Pyramid elements for maintaining tetrahedra to hexahedra conformability
Steven James Owen, Scott A. Canann, Sunil S. Saigal · American Society of Mechanical Engineers, Applied Mechanics Division, AMD · 1997
A method is proposed whereby an existing non-conforming, mixed hexahedra-tetrahedra element mesh, is altered to conform by the insertion and formation of five-node or thirteen-node pyramids. Local tetrahedral transformations are performed to provide the topology enabling the merging of two adjacent tetrahedra into one pyramid. Local smoothing and cleanup operations improve the quality of the transition region. Other methods for the creation of transition pyramid elements are also discussed. Results show superior performance of the resulting elements in a commercial finite element code over non-conforming interface conditions. INTRODUCTION While many automated tetrahedra methods have now become commonplace in the industry, all-hexahedra free meshing methods have proven to be challenging research topics (Blacker, 1993; Price, 1995; Schneiders, 1996; Tautges, 1996). Some engineering disciplines have shown a preference for hexahedral elements over tetrahedra (Cifuentes, 1992; Benzley, 1995). While all-hexahedral element meshes may be preferred, some tetrahedra elements may be acceptable within the same model. For example, blocky or easily mapped regions of the solid may be first filled with hexahedra. Regions that may be more critical to the analysis, such as boundary layers or regions of high stress may also be better served by hexahedra. Tetrahedra elements may fill the remaining, more geometrically complex, or less critical regions of the solid. Since, geometrically, two tetrahedra faces are required to interface with a single hexahedron, discontinuities will arise at the boundary between the two element types. Traditional uses of the finite element method require that elements conform. In two-dimensions, this principle implies that no single element edge will have more than two elements adjacent. In three-dimensions, no single face will have more than two adjacent elements. Edge a-b and Face c-d-e-f in Figure 1 have more than the maximum two adjacent elements, thus rendering the mesh mathematically deficient for finite element analysis. This paper presents several solutions to the problem of non-conforming meshes that contain tetrahedra and hexahedra elements.