Author(s)

SHINSEI SATO, YI CUI, TORU TAKAHASHI, TOSHIRO MATSUMOTO

Abstract

This paper presents a treatment of the topology optimization problem for two-dimensional fields governed by Laplace’s equation. The study considers various boundary conditions, including Dirichlet, Neumann, Robin, and nonlinear radiation boundary conditions. Additionally, the topological derivative for a general objective functional comprising solely of boundary quantities is derived, with a special focus on the case of a radiation boundary condition in a black body. The accuracy of the derived adjoint problem and topological derivative is validated through several boundary element method calculations.

Keywords

topology optimization, nonlinear boundary condition, Laplace’s equation, adjoint problem, topological derivative