Critical study of design parameterization in topology optimization; The influence of design parameterization on local minima

In the past decade, SIMP-based topology optimization methods have become increasingly popular. They offer the designer the possibility to perform design optimization in an early stage of the design process for a wide range of applications. The specific design parameterization used in SIMP is the result of many attempts to eliminate numerical artifacts in the results of topology optimization problems. However, any choice of design parameterization also influences the shape of the response functions. For a gradient-based optimization method it is important to obtain a smooth and, if possible, convex response. This research aims to point out relevant consequences of using the SIMP design parameterization in combination with density filters on the response functions. In this contribution we show the effects of the power of the penalization and the size of the density filter on the response functions. The introduction of penalization has two effects. Firstly, increasing the introduction of a density filter is not only useful to avoid checkerboard patterns, control minimum member size and achieve mesh-independence, but it also reduces the immobilizing effect that penalization has on the mobility of the boundary of the structure. This effect and its dependence on the power of the penalization and the size of the density filter are illustrated using several elementary numerical examples involving compliance minimization. The results are expected to be relevant for any type of structural topology optimization. Keywords: Topology optimization, design parameterization, penalization, density filter, local minima