Filters in topology optimization

In this article, a modi ed (` lteredʹ) 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 eld by the mean of a convolution operator. In this setting it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of nite elements can be obtained. This is illustrated through some numerical experiments. The ` lteringʹ technique is also shown to cope with two important numerical problems in topology optimization, checkerboards and mesh dependent designs