A knowledge -based approach to automatic finite element mesh generation
This thesis describes the development of a new approach to finite element mesh generation for two-dimensional linear elasticity problems. Unlike other approaches, the proposed technique incorporates the information about the object geometry as well as the boundary and loading conditions to generate an a-priori finite element mesh which is more refined around the critical regions of the problem domain. A blackboard architecture expert system was developed to intelligently identify critical regions and to choose the proper mesh size for them by performing an approximate stress calculations. This involves the decomposition of the original structure into substructures for which an initial and approximate analysis can be performed using analytical solutions and heuristics.^ From the results of the expert system, nodes are generated in the problem domain using the new concept of wave propagation. The wave propagation technique is fully automatic and does not require user-provided information except the data that defines the object geometry and boundary conditions. After nodes are generated, well-shaped triangular elements are formed ensuring the Delaunay property. During the triangulation process and to reduce the computation time for checking the overlapping problem, a new and efficient algorithm was proposed which restricts the search domain for which the overlapping check with the previously generated elements and boundary segments is required. The algorithms for node and element generation were successfully tested for several examples, resulting in reduced computation time for generating well-shaped triangular elements.^ When incorporated into and compared with the traditional approach to the adaptive finite element analysis, the proposed approach, which starts the process with near optimal initial meshes, results in lower levels of error and faster convergence of the solution to the desired accuracy in less time and at less cost. For all the test problems, the mesh quality, element error distributions, and the computational efficiency of the proposed approach were superior to those of the conventional approach. ^
Major Professor: Kamyar Haghighi, Purdue University.