A fuzzy logic knowledge-based system for finite element mesh generation and analysis

Wa Kwok, Purdue University

Abstract

An adaptive finite element analysis methodology with fuzzy logic techniques is proposed to solve 2-D elasticity problems. This approach initiates the adaptive process with a high quality initial mesh that is more refined around the critical points/regions in the problem domain. The heuristic knowledge, experience and ad hoc methods of finite element specialists are incorporated into the knowledge base. Using the linguistic variable concept and approximate reasoning techniques, the fuzzy system makes expert decisions about the initial mesh design by considering the geometric information, as well as the boundary and loading conditions. The decision process includes the determination of criticality of critical points/regions and the prediction of mesh sizes for them. According to the mesh size information, a near-optimal initial mesh is created with an automatic mesh generator, that is based on a new modified and more efficient version of the advancing front mesh generation technique.^ Two new and efficient approaches have been developed to improve the mesh generation scheme. One is to optimize the front operations, while another is to use a mesh size function (linear, quadratic or exponential) to specify mesh sizes at various points in the domain. Several example problems were solved to evaluate the performance of the fuzzy system and the new mesh generation scheme. When the solution error exceeds a user-specified limit, the mesh is completely re-designed with the h-version refinement strategy. The proposed approach results in lower levels and more accurate estimates of errors. Consequently, using this starting mesh, the problem is solved with higher accuracy and in less time.^ Compared with p = 1, the p = 2 adaptive process has higher rates of convergence and needs less computational time to solve a given example problem. For a non-singular problem, both approaches predict about the same maximum stress. However, for a problem with strong singularities, the p = 2 process gives better estimates of the stress around the singularity points. In addition, use of a strongly graded initial mesh allows better error estimates, especially around the singularity points, resulting in higher solution accuracy and in less time. ^

Degree

Ph.D.

Advisors

Major Professor: Kamyar Haghighi, Purdue University.

Subject Area

Engineering, Agricultural|Engineering, Electronics and Electrical

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