Background

Successful topology optimization necessitates fine FE meshes with element edge lengths being as uniform as possible throughout the optimization domain. Often, this is not the case because of two reasons:

• A moderately fine mesh is generated on purpose in order to make the process of model preparation, correction, and fine tuning faster; additionally, fixed regions do not necessitate a very fine mesh and should be made only moderately fine to keep the FEA times reasonably low.
• The FEA mesher has difficulties in generating an adequate and uniform mesh.

In both cases the mesh should be properly refined at least before doing the final optimization run. This will make possible to get high quality optimization results.

█ Inspecting the mesh

Each material region of the mesh should be inspected visually and numerically by the Analyze command. Among the reported analysis results, the maximal and average element edge lengths are the most important parameters.

Figure. Material region with bad initial mesh: large variations in element edge lengths are present.

The mesh in the figure is problematic because it exhibits large variations in element edge lengths. Either some of the edges are:

• too long and the optimization result will be bad, or,
• unnecessarily short and the optimization process will be computationally inefficient.

Any of these situations should be corrected.

█ Defining the edge subdivide threshold

The edge subdivide threshold defines the maximal edge length after subdivision. Thus, it has to be carefully chosen with respect to:

• required fineness of the optimized design and
• eventual minimum thickness limits, if shell or lattice configurators will be engaged.

For the case that shell or lattice configurators will be used, one should keep in mind that the prescribed minimum thickness should accommodate for at least 2 or 3 finite elements. In other words, the maximum edge length should be at least one half or one third of the prescribed minimum thickness.

Figure. Refined mesh with edge subdivide threshold set to 4.0.

█ Defining the region bandwidth

The region bandwidth parameter defines the number of finite element layers to be included into the mesh refinement process in order to:

• assure a smooth transition between the refined and neighboring regions and
• prevent excessive finite element distortion in the neighboring regions.

Finite elements within the bandwidth layers will also be subdivided in a way to assure a smooth transition in element fineness between two regions.

Figure. Refined mesh of the free region with bandwidth parameter set to 0.

Figure. Refined mesh of the free region with bandwidth parameter set to 1.

Typically, a bandwidth of 1 should be fine, but this can be raised to 2 or 3 in case of very large edge length variations between various material regions.