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I want to generate a 2D finite element mesh which consists of heptagons and other polygons except triangles, bounded by a rectangle. I am very new to coding I don't know how to start. Can anyone please help to devise an algorithm to produce the required mesh? It would be helpful to get sources to learn how this kind of mesh can be produced.

prem
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  • Do you want to partition a rectangle into heptagons? What are the requirements for the partitioning? Should it be as uniform as possible? How many heptagons are desired? What about the other polygons? Should they only appear here and there or can they be in the same quantity as heptagons (or more)? And finally, are you sure you want heptagons (a polygon with seven corners)? This does not sound like a nice domain for FE stuff. – Nico Schertler Oct 22 '18 at 16:19
  • I'm not aware of any system with heptagon elements. I've used NASTRAN, MARC, LS-Dyna, and ABAQUS; I've never seen 2D elements other than triangles and quads of varying order. What do the shape functions for a heptathon element look like? What is the local element definition? – duffymo Oct 22 '18 at 19:58
  • @Nico Schertker Yes i want to mesh a rectangle into heptagons. There is only one requirement that to have maximum number of heptagons which is possible geometrically. Graph theory shows you cannot make heptagons more than a limit, so rest of the polygons in the mesh will be of sides lower than 7. Polygons other than heptagons will mostly appear on boundary of rectangle and might be in voids between heptagons. By the way I am working on polygonal FE thats this kind of mesh is required. Can you please help me to solve this problem? – prem Oct 22 '18 at 20:23
  • @duffymo polygonal finite elements have not been used in commercial softwares you mentioned yet. You will find literature about polygonal FE which will include the definition and shape function information. – prem Oct 22 '18 at 20:26
  • @prem - thank you, I haven't done FEA for a living in 20 years. Google found several articles. Looks like it's an area of academic research: http://dilbert.engr.ucdavis.edu/~suku/polyfem/ – duffymo Oct 22 '18 at 20:31

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