Enhancing interactivity and automation through finite element neighbours

Abstract

AbstractIn finite element analysis, each element is defined by a set of node numbers and stored. In this paper, it is shown that by storing the three neighbouring triangles of each triangular element, In addition to the three vertices, the interactivity and automation of the design station may be greatly enhanced. This enhancement results from the use of the data on neighbours in: Identifying triangles pointed to on a graphics screen, through a digitizer. This is used for extracting potentials and field intensities at points, for refining meshes by adding points, and for imposing Neumann boundary conditions on the boundary edges and performing integrations, such as of force, over trianggles. Following a path defined as a straight line for extracting graphs of potential and field intensity and performing contour integrations, like Maxwell stress, along such lines. Checking the optimality of the mesh using the Delaunay criterion. Determining discontinuities of field intensity at material interfaces. Comparing the field intensities in adjacent triangles to measure error for adaptive refinement. Alternatively, in an environment where memory for storing the neighbours is scarce, such as when using microcomputers, it is shown that the values may be computed when they are required, at the expense of speed.