Solution to Shape Optimization Problems of Continua on Thermal Elastic Deformation

Abstract

This paper presents a numerical solution to shape optimization problems of continua minimizing steady-state thermal elastic deformation. The potential energy by thermal elastic strain was used as an objective functional. Coupling boundary value problems of partial differential equations for steady-state heat-transfer and linear elastic deformation were employed as state equations. The shape gradient function of the shape optimization problem was theoretically derived using the Lagrange multiplier method, or the adjoint variable method, and the formulae of the material derivative. Reshaping was carried out by the traction method that was proposed by one of the authors as an approach to solving domain optimization problems. The validity of the presented method was confirmed by results of numerical analyses.