Design of Architected Materials for Thermoelastic Macrostructures Using Level Set Method

A level set topology optimization method is introduced and used to design periodic architected materials optimized for the maximum macrostructural stiffness considering thermoelasticity. The design variables are defined at the microscopic scale and updated by minimizing the total structural compliance induced by mechanical and thermal expansion loads at the macroscopic scale. The two scales are coupled by the effective elasticity tensor calculated through the homogenization theory. A decomposition method is constructed to formulate several subproblems from the original optimization problem, enabling the efficient solution of this otherwise computationally expensive problem, especially when the number of material subdomains is large. The proposed method is demonstrated through several numerical examples. It is shown that the macrostructural geometry and boundary conditions have a significant impact on the optimized material designs when thermoelastic effects are considered. Porous material with well-designed microstructure is preferred over solid material when the thermal load is nonzero. Moreover, when a larger number of material microstructures is allowed in optimization, the overall performance is improved due to the expanded design space.