 +100. (Element Size)

(Default), Proximity and Curvature

, Relevance ( )

. (Proximity) -

.

2.3.(Shape Checking)

( . 5.17). -

(Standard Mechanical), -

-

(Aggressive Mechanical).

179

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. 5.15

. 5.16

2.4. (Initial Size Seed)

,

( . 5.18).

. 5.17

. 5.18

180

5.3.MESH CONTROL

Mesh Control

,

.

Method Mesh Control

( . 5.19, ) -

, Scope

) Geometry

Apply. -

-

( . 5.19, ):

Automatic ( ) – -

, ,

;

Tetrahedrons ) – -

;

Hex Dominant ) – ,

, , ,

;

Sweep ) – .

 

 

. 5.19

. 5.1.

181

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5.1

2 –

Method

1 – Method

Mesh Control

4 – Geometry

3 –

5 –

6 – Method

 

Tetrahedrons

182

. 5.1

8 –

, Update,

Generate Mesh

7 –

Patch Conforming Method

9 –

 

Mesh

10 –

 

 

Hex Dominant.

-

, .

.

183

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. , -

-

. ,

.

:

1..

2.Design Modeler

, .

.

-

.

, .

. 5.2.

 

 

5.2

 

 

 

1 – Method

 

2 –

 

Method

Mesh Control

 

 

 

 

 

3 –

 

4 – Geometry

 

 

 

 

 

 

 

184

 

 

. 5.2

 

 

 

5 –

 

6 – Method

 

 

Hex Dominant

 

 

 

 

 

8 –

 

 

, Update,

 

 

 

 

 

Generate Mesh

7 – Hex

 

 

Dominant Method

 

 

 

 

 

9 –

 

10 –

Mesh

 

 

 

 

 

 

 

 

 

 

 

185

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, , -

. 5.20. ,

, , -

, ,

Tetrahedrons.

,

. 5.20

(Sweep Method) -

.

.

,

,

.

. -

( -

), .

-

. 5.3.

186

5.3

2 –

Method

1 – Method

Mesh Control

4 – Geometry

3 –

6 – Method

5 – Sweep

187

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. 5.3

8 –

, Update,

Generate Mesh

7 –

Sweep Method

9 –

Mesh

10 – -

188

Workbench .

Sizing ( ) Mesh Control , -

. Type :

Element Size ( )

;

Number of Divisions ( ) -

;

Sphere of Influence ( )

,

.

Sizing -

, -

, .

, . 5.4.

,

.

 

 

 

5.4

 

 

 

 

 

 

(sphere of influence)

 

 

 

 

 

 

Bodies

 

 

 

 

Faces

 

 

 

 

Edges

 

 

 

 

Vertices

 

 

 

 

. 5.5.

189

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5.5

2 – Sizing

1 – Sizing

3 –

4 – -

, -

5 –

6 –

Vertex Sizing

190

. 5.5

7 – Sphere Radius -

 

, -

8 –

;

Element Size

,

 

 

9 –

Generate Mesh -

Update

10 –

Mesh

10 – , ,

191

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. 5.6.

5.6

1 – Sizing -

2 – Sizing

 

Mesh Control

 

3 –

4 –

,

5 –

6 –

Face Sizing

192

. 5.6

 

8 – Type -

7 –

Sphere of Influence,

Sphere

 

Center, Sphere Radius Element Size

9 –

10 – Sphere Radius

-

,

(Global Coordinate System)

Element Size

 

 

(Coordinate System)

 

12 –

, Update,

Generate Mesh

11 – -

193

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. 5.6

13 – -

Vertex Sizing

Mesh , -

,

14 –

Mesh

15 – , ,

16 –

194

,

, , -

-

.

5.3.3.

Contact Sizing (

) Mesh Control ,

-

.

. Element Size

Relevance Type -

( . 5.21).

. 5.21

5.3.4. REFINEMENT

Refinement ( )

Mesh Control ,

, .

. -

,

195

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, -

. Refinement, 1,

. ,

, . , -

Refinement ,

. Refinement, -

.

Refinement -

. 5.7.

5.7

 

2 –

1 – Refinement

Refinement, ,

 

 

 

 

3 –

4 –

 

Refinement

 

196

. 5.7

 

 

6 –

 

 

.

5 –

 

Refinement, 1,

 

 

,

 

 

 

 

 

 

 

 

 

 

 

 

8 –

 

 

 

 

 

Refinement

 

 

 

7 –

 

Update

 

 

 

 

 

 

 

 

 

 

10 –

9 –

 

 

Mesh

 

Refinement =1. -

 

 

 

 

 

 

 

 

 

197

 

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Sizing Refinement

. 5.22) . -

Sizing

-, -

-

.

Refinement -

. -

, -

-

. Sizing Refinement

. 5.22

-

. Sizing

, Refinement

.

5.3.5.

(Mapped Face Meshing)

.

. -

(quadrilateral) (triangular) , -

, -

.

, , -

.

(Mapped Face Meshing)

. 5.8.

198

5.8

 

2 –

 

Mapped Face Meshing, -

1 – Mapped Face Meshing

, -

 

3 –

Mapped Face Meshing 4 –

,

5 –

6 –

199

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. 5.8

7 – -

Refinement

Update

8 –

Mapped Face Meshing

, ,

9 –

(Mapped Face Meshing)

,

200

5.3.6.

Match Control -

. 5.23)

-

-

-

( . 5.24). -

-

.

-

. 5.23

-

 

:

 

Match Control -

Mesh;

-

;

. Z -

.

. 5.24

201

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5.4.

,

.

New Section Plane ( ),

. (Section Plane)

.

. :

;

;

.

. 5.9.

5.9

1 – New Section Plane

2 –

202

. 5.9

3 –

4 – ,

 

 

 

 

5 –

6 –

7 –

8 – -

 

 

« »

 

 

 

 

 

203

 

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5.5.

,

.

, -

Problematic Geometry ( ), -

.

:

-, -

;

-

CAD, -

;

( Aggressive).

:

-

( Sizing);

,

;

CAD-

,

;

,

.

5.6.

(Virtual Topology) -

.

, -

Model. ,

204

, -

, (Model)

. 5.25). (Virtual Cell)

-

.

.

,

. -

. -

. -

, , -

( ).

.

. 5.25

Virtual Cell

), -

. -

, -

. -

-

. , -

, -

. Model ,

, .

-

Virtual Topology, -

( . 5.25). -

( . 5.26, )

205

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( . 5.26, ).

,

-

( . 5.27, ). Virtual Face ( -

) ( . 5.27, ), Geometry

) . ,

. -

. -

.

 

 

. 5.26

 

 

. 5.27

. 5.28, -

. -

– .

.

-

206

. -

-

( . 5.28, ).

 

 

. 5.28

, -

, -

-

( .).

, -

. -

-

.

.

. -

:

:

;

;

;

,

.

207

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5.7.

MECHANICAL ANSYS

-

ANSYS.

Part Relevance

SMRTSIZE .

Sizing (Element Size Number of Element Divisions – ) LESIZE ASIZE. -

Sphere of Influence ANSYS .

Contact Sizing ANSYS,

AESIZE , .

Refinement KREFINE, LREFINE,

AREFINE.

Element Size ESIZE.

Proximity and Curvature SMRTSIZE.

.

.

Shape Checking ( ) -

SHPP, LSTET,ON. -

(SHPP, LSTET,ON)

(Standard), . -

(SHPP, LSTET,OFF)

(Aggressive), . -

, -

. ANSYS

(SHPP, OFF), ANSYS

.

Mapped Face Meshing ( ) -

MSHKEY,1 -

MSHAPE.

208

Element Shape ( )

VMESH ( ) VSWEEP.

Part Proximity ( )

SMRTSIZE.

(Hex-dominant) -

ANSYS. , , SOLID45, .

ANSYS

(hex-to-tet) , -

,

,

. ANSYS -

Workbench.

1.-

?

2..

3..

4.,

, ?

5.Ansys Workbench

?

6.-

. -

:

, , , -

, , ?

?

?

Defaults ?

?

Statistics -

?

209

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7..

. -

Relevance Relevance Center. -

,

.

8.-

Sizing ?

9.. -

.

10.?

11.-

Extrude. -

(Sweep Method).

12.. -

. -

.

13.-

Extrude.

. -

Refinement Refinement, 2.

.

?

?

15.Match Control -

?

16.New Section Plane -

?

17., -

. . -

, -

.

18.-

.

19.Virtual Topology ?

20.(Virtual Cell)?

210

6. .

-

-

( , .) .

. « » « »

,

, . « -

» Workbench : , -

,

; »

(

) ( ) .

Workbench , . 6.1.

:

.

-

.

;

(Outline). -

;

(Details of “…”). -

.

( ,

Mesh Details of “Mesh”);

(Geometry). -

, ;

(Graph).

-

;

211

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(Tabular Data). -

,

.

. 6.1

-

, ,

, -

, , -

.

. -

,

. , -

.

. 6.2.

212

. 6.2

.

-

.

Definition Suppressed -

( Yes).

6.1.

Environment . 6.3), . -

Static Structural . Environment -

, :

Inertial – , -

;

Loads – – , -

;

213

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Supports – , ,

;

. 6.3

Environment -

Static Structural.

-

-

. -

(Global Coordinate System)

-

. -

-

Coordinate Systems.

-

,

. 6.4 ( . 6.4).

-

,

Coordinate Systems -

( . 6.5). -

-

. 6.5

– -

Coordinate Systems,

Insert Coordinate System.

214

, -

Coordinate Systems , Rename

.

-

( . 6.6), -

.

Define By):

Geometry Selection -

, Geometry;

Global Coordinates -

;

(Origin) .

-

-

-

, -

, , -

, , -

Geometry,

, Apply.

-

Principal Axis Orientation About Principal Axis -

.

Axis, Define By -

. 6.6

,

.

215

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-

. 6.7). -

.

, -

( . 6.8).

. 6.7

.

Geometry, -

: , -

. 6.7 . 6.8 , , ,

. -

) ) ,

,

Apply. : -

Geometry, – -

Apply.

-

:

(Constant);

(Tabular);

(Function).

. -

-

( . 6.9). ,

Import… Export…, -

-

.

216

. 6.9

-

Magnitude Tabular Data.

. Number of Steps

Analysis Settings,

. 6.10 6.11).

Tabular Data, -

( . . 6.12).

. 6.10

. 6.11

:

;

;

;

.

217

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Graph -

. 6.13).

. 6.12

-

.

. 6.13

6.1.1.

, -

Workbench, :

Acceleration – ;

Standard Earth Gravity – ;

Rotational Velocity – .

. 6.14

Inertial,

.

-

. -

. 6.14 , -

.

218

(Acceleration)

( Define By):

(Vector).

Magnitude) ( Direction). -

( . . 6.7);

(Components) x, y z.

-

.

mks – 2.

(Global Coordinate System)

Coordinate System).

(

) ( . 6.15).

. 6.15

(Standard Earth Gravity) Workbench -

, .

9,80665 2.

-

. -

, Direction -

219

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. . 6.16, 6.16, -

z -

My Coordinate System.

 

 

. 6.16

Rotational Velocity -

.

, -

.

, -

.

(Define By Vector), ( Axis).

:

, -

;

,

.

Magnitude ( ).

-

(Define By Components)

.

220

Rotational Velocity

-

, -

( . 6.17).

. 6.17

. 6.18 -

x, y z -

.

. 6.18

6.1.2.

Workbench

Loads Environment ( . 6.19). -

:

Pressure – ;

Hydrostatic Pressure – ;

221

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Force – ;

Remote Force – ;

Bearing Load – ;

Bolt Pretension – ;

Moment – ;

Generalized Plane Strain – ;

Line Pressure – ;

Thermal Condition – ;

Joint Load – ;

Fluid Solid Interface – ( )

.

 

Pressure

.

-

( . 6.20). -

-

( . 6.21).

,

Geometry),

( Magnitude)

 

 

Define By).

. 6.19

(Define By Vector), -

 

(Define By Components) -

(Define By Normal To).

. 6.20

. 6.21

222

Magnitude

, – . -

mks – .

-

, -

.

( . 6.22).

. 6.22

Constant, – Tabular,

Function.

Magnitude

) .

Hydrostatic Pressure -

. -

( . 6.23).

(

Fluid Density).

(Vector) (Components) ( . 6.23).

(Magnitude) (Direction)

Hydrostatic Acceleration. ,

223

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9,8 2,

.

( Coordinate System) ( ).

-

. 6.24,

.

. 6.25 . -

, -

,

.

. 6.23

. 6.24

Force .

.

, .

Geometry. (Define By Vector) -

(Define By Components).

224

. 6.25

( Magnitude).

, ( . . 6.1).

.

, -

. -

,

.

. -

.

mks – .

. 6.26-6.28 -, .

225

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. 6.26

. 6.27

. 6.28

226

,

, -

,

Remote Force ( . 6.30).

, -

. -

( X Coordinate, Y Coordinate, Z Coordi-

nate) -

. 6.29

.

 

(Define By Vector)

(Define By Components).

,

( . . 6.1).

mks – .

. 6.30 -

. -

.

, – .

. 6.30

227

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-

Bolt Pretension

 

 

( ) -

 

Bearing Load.

. -

 

 

.

 

 

 

 

.

 

( . 6.31).

z, -

 

-

.

. 6.31

.

 

 

. Bolt Pretension

 

-

.

.

Workbench -

, .

: ( )

 

-

) . -

 

 

( Define By):

 

 

Load –

 

. -

Preload) ( . 6.34);

 

-

Adjustment

 

 

 

 

Preadjustment) . 6.35).

 

. 6.32. -

 

. 6.32

 

,

 

mks – .

 

 

, . -

 

. 6.36.

. 6.33.

 

 

 

 

. 6.34

. 6.35

Bolt Pretension -

,

. 6.33 2 . -

,

228

229

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. -

– – -

. -

(Lock).

. 6.36

Moment ,

, . -

Details of “Moment”.

Geometry .

(Define By Vector)

(Define By Components).

-

.

(Magnitude) -

, . -

mks – .

,

.

,

. -

. 6.37.

230

-

,

-

.

. 6.38), ( . 6.39) . 6.37

( . 6.40).

. 6.38

. 6.39

231

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. 6.40

Line Pressure -

. Geometry ,

. -

( Define By): (Components), -

(Vector) (Tangential).

. -

Line Pressure . 6.41.

-

-

.

mks – .

-

, -

. 6.41

,

. 6.42. , , ,

,

. -

.

232

. 6.42

Thermal Condition

. , -

Geometry ,

.

. Magnitude 22 . ,

, . 6.43.

. 6.43

233

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6.2.

( ) –

.

-

.

Workbench -

Supports -

Environment ( . 6.44)

:

Fixed Support – ;

Displacement – ;

Remote Displacement

;

Velocity – ;

Impedance Boundary – -

;

Frictionless Support

. 6.44 ;

Compression Only Support – ;

Cylindrical Support – ;

Simply Supported – ;

Fixed Rotation – ;

Elastic Support – ;

Coupling – ;

Constraint Equation – , .

(Fixed Support) -

, , .

,

Fixed Support ,

Details of “Fixed Support”

Apply Geometry.

234

, ( . 6.45).

. 6.45

, , -

Displacement.

Geometry.

( Define By):

x, y, z

(Components);

(Normal To).

 

« »

 

 

-

 

.

 

«0»

 

 

-

 

.

-

 

-

 

 

 

 

 

. 6.46

Free ).

, , -

, -

, -

235

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, . -

mks – .

-

. . 6.47

. . 6.48 -

.

. 6.47

. 6.48

-

Remote Displacement. Details of Remote Displacement” . 6.49) ,

. -

( X Coordinate, Y Coordinate, Z Coordinate).

mks – , -

– .

236

. 6.50

, -

.

,

– . -

-

, -

. . 6.49

. 6.50

Frictionless Support

.

.

« » ( -

).

Geometry Apply.

237

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-

. 6.51. -

.

. 6.51

Compression Only Support -

.

Geometry. -

. -

, ,

. -

.

-

,

. , , -

.

Compression Only Support -

. -

, , ,

.

-

. 6.52.

.

238

. 6.52

Cylindrical Constraint -

.

 

 

 

 

 

(Axial), (Radial) -

 

(Tangential)

 

. 6.53).

 

 

 

: Free – -

 

Fixed

. 6.53

-

 

( ).

, -

(Radial, Axial Tangential) . -

Cylindrical Constraint . 6.54.

. 6.54

239

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Simply Supported

.

-, . -

-

, Apply Geometry.

-

. -

Simply Supported . 6.55.

Rotation X, Rotation Y, Rotation Z: Fixed – , Free

. -

Fixed. -

, –

(Global Coordinate System) .

-

.

. 6.57.

. 6.55

Fixed Rotation

,

. Fixed Rotation

, .

-

, Apply

Geometry.

( . 6.56).

240

. 6.56

. 6.57

6.3.

. ,

.

(Static Structural) -

:

1. Step Controls ( ):

Number Of Steps – ;

Current Step Number – ;

Step End Time – ;

Auto Time Stepping – .

241

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2.Solver Controls ( ):

Solver Type – ;

Weak Springs – ;

Large Deflection – ;

Inertia Relief – .

3.Nonlinear Controls ( ):

Force Convergence – ;

Moment Convergence – ;

Displacement Convergence – -

;

Rotation Convergence – -

( );

Line Search

.

4.Output Controls ( ):

Calculate Stress – ;

Calculate Strain – ;

Calculate Contact – ;

Calculate Results At – .

5.Analysis Data Management ( ):

Solver Files Directory – ;

Future Analysis – ;

Scratch Solver Files Directory – ;

Save ANSYS db – -

ANSYS;

Delete Unneeded Files – ;

Nonlinear Solution – ;

Solver Units – ;

Solver Unit System – , -

.

6.Visibility ( ).

242

6.3.1.

Step Controls ( . 6.58)

: -

.

-

,

. . 6.58

,

, -

, .

,

. -

.

.

, , -

,

.

Number Of Steps.

Tabular Data ( . . 6.11) -

.

Current Step Number

. Step End Time

.

.

.

Auto Time Stepping

.

243

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-

.

(Program Controlled), (On)

(Off) .

“On”

Define By): (Substeps)

(Time).

, -

(Initial Substeps), (Minimum Substeps) (Maximum Substeps) -

( . 6.59). -

(Initial Time Step), -

(Minimum Time Step) (Maximum Time Step) ( . 6.60).

. 6.59

. 6.60

Off

( Define By): -

(Number of Substeps)

(Time Step).

244

 

6.3.2.

 

Solver

 

Controls -

 

( . 6.61).

 

Solver Type

 

. Workbench

 

:

 

 

(Direct Solver) -

 

(Iterative

Solver). -

. 6.61

-

 

(Program Controlled).

 

-

, . -

.

Weak Springs -

.

,

.

.

COMBIN14.

(Program Controlled). -

. -

-

Messages.

(“On”) (“Off”) -

. “On”,

Solver Controls Springs Stiffness,

245

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-

:

Program Controlled – -

;

Factor – , -

( -

Stiffness Factor) ( . 6.62);

Manual – -

( Springs Stiffness Value) ( . 6.63).

. 6.62

. 6.63

Large Deflection -

, -

. -

. , “On”.

Large Deflection ,

,

.

Inertia Relief

. (“Off”).

(“On”) , -

.

. , -

.

246

 

6.3.3.

Nonlinear

 

Controls -

 

 

 

 

 

, , -

 

( . 6.64).

 

 

 

 

 

-

. 6.64

-

 

 

 

 

. ,

, . ,

, :

Force Convergence – ;

Moment Convergence – ;

Displacement Convergence – ;

Rotation Convergence – .

:

Program Controlled – -

;

On – ;

Remove – -

.

On” :

Value – , -

. (ANSYS Calculated)

, .

-

;

247

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Toleran e – ,

, -

. ;

Minimum Reference – .

,

.

Value Minimum Reference .

, -

, . 6.65.

. 6.65

Line Search

-

. :

(

);

;

.

248

6.3.4.

Output Controls -

( . 6.66):

 

Calculate Stress;

 

 

Calculate Strain;

 

 

Calculate Contact;

 

 

Calculate Results At.

. 6.66

 

 

 

:

(Stress), (Strain), (Contact). (Calculate Results At)

, -

:

All Time Points – ;

Last Time Point – ;

Equally Spaced Time Point – -

.

(Number Of Time Points). , -

ANSYS -

, ,

1000.

6.3.5.

Analysis Data Management

( . 6.67).

, ,

Solver Files Directory.

.

249

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Future Analysis -

,

-

( -

) .

: None

Prestressed analysis.

Scratch Solver Files Directory, -

, -

. 6.67 , -

. , -

.

Save ANSYS db

ANSYS. ,

Mechanical APDL (ANSYS

).

Delete Unneeded Files -

Workbench .

Yes”, .

.

, .,

. -

,

Nonlinear Solution. ,

,

.

Solver Units -

: Active System

Manual – .

( )

250

, Unit . -

( . 6.68). (Solver Unit System)

. Manual -

Solver Unit System

. Workbench

. 6.1.

. 6.68

 

 

6.1

 

 

 

 

 

 

1

Metric (m, kg, N, s, V, A)

mks

 

 

 

2

Metric (cm, g, dyne, s, V, A)

cgs

 

 

 

3

Metric (mm, kg, N, s, mV, mA)

nmm

 

 

 

4

Metric (mm, t, N, s, mV, mA)

nmm

 

 

 

5

Metric (mm, dat, N, s, mV, mA)

nmm

 

 

 

6

Metric ( m, kg, N, s, V, mA)

mks

 

 

 

7

U.S. Customary (ft, lbm, lbf, ºF, s, V, A)

Bft

 

 

 

8

U.S. Customary (in, lbm, lbf, ºF, s, V, A)

Bin

 

 

 

251

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6.3.6.

Visibility -

. -

( . 6.69).

-

( . 6.70).

. 6.69 -

Display Omit.

. 6.70

. . :

Graph Tabular Data?

Graph

Tabular Data?

Environment?

Details of"../?

, -

Workbench.

, Loads -

Environment.

Supports -

Environment?

2., -

. .

252

Number of Steps Analysis Settings. -

Tabular Data?

4.(Acceleration).

:

, -

?

?

?

(Components)

?

5.(Standard Earth Gravity). (

) .

6.Rotational Velocity. ?

7.. 10

.

8.Magnitude?

9..

?

10., .

:

?

-

?

, ?

11.Remote Force. -, 4 , .

12., ,

Moment.

13.Fixed Support .

14.Displacement

-5 X. :

?

«0» ?

«Free» ?

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15.Frictionless Support,

. :

?

?

?

16.,

(Compression Only Support). :

?

Compression Only Support?

17.. -

(Cylindrical Constraint) , -

. :

«Free» «Fixed»?

?

18.( ) .

Simply Supported .

:

?

?

19.X (Fixed Rotation). :

?

-

?

?

20.Analysis Settings .

:

-

(Step Controls)?

{Solver Controls)?

-

( Nonlinear Controls)?

-

(Analysis Data Management)?

21.?

22.Weak Springs?

23.Delete Unneeded Files?

254

ANSYS Workbench .

A

 

Acceleration –

 

Active assembly –

 

Active system –

 

Add –

;

Add frozen –

 

Add material –

 

Adjustment –

 

Advanced –

,

Alignment –

 

All time points –

 

Always –

 

Analysis data management –

Analysis settings –

 

Angle –

 

Animate –

;

Apply –

 

Arbitrary –

,

Arc –

 

Auto constraints –

 

Auto time stepping –

 

Axial –

 

Axis –

,

Axis of rotation –

 

B

 

Base object –

 

Bearing load –

 

 

255

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Behavior –

 

Constraint equation –

,

Bend –

,

Constraints –

 

Body centroids –

 

 

 

Body operation –

 

Construction point –

 

Bolt pretension –

 

Construction point at inter-

 

Boolean –

 

section –

 

Both asymmetric –

 

Contact region –

( )

Both symmetric –

 

Contact sizing –

-

Boundary –

 

 

 

Box –

 

Coordinate systems –

 

 

 

Copies –

 

C

 

Copy –

 

Calculate contact –

 

Corner –

 

Calculate results at –

 

Coupling –

 

Calculate strain –

 

Create –

 

Calculate stress –

 

Cross section –

 

Cancel –

;

Current step number –

 

Chamfer –

 

Cursors –

 

Children –

 

Curve –

 

Circle –

 

Cut –

;

Circular –

 

Cut material –

 

Clear selection –

 

Cycles –

 

Coarse –

 

Cyclic –

 

Coincident –

 

Cylinder –

 

Collapse features –

 

Cylindrical support –

 

Components –

 

 

 

Compression only support –

 

D

 

Concentric –

 

Defaults –

 

Concept –

,

Define by –

( ) …

Cone –

 

Defined –

 

Constant –

 

Definition –

,

Constrain –

 

Deformable –

 

 

256

 

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Delete –

 

Ellipse –

 

Delete unneeded files –

 

Environment –

 

Depth –

 

Equal distance –

 

Details –

,

Equal length –

 

Details of “…” –

 

Equal radius –

 

Diameter –

 

Equally spaced time point –

Dimensions –

 

Evenly spaced –

 

 

 

Expand –

,

Direct solver –

 

Export –

 

Direction –

 

Extend –

 

Direction –

 

Extend type –

 

Direction vector –

 

Extrude –

 

Displacement –

 

 

 

Displacement convergence –

 

F

 

Display names –

 

Face delete –

 

 

 

Factor –

,

Display values –

 

Fast –

 

 

 

Fill –

 

Distance –

,

Fillet –

 

Divisions –

 

Fine –

 

Drag –

 

Fixed –

, , -

Draw –

 

 

,

Dropped –

 

Fixed rotation –

 

Duplicate –

 

Fixed support –

 

 

 

Fluid density –

 

E

 

Fluid solid interface –

( )

Edge delete –

 

 

 

Edit –

 

Force –

 

Elastic support –

 

Force convergence –

 

Element midside nodes –

 

Free –

 

Element size –

 

Freeze –

,

Elements –

 

Frictionless support –

 

 

258

 

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Full assembly –

 

Inertial –

 

Full circle –

 

Initial size seed –

 

Function –

 

Initial substeps –

 

Future analysis –

 

Initial time step –

 

 

 

Integrated –

 

G

 

Intersect –

 

General –

 

Inward thickness –

,

Generalized plane strain –

 

 

 

Generate mesh –

( ) -

Iterative solver –

 

 

 

J

 

Geometry –

,

 

Joint load –

 

Geometry selection –

 

 

 

Global coordinate system –

 

K

 

Graph –

,

 

Kept –

 

 

 

 

 

 

Graphics annotation –

 

L

 

Grid –

 

 

Large deflection –

 

 

 

H

 

Last time point –

 

 

Length –

 

Healing –

»

Length/distance –

,

Hide sketch –

 

Line –

 

High –

 

Line body –

 

Horizontal –

 

Line by 2 tangents –

,

Hydrostatic pressure –

 

Line from points –

 

 

 

I

 

Line pressure –

 

 

Line search –

-

Ignore axis –

 

 

 

Impedance boundary –

 

 

Loads –

Import –

,

 

,

Imprint faces –

,

 

Look at –

 

 

 

 

Loose –

 

Inertia relief –

 

Low –

 

 

 

 

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M

 

N

 

Magnitude –

 

Named selection –

 

Major grid spacing –

 

New section plane –

 

Manual –

;

No selection –

 

Mapped face meshing –

 

Nodes –

 

 

 

Nonlinear controls –

 

Master geometry –

 

Nonlinear solution –

 

Match control –

-

Normal to –

 

 

Number of steps –

 

Maximum substeps –

 

Number of time points –

 

Maximum time step –

 

 

 

Medium –

 

O

 

Mesh –

 

Off –

 

Mesh control –

 

Offset –

 

Message –

 

On –

 

Method –

,

Operation –

 

Midpoint –

 

Orientation about principal

 

Mid-surface –

-

axis –

 

 

 

Origin –

 

Minimum edge length –

 

Output controls –

 

Minimum reference –

 

Outward thickness –

,

Minimum substeps –

 

 

 

Minimum time step –

 

Oval –

 

Minor-steps per major –

 

 

 

Mirror –

 

P

 

Model –

 

Parallel –

 

Modeling –

 

Parallelepiped –

 

Modify –

 

Parents –

( )

Moment –

 

Part –

,

Moment convergence –

 

Paste –

 

Move –

,

Paste handle –

 

 

 

Path –

 

 

262

 

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Pattern –

 

Redo –

 

Perpendicular –

 

Reference only –

 

Please define –

,

Refinement –

,

Point –

 

Refresh –

,

Polygon –

 

Relevance –

,

Polyline –

 

Remote displacement –

 

Preadjustment –

 

Remote force –

 

Preload –

 

Remove –

,

Preserve –

 

Rename –

 

Pressure –

 

Replicate –

 

Preview –

 

Report –

,

Preview surface mesh –

 

Reset –

,

 

 

Reversed –

 

Primitives –

,

Revolve –

 

Principal axis –

 

Rigid –

,

Print preview –

 

Rotate –

 

Prism –

 

Rotation –

 

Profile –

 

Rotation convergence –

 

Program controlled –

 

 

( )

Project –

 

Rotational velocity –

 

Pyramid –

 

Ruler –

 

Q

 

S

 

Quadrilaterals –

,

Save ANSYS db –

 

 

 

 

ANSYS

R

 

Scale –

,

Radial –

 

Scaling factor –

 

Radius –

 

Scope –

( )

Ratio –

,

Scoping method –

,

Rectangle –

 

 

 

Rectangle by 3 points –

 

Scratch solver files directory

 

Rectangular –

 

 

 

264

 

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Section –

 

 

 

Select multiple –

 

Solver units –

 

Select new symmetry axis –

 

 

 

Selection –

 

Span –

,

Semi-automatic –

 

Sphere –

 

Setting –

,

Spline –

,

Sew –

,

Spline edit sphere –

 

Shape –

 

Split –

 

Shape checking –

 

Split at select –

,

Show dependencies –

( )

 

 

 

 

Split edge into n equal seg-

n

Simplify –

 

ments –

 

Simply supported –

 

Split edges –

 

Sizing –

 

Split edges at all points –

 

Sketch instance –

 

 

 

Sketching toolboxes –

 

Split edges at point –

, -

Skin/loft –

 

 

 

Slave geometry –

 

Springs stiffness –

 

Slice –

 

Springs stiffness factor –

 

Slice by faces –

 

Standard earth gravity –

 

Slice by plane –

 

Static structural –

 

Slice by surface –

 

Statistics –

 

Slice off edges

 

Step control –

 

Slow –

 

Step end time –

 

Smoothing –

,

Substeps –

 

Snaps per minor –

 

Subtract –

 

Solid –

,

Supports –

,

Solids –

 

 

 

Solver controls –

 

Suppressed –

,

Solver files directory –

 

Surface body –

,

Solver type –

 

Sweep –

 

Solver unit system –

, -

Symmetry –

 

 

266

 

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T

 

Use global setting –

( ) -

Tabular –

 

 

 

Tabular data –

 

User define –

 

Tangent –

 

 

 

Tangent line –

,

V

 

Tangential –

 

Value –

 

Thermal condition –

 

Vector –

 

Thickness –

 

Velocity –

 

Through all –

 

Vertical –

,

Time –

 

 

Y)

Time step –

 

View advanced options –

 

Timestamp –

 

Visibility –

 

Tolerance –

 

 

 

Torus –

 

W

 

Transformation –

 

Weak springs –

 

Transition –

,

Wizard –

 

Translate –

 

 

 

Tree outline –

 

 

 

Triad –

 

A, mA

,

Triangles –

 

kg, g, t, dat

, , ,

Trim –

 

m, cm, mm, m

, , ,

Trim 1st –

 

N, dyne, N

, ,

Trim both –

 

s

 

Trim none –

 

V, mV

,

Type –

 

 

 

U

 

 

 

Undo –

,

 

 

 

 

 

 

Unite –

 

 

 

Update –

 

 

 

Use advanced size function

 

 

 

 

 

 

 

268

 

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1.., . -

/ . . – .: , 1982. – 448 .

2.. : . – .:

. ., 2005. – 840 .

3.. . / . . – .: , 1984. – 428 .

4.. : . – .

« ». – .: , 1970. – 6. – . 90-103.

5.. / . . – .: , 1975. – 541 .

6., . / . . –

.: , 1981. – 304 .

7.., ., .

: .

. . . – .: . ., 1985. – 392 .

8.. /

. . – .: , 1976. – 464 .

9.. / . . – .:

, 1979. – 392 .

10.., . / . . – .:

, 1977. – 349 .

11.Clough R.W. The finite element method in plane stress analysis. J. Struct. Div., ASCE, Proc. 2nd A.S.C.E. Conf. on Electronic Computation, Sept. 1960, p. 345-378.

12.Courant R. Variational Method for the Solution of Problems of Equilibrium and Vibration. Bull. Amer. Math. Soc., 49, 1943, p. 1-43.

13.ANSYS Help.

270

,

, ,

ANSYS Workbench

I

.

.

.

24.09.10

60 84 1/16. .

. . . 15,75. .- . . 15,72.

50 . . 137/10

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