# Filters in topology optimization

Blaise Bourdin

Research output: Book/ReportReportResearchpeer-review

## Abstract

In this article, a modified (filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The filtering'' technique is also shown to cope with two important numerical problems in topology optimization, \emph{checkerboards} and \emph{mesh dependent} designs.
Original language English
Number of pages 22 Published - 1999