Shape Optimization of Thermoelastic Fields for Mean Compliance Minimization

Abstract

This paper presents a numerical analysis method for shape optimization in order to achieve stiffness maximization in thermoelastic fields. Mean compliance is used as an objective functional for the shape optimization problem. The mean compliance minimization problem on the thermoelastic fields is formulated on volume constraint condition. The shape gradient of the shape optimization problems is derived theoretically using the adjoint variable method, the Lagrange multiplier method and the formulae of the material derivative. Reshaping is accomplished using a traction method that was proposed as a solution to shape optimization problems. In addition, a new numerical procedure for the shape optimization is proposed. The validity of the proposed method is confirmed based on the results of 2D numerical analysis.