Topology Optimization of Three-Dimensional Elastic Structures Using Boundary Elements

Abstract

Topological optimization provides a powerful framework to obtain the optimal domain topology for several engineering problems. The topological derivative is a function which characterizes the sensitivity of a given problem to the change of its topology, like opening a small hole in a continuum or changing the connectivity of rods in a truss.
A numerical approach for the topological optimization of three-dimensional linear elastic problems using boundary elements is presented in this work. The topological derivative is computed from strain and stress results which are solved by means of a standard boundary element analysis. Models are discretized using linear or constant elements and a periodic distribution of internal points over the domain. The total potential energy is selected as cost function. The evaluation of the topological derivative is performed as a post-processing procedure. Afterwards, material is removed from the model by deleting the internal points and boundary nodes with the lowest values of the topological derivate. The new geometry is then remeshed creating “holes” at those positions where internal points and boundary points have been removed. The procedure is repeated until a given stopping criterion is satisfied.
The proposed strategy proved to be flexible and robust. A number of examples are solved and results are compared to those available in the literature.