Investigation of concurrent multiscale topology optimization for designing lightweight macrostructure with high thermal conductivity

Abstract

Lightweight and high heat conductive solid structures are playing important role in various fields of engineering. To maximize the design performance for such structures, we investigated multiscale topology optimization for excessive lightweight heat-conductive porous structures and introduced a mathematical optimization model formulation for concurrently optimizing the structures (macrostructure) and the constitutive pores (microstructure). The microscale is considered a representative volume element and designed using the asymptotic homogenization method. For each iteration, the effective heat conductivity tensor of the microstructure is evaluated during the optimization process and used as the heat conductivity of the macrostructure. Sensitivity analysis on this concurrent optimization scheme was derived to address the macro and microstructure coupling. To broaden the scope of the research applicability, three topology optimization methods, i.e., SIMP, level set and ESO are investigated, and the results are compared and discussed. The suggested formulations showed a successful application of the concurrent multiscale optimization formulations and good coupling on the macro and microscale. Also, the formulations demonstrated a strong influence between the macro and the microscale of the design problem for the topology optimization methods. Increasing the design freedom by introducing various microstructures for the macro design domain showed superior performance associated with attaining high weight reduction. In addition, the concurrent optimization scheme has enabled the microstructures to attain a good spatial layout of materials while taking into account the weight reduction constraint. The spatial arrangements of the designed microstructures have achieved conducting heat in a shorter path toward the heatsink zone of macrostructure design. This allows attaining good performance with high weight reduction. Furthermore, numerical examples of different mesh numbers were used to study mesh dependency of multiscale topology optimization. The scope of the study was broadened by the inclusion of 3D case studies. Implementing Isosurface technique to achieve high detail model was also used to attain high detailed concurrently optimized design with minimal mesh number to minimize the computational cost. The 3D optimized case was investigated experimentally.