Topology optimization for coupled thermomechanical problems with approximated thermal radiation boundary conditions depending on design variables

Abstract

In this study, a topology optimization method for coupled thermomechanical problems is proposed by incorporating approximated thermal radiation boundary conditions that depend on design variables. The challenge of designing mechanical structures influenced by thermal radiation is briefly discussed. Partial Differential Equations are introduced to represent the geometric features influenced by thermal radiation. The boundary under thermal radiation conditions is expressed using the solution. In addition, a mathematical model is developed to approximate the view factor, which is related to the contribution of thermal radiation. To address this, the historical temperature data calculated during the optimization iterations are employed to create a linear approximation of the sensitivity analysis. The objective functional for temperature and displacement are evaluated using the weighted sum method. Furthermore, a specific optimization algorithm using the finite element method is proposed. The proposed method is applied to two- and three-dimensional problems to confirm the effectiveness and applicability of the proposed method.