An algorithm for generating solid elements in objects with holes

摘要

An algorithm for dividing an object with holes into solid elements for finite element preprocessing is presented. Since a tetrahedron can always be subdivided into prisms and cuboids, the approach of first dividing the given object into disjoint tetrahedra is taken.Objects without holes are dealt with first. Two mesh operators, each generating a single tetrahedron, are presented. In addition to the construction procedure, it is shown that they handle all objects without holes. The algorithm for objects with holes requires a third operator. In addition to showing the necessary and sufficient condition for applying such an operator, it is shown that it effectively reduces the number of holes in an object by one while yielding three tetrahedra. The algorithm which sequences the three operators thus reduces a given polyhedron to a single tetrahedron iteratively. Data structure requirements and update procedures are also given in this paper.