TREATMENT OF TOPOLOGY OPTIMIZATION OF A TWO-DIMENSIONAL FIELD GOVERNED BY LAPLACE’S EQUATION UNDER NONLINEAR BOUNDARY CONDITION
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
Related Book
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