Parametric Study on the Element Size Effect for Optimal Topologies

Abstract

Topology optimization is complex engineering design tool. It needs intensive mathematical, mechanical and computing tools to perform the required design. During its hundred years of history it has become clear that the non-unique solution property of the method is affected by the material parameters (Poisson ratio) and the ways of the discretization. The aim of the paper is to investigate the influence of parameter changes to optimal design property in tasks with great number of degrees of freedom. The parametric study includes influence of material parameter (Poisson ratio) as well as the size of the ground elements which are commonly applied during the discretization. Increasing the size of the ground elements while the total number of the finite elements is constant, the computational time is significantly reduced. Therefore the study on changing accuracy versus ground element resolution may be important factor in choosing ground element size. In addition to it the effective properties of arrangements of the strong and weak materials (black and white elements) in a checkerboard fashion are also investigated. The Michell-type problem is investigated by the minimization of the weight of the structure subjected to a compliance constraint.