VOLUME COORDINATE METHOD FOR HEXAHEDRAL ELEMENTS

Based on the successful applications of the area coordinate method for quadrilateral elements in 2D problems, a new volume coordinate method is proposed for hexahedral elements in 3D problems, including: 1) the definition of characteristic parameters of a convex hexahedron, and related characteristic conditions under which a hexahedron degenerates into other special solids; 2) the definition of the volume coordinates for hexahedral elements; 3) the transformations between the volume coordinates and the Cartesian and isoparametric coordinates; 4) differential formulas for hexahedral volume coordinates. It can be readily observed that besides keeping the advantages of local natural coordinate system, the new coordinate system has the linearity with the global coordinate system. The volume coordinate method provides a new tool for developing high performance hexahedral elements which are insensitive to mesh distortion.