Such small angles may be unnacceptable for some analysis packages,and situations,unless,perhaps such a pyramid template can be kept away from crucial areas of an overall mesh,and,somehow,used sparingly. The hexahedra are not degenerated,but the internal angles,between faces and/or edges,for some of the elements,go down to as little as around 10 to 15 degrees. Now to Robert Schneider's problem.This is probably the tougher problem,but I have a solution.It involves 298 Hexes in my original pattern,and 470 Hexes in a later pattern that has better shapes. I do have an alternative to the Geode pattern for use in Selina's problem,but my Geode alternative is radically different and involves many more hexahedra - around 300 more at least - although it may have better shaped hexahedra. In fact,I have only imagined this pattern so far, and not had time to check it out in detail.The last 'squeezing stage' looks a bit dangerous as regards the effects on the Geode part of the pattern,but I think it looks as if the hexes in the geode pattern should still be okay,depending on how steeply the pyramid sides slope.We can also squeeze the geode part down towards the bottom of the pyramid in order to make its hex shapes better. Now we carefully squeeze the whole pattern from, essentially,a pyramid on top of 2 cubes,in to just one Egyptian pyramid,taking care to move the internal nodes accordingly to preserve the best shapes. Time constrains me from describing this bottom 9 hexahedra transition pattern in detail,which I have definitely found,but it should not be too difficult for someone with a reasonable amount of experience with hexahedral patterns to derive for his/her self. Now we imagine a cube placed at the bottom of the Geode Template,and split this cube in to 9 hexahedra,in such a way that it provides a transition from the 4 quadrilateral faces at the bottom of the Geode template,to the single quadrilateral face required at the bottom of the Egyptian pyramid by Selina. Then split these upper 2 tetrahedra into 4 hexes each.This upper construction of 8 hexahedra is shown,in fact,in Joern Beilke's earlier communications to the CFD forum. Now place a pyramid on top of the Geode template, then split it in to 2 tetrahedra,to match with the the base quadrilateral face split along a diagonal to match the top diagonal of the Geode Template. Scott Mitchell/Sandia have PATENTED the GEODE Template,at least in the US,although it is probably not patented,nor,possibly,patentable in the UK or various other countries. You can get a copy of Scott Michell's paper on his Geode template from his Sandia labs based web-site,probably at. Here is the solution,at least for the really difficult bits,for Selina's Egyptian Pyramid Problem,with ONE quadrilateral at the base.įirst use Scott Mitchell's excellent 'Geode' template. The element shapes for the solution of Selina's problem,are,in fact,relatively good.īoth these Egyptian pyramid problems are very tough indeed.įor Selina's problem,with ONE quadrilateral face at the base,as in her 23rd March 2001 amendment to the problem,the solution involves 43 hexahedra. I have solutions for All-hex meshes of both of your Egyptian Pyramid Patterns,WITHOUT degenerated elements, AND with interior angles between faces which are less than 180 degrees, AND with interior angles between edges which are less than 180 degrees. SUBJECT: SOLUTIONS for ALL-HEX MESHES of BOTH of yourĮGYPTIAN PYRAMID Patterns, WITHOUT DEGENERATED
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |