# GRAND — Ground structure based topology optimization for arbitrary 2D domains using MATLAB

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## Abstract

The present work describes in detail an implementation of the ground structure method for non–orthogonal unstructured and concave domains written in MATLAB, called GRAND — *GRound structure ANalysis and Design*. The actual computational implementation is provided, and example problems are given for educational and testing purposes. The problem of ground structure generation is translated into a linear algebra approach, *which is inspired by the video–game literature*. To prevent the ground structure generation algorithm from creating members within geometric entities that no member should intersect (e.g. holes, passive regions), the concept of “restriction zones” is employed, *which is based on collision detection algorithms used in computational geometry and video–games*. The aim of the work is to provide an easy–to–use implementation for the optimization of least–weight trusses embedded in any domain geometry.

### Keywords

Ground structure method Topology optimization of trusses Optimal structures Unstructured meshes Linear programming## Notes

### Acknowledgments

The authors appreciate constructive comments and insightful suggestions from the anonymous reviewers. We are thankful to the support from the US National Science Foundation under grant CMMI #1335160. We also acknowledge the support from SOM (Skidmore, Owings and Merrill LLP) and from the Donald B. and Elizabeth M. Willett endowment at the University of Illinois at Urbana–Champaign. Any opinion, finding, conclusions or recommendations expressed here are those of the authors and do not necessarily reflect the views of the sponsors.

## Supplementary material

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