Topology Optimization of 2D Potential Problems Using Boundary Elements

A. CISILINO

París, Francia

Conferencia; International Conference on Boundary Element Techniques BETEQ 2006; 2006

Ecole Nationale des Ponts et Chaussess e Imperial College

A classical problem in engineering design consists in finding the optimum geometric configuration of a body that maximizes or minimizes a given cost function while it satisfies the problem boundary conditions. The most general approach to tackle these problems is by means of topological optimization tools, which allow not only to change the shape of the body but its topology via the creation of internal holes. Topological optimization tools are capable of deliver optimal designs with an “a priori” poor information on the optimal shape of the body. Homogenization methods are possibly the most used approach for topology optimization [1], but they present the limitation of producing designs with infinitesimal pores that make the structure not manufacturable. An alternative approach aiming to solve the aforementioned limitation of homogenization methods is the Topological Derivative (DT) method [2]. The basic idea behind the DT is the evaluation of cost function sensitivity to the creation of a hole. Wherever this sensitivity is low enough (or high enough depending on the nature of the problem) the material can be progressively eliminated.