Topology optimization with manufacturing constraints: A unified projection-based approach

Sandro L. Vatanabe, Tiago N. Lippi, Cícero Lima, Glaucio H. Paulino, Emílio C.N. Silva

Research output: Contribution to journalArticlepeer-review

129 Scopus citations


Despite being an effective and a general method to obtain optimal solutions, topology optimization generates solutions with complex geometries, which are neither cost-effective nor practical from a manufacturing (industrial) perspective. Manufacturing constraint techniques based on a unified projection-based approach are presented herein to properly restrict the range of solutions to the optimization problem. The traditional stiffness maximization problem is considered in conjunction with a novel projection scheme for implementing constraints. Essentially, the present technique considers a domain of design variables projected in a pseudo-density domain to find the solution. The relation between both domains is defined by the projection function and variable mappings according to each constraint of interest. The following constraints have been implemented: minimum member size, minimum hole size, symmetry, pattern repetition, extrusion, turning, casting, forging and rolling. These constraints illustrate the ability of the projection scheme to efficiently control the optimization solution (i.e. without adding a large computational cost). Illustrative examples are provided in order to explore the manufacturing constraints in conjunction with the unified projection-based approach.

Original languageEnglish (US)
Pages (from-to)97-112
Number of pages16
JournalAdvances in Engineering Software
StatePublished - Oct 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • General Engineering


  • Manufacturing constraints
  • Minimum hole size
  • Minimum member size
  • Projection scheme
  • Topology optimization


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