Level set-based BEM topology optimization method for maximizing total potential energy of thermal problems

Abstract

A topology optimization for maximizing total potential energy by combining the level set method and boundary element method is proposed. The objective function is considered a function of temperature and thermal flux defined on boundaries with Neumann boundary condition. An adjoint field is constructed for the topology optimization problem of total potential energy maximization with previously derived topology sensitivity, which is verified by finite difference approximation. The effectiveness of the present method is validated by comparing it with the result in the literature. The present method proves to initial configuration independent by placing circular and rectangular holes in initial configurations, respectively. An example of topology optimization on replacing the boundary conditions on certain boundaries is studied, with the optimization result a different material distribution. It will help with making versatile configurations by simply changing boundary conditions on existing boundaries. The major novel aspect of this paper, in summarization, is a level set-based topology optimization method is developed for maximizing the total potential energy of thermal problems, as well as the enlightenment of obtaining versatile results by changing boundary conditions.