Journal
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
Volume 45, Issue 3, Pages 309-328Publisher
SPRINGER
DOI: 10.1007/s00158-011-0706-z
Keywords
Topology optimization; Polygonal elements; Centroidal Voronoi tessellations; Implicit geometries
Categories
Funding
- Department of Energy, Office of Science
- National Nuclear Security Administration in the Department of Energy [DE-FG02-97ER25308]
- Tecgraf (Group of Technology in Computer Graphics), PUC-Rio, Rio de Janeiro, Brazil
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We present a simple and robust Matlab code for polygonalmesh generation that relies on an implicit description of the domain geometry. The mesh generator can provide, among other things, the input needed for finite element and optimization codes that use linear convex polygons. In topology optimization, polygonal discretizations have been shown not to be susceptible to numerical instabilities such as checkerboard patterns in contrast to lower order triangular and quadrilaterial meshes. Also, the use of polygonal elements makes possible meshing of complicated geometries with a self-contained Matlab code. The main ingredients of the present mesh generator are the implicit description of the domain and the centroidal Voronoi diagrams used for its discretization. The signed distance function provides all the essential information about the domain geometry and offers great flexibility to construct a large class of domains via algebraic expressions. Examples are provided to illustrate the capabilities of the code, which is compact and has fewer than 135 lines.
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