An 808 line phasor-based dehomogenisation Matlab code for multi-scale topology optimisation An 808 Line Phasor-Based Dehomogenisation

• Published in: Structural and multidisciplinary optimization Vol. 67; no. 12
• Main Authors: Woldseth, Rebekka Varum, Sigmund, Ole, Jensen, Peter Dørffler Ladegaard
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024
• Subjects: Computational Mathematics and Numerical Analysis; Educational Paper; Engineering; Engineering Design; Theoretical and Applied Mechanics
• ISSN: 1615-147X; 1615-1488
• DOI: 10.1007/s00158-024-03880-1

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 Github .