Multidisciplinary free-form optimization of solid structures for mean compliance minimization and time-dependent temperature control

A parameter-free free-form optimization method to solve multidisciplinary shape optimization problems of solid structures is presented in this paper. The design objective is both to minimize the mean compliance of linear elastic structures and to control the temperature at arbitrary locations and time periods for arbitrary loadings and under volume constraint, simultaneously. The multidisciplinary design problem is formulated as a distributed-parameter shape optimization problem based on the variational method, and the global objective function is defined using an original normalized weighted sum method. The shape gradient density functions with respect to the shape variation are derived based on the material derivative and the adjoint variable methods. The shape gradient density functions theoretically derived are applied to the H¹ gradient method, a gradient method in the function space, to obtain the optimal shape while maintaining the smoothness of the shape. Numerical examples are considered to demonstrate the validity and the effectiveness of the developed optimization method.