Toward multiphysics multiscale concurrent topology optimization for lightweight structures with high heat conductivity and high stiffness using MATLAB

Abstract

Structural light weighting is vital for increasing energy efficiency and reducing CO₂ emissions. Furthermore, for many applications, high heat conductivity is necessary to attain efficient energy transfer while increasing the product stiffness and reducing the weight. In recent years, with the development of 3D printing technology, attention has been directed toward porous materials that greatly contribute to weight reduction. As such, this educational research is aiming toward introducing the methodology of concurrent multiscale topology optimization attaining designs of lightweight, high heat conductive, and stiff porous structures utilizing multi-objective optimization method. The normalized multi-objective function is used in this research to maximize heat conductivity and stiffness. Therefore, the objective criteria are consisting of heat and mechanical compliance minimization. Utilizing the SIMP method, the multiscale sensitivity analysis, and optimization formulation were driven theoretically using adjoint method to reduce the computational cost and presented in a MATLAB code. 2D cases were studied, and a proper Pareto front was attained. The results showed good coupling of the macro and microscale design. The MATLAB code is explained and included in the appendix and it is intended for educational purposes.