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Generalized Method of Decomposing Solid Geometry into Hexahedron Finite Elements

Holmes, David I.

Proceedings, 4th International Meshing Roundtable, Sandia National Laboratories, pp.141-152, October 1995



ACRONEM is an automatic finite element mesh generator that works on a general assortment of geometries. This software produces meshes with the optimum least-number of highly orthogonal hexahedron elements. The algorithm is based on a decomposition approach, where geometry is processed from a standard format of outer shell surface facets. Beginning with these facets, the element grids are generated with nodes that are coincident to external surfaces. This patented approach demonstrates that transforming the meshing operation from the Cartesian domain of space into a system of generic decompositions based on external surface connectivity can be very practical.

Decomposing geometry in terms of a function of external features is novel in that it utilizes the relationship of the solid geometry outer surface connectivity with respect to the number of edges on a solid independant of an assessment of the solid's interior. This is desirable because it does not require knowledge of the internal structure of the object. Instead decomposition requires only the identification of local exterior shapes on an outer "known" geometry. The fact that solids are limited to the physical constraints of three-dimensional space implies that any 2 1/2 dimensional component, ie. an extrusion, is part of a factorial of three-dimensional space. One interpretation of a concatenated 2 1/2 dimensional space utilized in this process is the definition of complex solids in terms of less complex sub-volumes. These are held in a rectangular three-dimensional array data structure. This is of particular commercial value since the capacity for breaking down complex solids into easily meshed shapes has been demonstrated to be a function of extracting complex subregions representing extreme geometric distortions from the exterior of an object. The majority of the remaining solid is easily meshed with the smooth transition boundary of the sub-volume. Tests confirm compatibility with both commercially viable geometry representations and basic principles of data management, wholly contingent with the final production of map meshable sub-volume extrusions.

Reducing external complex shape characteristics to a level compatible with generic geometry is interfaced with various shape recognition conditions for identifying local configurations such as: reentrant edges, multiple surface solid geometry in compacted transition regions, and various hybrid solids, such as the filletted trailing edge of a turbine blade. Due to the linearity of smooth low-order edge cross sections of medial surface boundaries, commercial feasibility of programming this algorithm is enhanced. Processing a variety of geometries with varying characteristics is dependant on the creation of peripheral shape recognition steps for reducing the complexity of external surface connectivity.

Two distinct outcomes resulting from a thorough investigation of mesh generation with ACRONEM, are that it is feasible to generate mesh geometry comrised solely of finite elements bounded by quadrilateral faces and that medial surfaces placed in a limited distortion field augment all possible mesh map node points forming a system of highly orthogonal elements in terms of local gauss-point sub-spaces. This is especially intriguing because ACRONEM does not employ post-meshing optimization algorithms.

Testing has shown that existing analysis packages can support mesh geometries of even the most distorted elements that collectively simulate orthogonal space. Maintaining the orthonormal quality of geometry is done through the angular distortion of individual sub-solids through the whole decomposition process. Rather than attempting to decompose geometry with one universal approach, the process is a series of steps compatible with the Jacobian transform of finite element geometry.

ACRONEM software exists in a rudimenray component state that is easily reorganized by coupling functional procedures with conditional applications using vectors in Cartesian space to assess the quality of geometry. In fact ACRONEM decomposes a large variety of solid geometries even in the existing rigid serial state. Multiply connected regions, highly complex super volumes, and variations on reentrant edges are a few of the commercially feasible cases to which the software modules are easily adapted. The software produces smooth highly orthogonal meshes using a core process that shows great potential to advance the level of mesh generation technology. Minimal memory usage, speed, robust performance, and ease of use, make ACRONEM an outstanding example of one direction automatic mesh generation is taking. ACRONEM is a truly automatic mesh generator that produces the least number of optimum hexahedron elements for all solid geometry.

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