Level set-based topology optimization of micropolar solids under thermo-mechanical loading

TL;DR

This paper introduces a level set-based topology optimization method for micropolar solids that incorporates microstructural size effects and thermo-mechanical loading, demonstrating improved accuracy for size-dependent materials.

Contribution

It develops a non-local topology optimization approach using micropolar theory and open-source Julia libraries, addressing size effects under thermo-mechanical conditions.

Findings

Microstructure and temperature significantly influence optimized topologies.

The method accurately captures size-dependent effects in solids.

Open-source implementation ensures reproducibility.

Abstract

We propose a novel level set-based topology optimization for micropolar solids subjected to thermo-mechanical loading. To capture the size effects, we have incorporated the microstructural length-scale information into the level set-based topology optimization method by adopting a micropolar theory. The proposed non-local topology optimization method can provide accurate topology optimization for size-dependent solids under thermo-mechanical loading. We have demonstrated the effectiveness of the proposed method through a few representative two-dimensional benchmark problems. The numerical results reveal the substantial influence of underlying micro-structures, incorporated in the model through micropolar parameters, and temperature on topology optimization, highlighting the necessity of the proposed thermo-mechanical micropolar formulation for materials with pronounced non-local effects. For the numerical implementation of the proposed model, we have used open-source finite element libraries, \texttt{Gridap.jl}, and \texttt{GridapTopOpt.jl}, available in Julia, to ensure transparency and reproducibility of the reported computational results.