Settings of the Mesh Filter

The result of the optimization of a bending beam, see the following figure, shows a numerical instability effect. The structure contains checkerboard-like areas with soft (void) and hard elements. In a structure like this, many hard elements have only the point contact to other hard elements. This result is not a valid design because the checkerboard effect is a numerical instability. This effect has been analyzed by BENDSØE and SIGMUND (M. P. Bendsøe, O. Sigmund, Topology Optimization Theory, Methods and Applications Springer-Verlag 2003) and references therein.

The following figure shows a checkerboard effect for a bending beam:

This checkerboard effect depends on the mesh and the discretization, which is obvious in the next figure. The mesh is refined in parts of the model.

Checkerboard structures cannot be manufactured in practice. The user also wants to obtain a mesh-independent result from the optimization. Due to these demands, SIMULIA Tosca Structure has a filter technique implemented to avoid mesh dependence. A specification of a filter radius (FILTER_RADIUS parameter) is necessary for applying the filter. If the radius of the filter is not specified, the optimization is performed using a filter having a default radius. This radius might be too large for coarse meshes.

Important: If the radius is too large, the optimization result will not show a detailed structure. A small value of the radius leads to a fine structure. It is recommended to choose the filter radius equal to twice the mean element edge length.

The filter radius is defined in OPT_PARAM command as follows:

OPT_PARAM
 ID_NAME = optimization_control
 OPTIMIZE = id_of_optimize
 ...
 FILTER_RADIUS = 5.
END_