Embedding of polytopes for topology optimization

  • Regis Thedin
  • Ivan F. M. MenezesEmail author
  • Anderson Pereira
  • Marcio S. Carvalho
Technical Paper


A methodology for solving three-dimensional topology optimization problems through a two-level mesh representation approach is described and evaluated. Structural topology optimization problems are executed on a polytope-based mesh, which carries the design variable (and subsequently the density). Displacement field is determined using tetrahedron elements, embedded within the polytopes. The proposed mapping-based framework decouples the analysis routine and optimization algorithm from the specific choice of topology optimization formulation. The mapping-based formulation allows easy applicability of features such as regularization and density filters and symmetry through a mapping matrix. The embedding approach is demonstrated on minimum compliance problems and solid–void solution is obtained by employing continuation on the solid isotropic material with penalization penalty parameter. We show that the proposed approach is able to achieve solutions free of numerical anomalies (e.g., checkerboard pattern and one-node connections) without the application of any explicit regularization scheme nor filtering. Our solutions approach the theoretical solution as mesh size increases.


Topology optimization Polyhedral design variable meshes Tetrahedral finite element meshes Embedding technique Compliance minimization 



Regis Thedin acknowledges financial support provided by CNPq. Ivan Menezes and Anderson Pereira acknowledge the support provided by Tecgraf/PUC-Rio (Group of Technology in Computer Graphics).


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  • Regis Thedin
    • 1
    • 2
  • Ivan F. M. Menezes
    • 1
    Email author
  • Anderson Pereira
    • 1
  • Marcio S. Carvalho
    • 1
  1. 1.Pontifical Catholic University of Rio de JaneiroRio de JaneiroBrazil
  2. 2.The Pennsylvania State UniversityUniversity ParkUSA

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