GRAND3 — Ground structure based topology optimization for arbitrary 3D domains using MATLAB

Tomás Zegard, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review

98 Scopus citations


Since its introduction, the ground structure method has been used in the derivation of closed–form analytical solutions for optimal structures, as well as providing information on the optimal load–paths. Despite its long history, the method has seen little use in three–dimensional problems or in problems with non–orthogonal domains, mainly due to computational implementation difficulties. This work presents a methodology for ground structure based topology optimization in arbitrary three–dimensional (3D) domains. The proposed approach is able to address concave domains and with the possibility of holes. In addition, an easy–to–use implementation of the proposed algorithm for the optimization of least–weight trusses is described in detail. The method is verified against three–dimensional closed–form solutions available in the literature. By means of examples, various features of the 3D ground structure approach are assessed, including the ability of the method to provide solutions with different levels of detail. The source code for a MATLAB implementation of the method, named GRAND3 — GRound structure ANalysis and Design in 3D, is available in the (electronic) Supplementary Material accompanying this publication.

Original languageEnglish (US)
Pages (from-to)1161-1184
Number of pages24
JournalStructural and Multidisciplinary Optimization
Issue number6
StatePublished - Dec 1 2015
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Control and Optimization
  • Control and Systems Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


  • Ground structure method
  • Intersection tests
  • Three-dimensional optimal structures
  • Topology optimization of three–dimensional trusses
  • Unstructured meshes


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