Macroelement and Macropatch Approaches to Structural Topology Optimization Using the Ground Structure Method

Xiaojia Zhang, Sushant Maheshwari, Adeildo S. Ramos, Glaucio H. Paulino

Research output: Contribution to journalArticlepeer-review


Topology optimization can be divided into continuum and discrete types, the latter being the emphasis of the present work. In the field of discrete structural topology optimization of trusses, the generation of an initial ground structure is crucial. Thus, this paper examines the generation of ground structures for generic structural domains in two and three dimensions. It compares two methods of discretization, Voronoi-based and structured quadrilateral discretizations, and proposes two simple and effective ground structure generation approaches: the macroelement and macropatch approaches. Both can be implemented with either type of discretization. This work presents several features of these approaches, including the efficient generation of initial ground structures, a reduction in matrix bandwidth for the global stiffness matrix, finer control of bar connectivity, and a reduction in the number of overlapped bars. Generic examples and practical structural engineering designs are presented. They display the features of the proposed approaches and highlight the comparison with results from either the literature, the traditional ground structure generation, or the continuum optimization method.

Original languageEnglish (US)
Article number04016090
JournalJournal of Structural Engineering (United States)
Issue number11
StatePublished - Nov 1 2016
Externally publishedYes


  • Ground structure method
  • Macroelement approach
  • Macropatch approach
  • Structural optimization
  • Truss layout optimization
  • Voronoi-based mesh

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering


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