Density gradient based regularization of topology optimization problems

Abstract

In the present paper we focus on the regularization of topology design problems with regard to numerical instabilities such as the occurrence of optimal designs characterized by oscillating material density distributions, for example in the form of the well–known “checkerboard–like” patterns, as well as the dependence of the obtained designs on the used finite–element–mesh. In this context we discuss a regularization approach penalizing spatial oscillations of the material density by means of a penalty functional reflecting the global distribution of the density gradient. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)