HoneyTop90: A 90-line MATLAB code for topology optimization using honeycomb tessellation

TL;DR

HoneyTop90 presents a compact, efficient MATLAB code for topology optimization using honeycomb tessellation, inherently reducing checkerboard patterns and point connections, with detailed instructions and extensions for various design scenarios.

Contribution

The paper introduces a novel, minimal 90-line MATLAB code for topology optimization with hexagonal elements, simplifying mesh generation and analysis.

Findings

Efficient mesh generation for millions of hexagonal elements.

Inherent suppression of checkerboard patterns.

Flexible options for boundary conditions and filters.

Abstract

This paper provides a simple, compact and efficient 90-line pedagogical MATLAB code for topology optimization using hexagonal elements (honeycomb tessellation). Hexagonal elements provide nonsingular connectivity between two juxtaposed elements and, thus, subdue checkerboard patterns and point connections inherently from the optimized designs. A novel approach to generate honeycomb tessellation is proposed. The element connectivity matrix and corresponding nodal coordinates array are determined in 5 (7) and 4 (6) lines, respectively. Two additional lines for the meshgrid generation are required for an even number of elements in the vertical direction. The code takes a fraction of a second to generate meshgrid information for the millions of hexagonal elements. Wachspress shape functions are employed for the finite element analysis, and compliance minimization is performed using the optimality criteria method. The provided Matlab code and its extensions are explained in detail. Options to run the optimization with and without filtering techniques are provided. Steps to include different boundary conditions, multiple load cases, active and passive regions, and a Heaviside projection filter are also discussed. The code is provided in Appendix~A, and it can also be downloaded along with supplementary materials from \url{https://github.com/PrabhatIn/HoneyTop90}.