Multi-objective shape optimization for maximizing stiffness in thermo-elastic fields

Abstract

This paper presents a numerical solution to multi-objective shape optimization in order to achieve stiffness maximization in thermoelastic fields. Compliance evaluated by thermal deformation based on temperature distribution and by mechanical deformation based on surface force or body force is used as an objective functional by using weighting method. Shape gradient of the multi-objective shape problem is derived theoretically using the Lagrange multiplier method, adjoint variable method, and the formulae of the material derivative. Reshaping is carried out by the traction method proposed as an approach to solving shape optimization problems. Numerical analyses program for the shape optimization is developed based on FreeFem++, and the validity of proposed method is confirmed by results of 2D numerical analyses.