QMESH RENUM QPLOT, Mesh Generator on 2-D Bodies for Finite Element Method Analysis, with Plot Utility

1 - Description of problem or function: A set of five programs which make up a self-organising mesh generation package. QMESH generates meshes having quadrilateral elements on arbitrarily-shaped, two-dimensional (planar or axisymmetric) bodies. It is designed for use with two-dimensional finite element analysis applications. A flexible hierarchical input scheme is used to describe bodies to QMESH as collections of regions. A mesh for each region is developed independently, with the final assembly and bandwidth minimization performed by the independent program, RENUM or RENUM8. RENUM is applied when four-node elements are desired. Eight-node elements (with mid-side nodes) may be obtained with RENUM8., QPLOT and QPLOT8 are plot programs for meshes generated by the QMESH/RENUM and QMESH/RENUM8 program pairs, respectively. QPLOT and QPLOT8 automatically section the mesh into appropriately-sized sections for legible display of node and element numbers. An overall plot showing the position of the selected plot areas is produced. 2 - Method of solution: The mesh generating process for each individual region begins with the installation of an initial mesh which is a transformation of a regular grid on the unit square. The dimensions and orientation of the initial mesh may be defined by the user or, optionally, may be chosen by QMESH. Various smoothing algorithms may be applied to the initial mesh. Then, the mesh may be 'restructured' using an iterative scheme involving 'element pair restructuring', 'acute element deletion', and smoothing. In element pair restructuring, the interface side between two elements is removed and placed between two different nodes belonging to the pair of elements, provided that the change produces an overall improvement in the shapes of the two elements. In acute element deletion, an element having one diagonal much shorter than the other is deleted by collapsing the short diagonal to zero length The exact order in which restructuring, element deletion, and smoothing are performed may be controlled by use of 'scheme' input information. The scheme input provision also allows the user to control plotting and printing. The resulting mesh descriptions for individual regions are melded into an integrated mesh by the companion program, RENUM, which also performs bandwidth minimization using a modified Cuthill-McKee algorithm. RENUM8 performs essentially the same process as RENUM, then interpolates (linearly or by circular fit) to find mid-side node positions. It then re-labels the entire mesh to maintain near-minimal bandwidth. QPLOT and QPLOT8 automatically plot meshes processed by RENUM and RENUM8, respectively. Appropriate sections of the mesh for plotting are selected by an iterative techniques which determines the size and position of each section, so as to include the smallest as yet unlabelled element in each successive section. 3 - Restrictions on the complexity of the problem: QMESH - Maxima of: 1,000 nodes, 400 lines, 100 sides, 70 regions; RENUM- Maxima of: 15,000 nodes (Cray1, IBM3033), 10,000 elements (Cray1, IBM3033); QPLOT - Maxima of: 5,000 nodes, 4,800 elements; RENUM8 - Maxima of: 10,000 output nodes (Cray1, IBM3033), 5,000 input nodes, 4,800 elements; Non-straight lines should have at least two intervals, as mid-side node placement is always done linearly for lines with only one interval. Corner lines should not be used, as circular interpolation on region boundaries could produce unreasonable results near the actual corner. QPLOT8 - Maxima of: 20,000 nodes (Cray1), 10,000 elements (Cray1), 5,000 nodes (IBM3033), 4,800 elements (IBM3033)