Kubik: An automatic three‐dimensional finite element mesh generator

Abstract

Abstract This paper describes an automatic mesh generator for finite element problems in three dimensions, called KUBIK, KUBIK is based on a modular concept. First, a set of modules is generated, each with its own mesh inside. Then, the modules are placed in contact, and a matrix describing the connectivity of the entire mesh is determined. Finally, the geometry of the mesh is specified and all nodal co‐ordinates are determined by the computer. The user's labour required to specify a mesh which represents a certain physical configuration resumbles the labour involved when the configuration has to be specified to the machine shop workers who are supposed to build it. The modules are independent, except for the compatibility requirements between modules which are to be placed in contact. Structures of any degree of complexity can in principle be obtained using KUBIK. Only two types of modules are required, except when helicoidal structures are to be generated, in which case it is convenient to use a third type. The finite elements used are distorted cubes, but they can be divided into tetrahedra, prisms of pyramids. Nodes are placed at the corners of the cubes, and additional nodes can be introduced if desired in order to obtain other types of finite elements in use. Infinite elements of quadrilateral cross‐section are also a standard feature of KUBIK, and can be divided in order to obtain infinite prisms of triangular cross‐section. KUBIK can also generate two‐dimensional meshes, including meshing of a three‐dimensional surface for use with boundary elements.