Figure. Example of a very bad mesh for topology optimization - large element edge length variations are present
Finite element meshing of a part that will undergo topology optimization should be done by considering a few issues, not typically present if only usual FEA is planned. These issues are related to
Computational efficiency, which mostly depends on the finite element type chosen, is very important because the optimization process is a cyclic one and typically requires a large number of finite element analyses. On the other hand, the quality of the result is closely related to the geometrical quality of the mesh.
ProTOp has built in specialized finite elements that are derived from usual isoparametric finite elements but are modified and adopted for the employed topology optimization method in order to deliver better results and be more efficient than standard elements. The following table should help to make the right choice about which element to engage in a particular scenario.
| FE Type: | TTH4S | HXH8S | TTH10S |
|---|---|---|---|
| Based on: | Isoparametric linear tetrahedron; 4 nodes | Isoparametric linear hexahedron; 8 nodes | Isoparametric parabolic tetrahedron; 10 nodes |
|
Performance (quality of results) |
Good |
Very good (especially for structured FE meshes) |
Good |
|
Efficiency (CPU time and RAM consumption) |
Very good | Good | PROBLEMATIC (for equal element sizes the RAM consumption might be up to 16 times of what is needed for TTH4S) |
| Supported by all ProTOp tools | YES | NO | NO |
| Recommendation | Overall the most preferable element | Preferable, if a structured hexahedral mesh is available | Should be avoided, except if accurate displacements computation is essential (displacement targeting) |
In order to use a particular FE type from the table above, the meshing of the source model has to be done with a topologically compatible finite element. ProTOp replaces these elements with its own corresponding types as follows:
NOTE. ProTOp can also convert HXH8S and TTH10S elements into TTH4S elements.
NOTE. Only the TTH4S element is supported by all ProTOp tools.
The meshing procedure determines the geometrical properties of finite elements. For good optimization results, the mesh of the optimized region should be:
The figure below illustrates a very bad mesh for topology optimization: large element edge lengths variations are present within the optimization region.
Figure. Example of a very bad mesh for topology optimization - large element edge length variations are present
In general one can say that the finer the mesh, the better the results will be. Of course as the mesh is made finer, the size of the FE model increases very rapidly. Therefore, to assure acceptable computation efficiency, a good balance between mesh fineness and model size should be found.
NOTE. ProTOp contains a mesh refinement tool. This tool can be run globally or localized to specific regions in order to make the mesh more uniform and/or to decrease the edge lengths.
IMPORTANT. Finite element meshers often tend to generate large elements in the interior of a part. This problem is not visible as only the surface of a part is typically shown on the screen. Therefore, the mesh refinement tool should always be used to check and, if needed, correct the mesh before running optimization.