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Splitting Points

Conversely, the program may split n + 1 times if the solution has one point close to StartTime and another close to EndTime. (More than n + 1 splits should not occur.) Splitting n + 1 times is more likely to occur when n is a small value.

When a new mesh is created due to nonlinear adaptivity, the following message (or similar) is issued in the output file:

**** REGENERATE MESH AT SUBSTEP

7 OF LOAD STEP

1 BECAUSE OF NONLINEAR ADAPTIVE CRITERIA

**** NEW MESH HAS BEEN CREATED SUCCESSFULLY. CONTINUE TO SOLVE.

Loads and boundary conditions are mapped from the old mesh to the new mesh automatically.

5.4. How a New Mesh Is Generated

When remeshing occurs for 2-D and 3-D elements, splitting is used for mesh refinement.

In 2-D meshes, mesh morphing occurs after mesh splitting. The morphing operation can also modify elements that have not been split. The morphing process attempts to improve the element distortion metrics by optimizing the metrics immediately following splitting. If the shape metrics of specific elements cannot be improved without sacrificing the quality of the neighboring elements, then the element is

not changed via morphing. The morphing process is iterative and converges when a maximum number of iterations (set automatically depending on problem size and element type) are reached or no further element shape quality enhancement is possible. Morphing works by moving the nodes in the mesh (except for the nodes on the boundary).

In 3-D tetrahedron splitting, cotangent-weighted Laplacian mesh smoothing and topology correction (by 2-3, 3-2, 2-2, and 4-4 face swaps) occur automatically after splitting. 3-D mesh refinement is more tolerant of large deformation and mesh distortion than the same 2-D process because of the additional topology-correction step. As in the 2-D case, morphing in 3-D does not change node locations on the boundary; however, topology correction may modify elements on the boundary.

When energyand position-based criteria are used, solid elements are split directly and appropriate transitional elements are generated around a split region to ensure compatible transition with the unsplit regions. In such cases, parent elements within a component are split and the child elements are automatically made part of the component. Parent elements are dissociated from the component and removed from the simulation database during the splitting procedure. In this way, component information is automatically transferred from parent to child elements during the splitting procedure. For more information, see Geometry Details for Mesh Splitting (p. 105).

Elements supporting contact-based criteria are TARGE169, TARGE170, CONTA171, CONTA172, CONTA173, and CONTA174. Mesh nonlinear adaptivity has the same restrictions for contact and target elements as for rezoning.

For contact-based criteria, the candidate solid elements for splitting are selected indirectly. Nonlinear adaptivity criteria are applied to components of target elements and the decision to split the corresponding contacts is dependent on solution-based quantities at the specific substep at which criteria checking occurs. For example, consider the following figure, showing a 2-D target-contact interface at a subset on which contact-based mesh nonlinear adaptivity criteria are checked:

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How a New Mesh Is Generated

Figure 5.11: Rigid Target-Contact Interface

The mesh nonlinear adaptivity algorithm associates contact and target elements with each other using pinball radius values. For two components, CM1 and CM2 (where CM1 is consists of target element T1, and CM2 consists of both target elements T2 and T3), the following associations are made:

	C1	C2	C3	C4	C5	C6
T1	Y	Y	Y	Y	-	-
(CM1)
T2	-	-	-	Y	Y	-
(CM2)
T3	-	-	-	-	Y	Y
(CM2)

The program’s decision to split contact elements is determined by checking the total number of contact elements associated with a single target element of a particular target component, and the user-defined number of desired contact elements (NLADAPTIVE). The following commands assign the desired number of contact elements to be 3 and 5 for individual target elements of CM1 and CM2, respectively:

nladaptive,CM1,add,contact,numelem,3

nladaptive,CM2,add,contact,numelem,5

If the total number of contact elements assigned to a target element is smaller than the user-defined desired number during a substep where mesh nonlinear adaptivity criteria are checked, splitting occurs. If the total number of contact elements is greater than the user-defined desired number, no further refinement is done.

A size check also exists for contact-based criteria. The desired size of contact elements associated with

a particular target component is calculated by dividing the size of the target element by the user-defined desired number of elements. For example, the desired size for component CM1 in the previous example is (size of T1) / 3. If the individual contact element size for elements associated with a target element during a substep where mesh nonlinear adaptivity is checked is smaller than the desired size, no more refinement is done.

Contact-based mesh nonlinear adaptivity is used primary for gap filling simulation, such as a rubber seal simulations. As shown in the following figure, successive refinements of a mesh reduces the maximum gap significantly.

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Figure 5.12: Gap Reduction with Successive Mesh Refinement by Element Splitting

Besides size and number requirements, the decision to split an underlying solid element at a given substep also depends on the relative penetration or gap status of the corresponding contact element with respect to a previous reference substep, as shown in the following figure:

Figure 5.13: Contact-Status-Based Determination for Splitting

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Convergence at Substeps with the New Mesh

If the penetration increases (gap reduces), the contact element is moving toward the target, and therefore the underlying solid element is split to estimate a smaller pinball radius and improve gap reduction. In other cases, the underlying solid element is not split.

Should the splitting violate the size or number criteria, it does not occur. For a split to occur, all three criteria must be met in a substep where criteria checking occurs.

In certain cases, transitional elements can affect the size and number criteria. One such case occurs when neighboring target elements belong to different components with different size criteria defined via the NLADAPTIVE command. Consider the following simulation:

Figure 5.14: Effect of Transitional Element Generation on Size and Numbering Criteria

In this case, CM1 and CM2 are the two defined components. CM1 consists of target element T1, and CM2 consists of both target elements T2 and T3. The following mesh nonlinear adaptivity commands are issued:

nladaptive,CM1,add,contact,numelem,6

nladaptive,CM2,add,contact,numelem,4

Because T2 and T3 are of a much smaller size than T1, the size allowance of contact elements scoped to CM2 is much smaller than that of CM1. In substep 1, contact elements scoped to both CM1 and CM2 are candidates for refinement. In substep 2, however, only contacts scoped to CM2 are candidates, while contacts scoped to CM1 are not refined. Because transitional elements are generated for compatibility, some contact elements scoped to CM1 may be refined as an indirect consequence of refinements to the CM2 contacts. The program allows a small tolerance for the size criteria so that transition regions do not become over-refined during splitting.

5.5. Convergence at Substeps with the New Mesh

After mesh splitting, solutions from the previous unrefined mesh are mapped to the new mesh on the next substep after splitting. Residual forces due to differences in the mesh are applied along with the load increments of the substep. If there is convergence difficulty, the program may first reduce the time

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