Shape optimization for maximizing stiffness in unsteady thermo-elastic fields

Abstract

This paper presents a numerical solution for shape optimization problem to achieve stiffness maximization in unsteady-state thermo-elastic fields. Mean compliance is used as an objective functional for the shape optimization problem. Shape gradient of the shape optimization problem was derived theoretically using the adjoint variable method, the Lagrange multiplier method and the formulate of the material derivative. Reshaping was accomplished using a traction method that was proposed as a solution to shape optimization problems. A numerical analysis program for the shape optimization was developed based on FreeFem++, and the validity of proposed method was confirmed by results of 2D numerical results.