Topology optimization using wachspress-type interpolation with hexagonal elements

Cameron Talischi, Glaucio H. Paulino, Chau H. Le

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


Traditionally, standard Lagrangian-type finite elements, such as quads and triangles, have been the elements of choice in the field of topology optimization. However, finite element meshes with these elements exhibit the well-known "checkerboard" pathology in the solution of topology optimization problems. A feasible alternative to eliminate this long-standing problem consists of using hexagonal elements with Wachspress-type shape functions. The features of the hexagonal mesh include 2-node connections (i.e. 2 elements are either not connected or connected by 2 nodes), and 3 edge-based symmetry lines per element. In contrast, quads can display 1-node connection, which can lead to checkerboard; and only have 2 edge-based symmetry lines. We explore the Wachspress-type hexagonal elements and show their advantages in solving topology optimization problems. We also discuss extensions of the work to account for material gradient effects.

Original languageEnglish (US)
Title of host publicationMultiscale and Functionally Graded Materials - Proceedings of the International Conference, FGM IX
Number of pages6
StatePublished - 2008
Externally publishedYes
Event9th International Conference on Multiscale and Functionally Graded Materials, FGM IX - Oahu Island, HI, United States
Duration: Oct 15 2006Oct 18 2006

Publication series

NameAIP Conference Proceedings
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616


Conference9th International Conference on Multiscale and Functionally Graded Materials, FGM IX
Country/TerritoryUnited States
CityOahu Island, HI

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Checkerboard
  • Topology optimization
  • Wachspress interpolation functions


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