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Polygonal finite elements for topology optimization: A unifying paradigm
Author(s) -
Talischi Cameron,
Paulino Glaucio H.,
Pereira Anderson,
Menezes Ivan F. M.
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2763
Subject(s) - discretization , polygon mesh , voronoi diagram , topology optimization , topology (electrical circuits) , isotropy , mathematics , centroidal voronoi tessellation , finite element method , mathematical optimization , computer science , geometry , mathematical analysis , combinatorics , engineering , structural engineering , physics , quantum mechanics
In topology optimization literature, the parameterization of design is commonly carried out on uniform grids consisting of Lagrangian‐type finite elements (e.g. linear quads). These formulations, however, suffer from numerical anomalies such as checkerboard patterns and one‐node connections, which has prompted extensive research on these topics. A problem less often noted is that the constrained geometry of these discretizations can cause bias in the orientation of members, leading to mesh‐dependent sub‐optimal designs. Thus, to address the geometric features of the spatial discretization, we examine the use of unstructured meshes in reducing the influence of mesh geometry on topology optimization solutions. More specifically, we consider polygonal meshes constructed from Voronoi tessellations, which in addition to possessing higher degree of geometric isotropy, allow for greater flexibility in discretizing complex domains without suffering from numerical instabilities. Copyright © 2009 John Wiley & Sons, Ltd.