An 808 Line Phasor-Based Dehomogenisation Matlab Code For Multi-Scale Topology Optimisation

TL;DR

This paper introduces an 808-line Matlab code for multi-scale topology optimization and phasor-based dehomogenisation, enabling efficient high-resolution structural reconstruction with minimal performance loss and reduced computational effort.

Contribution

The work provides a compact, educational Matlab implementation for combined multi-scale topology optimization and dehomogenisation, demonstrating efficiency and accuracy improvements over traditional methods.

Findings

Efficient on-the-fly dehomogenisation to single-scale structures.

Minor structural performance loss compared to multi-scale solutions.

Reduced computational cost in topology optimization.

Abstract

This work presents an 808-line Matlab educational code for combined multi-scale topology optimisation and phasor-based dehomogenisation titled deHomTop808. The multi-scale formulation utilises homogenisation of optimal microstructures to facilitate efficient coarse-scale optimisation. Dehomogenisation allows for a high-resolution single-scale reconstruction of the optimised multi-scale structure, achieving minor losses in structural performance, at a fraction of the computational cost, compared to its large-scale topology optimisation counterpart. The presented code utilises stiffness optimal Rank-2 microstructures to minimise the compliance of a single-load case problem, subject to a volume fraction constraint. By exploiting the inherent efficiency benefits of the phasor-based dehomogenisation procedure, on-the-fly dehomogenisation to a single-scale structure is obtained. The presented code includes procedures for structural verification of the final dehomogenised structure by comparison to the multi-scale solution. The code is introduced in terms of the underlying theory and its major components, including examples and potential extensions, and can be downloaded from https://github.com/peterdorffler/deHomTop808.git.