Numerical aspects of X-SIMP-based topology optimization

Abstract

The discretization of topology design problems on the basis of the finite-element-method results in general in large-scale combinatorial optimization problems, which are usually relaxed by the introduction of a continuous material density function as design variable. To avoid optimal designs containing unfavourable microstructures such as the well-known “checkerboard” patterns, the relaxed problem can be regularized by the X-SIMP-approach, which penalizes intermediate density values as well as high density gradients within the design domain. In this context we discuss numerical aspects of the X-SIMP-based regularization such as the discretization of the regularized problem, the formulation of the corresponding stiffness matrix and the numerical solution of the discretized problem. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)