Lecture Notes: Introduction to Finite Element Method

Chapter 5. Plate and Shell Elements

III. Shells and Shell Elements

Shells – Thin structures witch span over curved surfaces.

Example:

•Sea shell, egg shell (the wonder of the nature);

•Containers, pipes, tanks;

•Car bodies;

•Roofs, buildings (the Superdome), etc.

Forces in shells:

Membrane forces + Bending Moments

(cf. plates: bending only)

© 1997-2002 Yijun Liu, University of Cincinnati

133

Lecture Notes: Introduction to Finite Element Method

Chapter 5. Plate and Shell Elements

Example: A Cylindrical Container.

p

p

internal forces:

p	p

membrane stresses dominate

Shell Theory:

•Thin shell theory

•Thick shell theory

Shell theories are the most complicated ones to formulate and analyze in mechanics (Russian’s contributions).

•Engineering ≠ Craftsmanship

•Demand strong analytical skill

© 1997-2002 Yijun Liu, University of Cincinnati

134

Lecture Notes: Introduction to Finite Element Method

Chapter 5. Plate and Shell Elements

Shell Elements:

	+
plane stress element	plate bending element

flat shell element

cf.: bar + simple beam element => general beam element. DOF at each node:

w	v
θy	u	θx

Q4 or Q8 shell element.

© 1997-2002 Yijun Liu, University of Cincinnati

135

Lecture Notes: Introduction to Finite Element Method

Chapter 5. Plate and Shell Elements

Curved shell elements:

i	w	θz
		v
	i	u	θx
	θy

•Based on shell theories;

•Most general shell elements (flat shell and plate elements are subsets);

•Complicated in formulation.

© 1997-2002 Yijun Liu, University of Cincinnati

136