Manufacturing and stiffness constraints for topology optimized periodic structures

Kenneth E. Swartz, Daniel A. Tortorelli, Daniel A. White, Kai A. James

Research output: Contribution to journalArticlepeer-review


Topology optimization (TO) is commonly applied to design the unit cells of periodic structures. For example, metamaterials, lattice structures, phononic crystals (PhC), and photonic crystals (PC) have all been previously designed via TO. Unfortunately, the optimal structures for certain design objectives, e.g., bandgaps, are often impossible to manufacture as they have disconnected regions or “islands” of solid material (ISM) that are not self-supporting. Further, designs with enclosed void space (EVS) are problematic for additive manufacturing (AM) since support material or pre-sintered powder cannot be removed after manufacturing. We present a series of constraints that may be incorporated into any TO framework to ensure structures are self-supporting without enclosed voids. Additionally, we employ homogenization-based constraints that allow the designer to tune the elastic stiffness and isotropy of the optimized design. The proposed constraints are evaluated on example microstructures and utilized in a simple optimization test problem to highlight their abilities and limitations so that guidelines for appropriate combinations of constraints may be proposed. Effective constraint combinations are demonstrated on the design of 3D photonic crystals for maximum bandgap subject to manufacturing and stiffness constraints.

Original languageEnglish (US)
Article number129
JournalStructural and Multidisciplinary Optimization
Issue number4
StatePublished - Apr 2022


  • Homogenization
  • Manufacturing constraints
  • Metamaterials
  • Periodic structures
  • Photonic crystals
  • Topology optimization

ASJC Scopus subject areas

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


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