On nonlinear filters in topology optimization

Abstract eng:
It is well known that material distribution topology optimization problems often are ill-posed if no restriction or regularization method is used. A drawback with the standard linear density filter is that the resulting designs have large areas of intermediate densities, so-called gray areas, especially when large filter radii are used. To produce final designs with less gray areas, several different methods have been proposed; for example, projecting the densities after the filtering or using a nonlinear filtering procedure. In a recent paper, we presented a framework that encompasses a vast majority of currently available density filters. In this talk, we present that these nonlinear filters ensure existence of solutions to a continuous version of the minimal compliance problem. Moreover, we show numerical experiments that illustrates that cascades of these nonlinear filters can be used to efficiently solve large-scale topology optimization problems.

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