Phasor Noise for Dehomogenisation in 2D Multiscale Topology Optimisation

TL;DR

This paper introduces a novel phasor noise-based dehomogenisation method for 2D multiscale topology optimization, producing high-quality, mesh-independent designs efficiently without complex optimization steps.

Contribution

It proposes a new phasor noise approach that improves dehomogenisation in topology optimization, avoiding least-squares problems and enabling efficient, parallelisable computations.

Findings

Achieves near-optimal structural performance within a few percent of the homogenized solution.

Mesh-independence and high parallelisability of the method.

Effective extension potential to 3D unstructured meshes.

Abstract

This paper presents an alternative approach to dehomogenisation of elastic Rank-N laminate structures based on the computer graphics discipline of phasor noise. The proposed methodology offers an improvement of existing methods, where high-quality single-scale designs can be obtained efficiently without the utilisation of any least-squares problem or pre-trained models. By utilising a continuous and periodic representation of the translation at each intermediate step, appropriate length-scale and thicknesses can be obtained. Numerical tests verifies the performance of the proposed methodology compared to state-of-the-art alternatives, and the dehomogenised designs achieve structural performance within a few percentages of the optimised homogenised solution. The nature of the phasor-based dehomogenisation is inherently mesh-independent and highly parallelisable, allowing for further efficient implementations and future extensions to 3D problems on unstructured meshes.