A Boundary Element Approach for Shape and Topology Design in Orthotropic Heat Transfer Problems

Abstract

A numerical approach for topology optimization of orthotropic potential problems using the boundary element methods (BEM) is introduced. The method is based on the evaluation of
topological derivative, adopting the total potential energy as the cost function. A hard-kill algorithm is devised to progressively remove material where it is less necessary. This developed procedure is an alternative to the homogenization technique, avoiding the use of intermediary density material. The topology optimization of non-isotropic media is addressed using conformal mapping techniques. The
method preserves BEM features, such as boundary-only discretization, reducing significantly the computational cost. Results obtained with the technique for Robin, Neumann and/or Dirichlet boundary conditions are compared and discussed with those available in the literature.