Topological optimization of thermoelastic composites with maximized stiffness and heat transfer

The topological optimization of composite structures is widely used while tailoring materials to achieve the required engineering physical properties. In this paper, the problem of topological optimization of the microstructure of a composite aimed at the construction of a material with most effective values of the bulk modulus of elasticity and thermal conductivity taking into account competing mechanical and thermal properties of the materials included in the composite is defined and solved. A two-phase composite consists of two base materials, one of which has a higher Young modulus but lower thermal conductivity, while the other has a lower Young modulus but higher thermal conductivity. A new class of problems for composites containing material pores or technological inclusions of different shapes is considered. Effective thermoelastic properties are obtained using the asymptotic homogenization method. A modified solid isotropic material with penalization (SIMP) model is used to regularize the problem. The problem of the isoperimetric constraints is solved by the method of moving asymptotes (MMA). The influence on optimal topology of the composite in the presence of two competing materials, and optimality criteria using linear weight functions are investigated. Pareto spaces that provide deep understanding of how these goals compete in achieving optimal topology are constructed.