Topology optimization of three-dimensional load-bearing structures using boundary elements

A numerical procedure for the topological optimization of three-dimensional linear elastic problems using boundary elements and the Topological Derivative (TD) is presented in this work. The TD is a function which characterizes the sensitivity of a given cost function to the change of the domain topology, like opening a small hole in a continuum. In particular, for this work the total potential strain energy is selected as cost function, and the TD is computed from the stress field by means of the Topological-Shape Sensitivity Method.The optimization problem is solved incrementally. In every step small portions of the model domain are removed by deleting small portions of material associated with the internal points. The new geometry is then remeshed and the resulting boundary element discretization checked (and if necessary fixed) in order to avoid geometrically invalid models. This procedure is repeated until a given stopping criterion is satisfied.The proposed strategy proves to be flexible and robust. A Furthermore, a number of examples are solved and the results discussed and compared to those available in the literature.