Topology optimization guided by a geometrical pattern library

Tanguy Navez*, Martin-Pierre Schmidt, Ole Sigmund, Claus B. W. Pedersen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


This work proposes an approach for structural Topology Optimization enforcing geometrical features on optimized designs using a predefined library of geometrical patterns. The approach applies a density-based Topology Optimization subject to a geometrical constraint guiding the design toward shapes matching the geometrical features found in the predefined pattern library. Multiple distance measures and suitable matching algorithms are studied to calculate local mappings between the design in each optimization iteration and the pattern library. An aggregated appearance constraint is evaluating the pattern matching. The gradient of the appearance constraint, objective function, and other constraints are applied in a gradient-based optimization scheme. A parameter for the appearance constraint dictates how closely the design should match the patterns defined in the library. The convergence behavior is studied on a variety of 2D and 3D optimization scenarios. The formulation is also applied to design variables controlling the material orientations alongside the material density as well as other optimization objectives such as stress minimization.
Original languageEnglish
Article number108
JournalStructural and Multidisciplinary Optimization
Issue number4
Number of pages15
Publication statusPublished - 2022


  • Topology optimization
  • Geometrical pattern library
  • Appearance constraint
  • Fast-matching algorithm


Dive into the research topics of 'Topology optimization guided by a geometrical pattern library'. Together they form a unique fingerprint.

Cite this