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This dissertation, Adaptive Finite Element Analysis for 2D Elastostatic Problems by 李子敬, Chi-king, Lee, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of Thesis Entitled: Adaptive Finite Element Analysis For 2D Elastostatic Problems submitted by LEE CHI KING for the degree of Master of Philosophy at The University of Hong Kong in October of 1992 iii Abstract The objective of an adaptive finite element procedure is to model a physical problem by the finite element method and to achieve a solution of specified accuracy in a most economic manner. A robust and fully automatic adaptive finite element procedure is a very powerful and useful tool to practical engineers. Through the adaptive process the user can, simultaneously, obtain an accurate solution of the physical problem and also a reliable estimate of the error of the finite element solution. This allows engineers and designers to have a better understanding of the behavior of the physical structure, and to optimize their designs and obtain more economical and safer designs. In this thesis, attentions will be paid to the adaptive refinement process for solving 2D elastostatic problems, in which three essential steps can be identified. These steps are development of, (i) an economical and reliable error estimation procedure which predicts the numerical error of the finite element method, (ii) an effective methodology for predicting and defining the necessary refinements needed to achieve the prescribed accuracy in an optimal manner, and (iii) a practical algorithm for the construction of the refined finite element model with specified mesh density and grading by means of an automatic mesh generation scheme. A new adaptive refinement procedure which integrates the latest advanced techniques developed in the above three aspects will also be proposed. This new refinement procedure will employ the Zienkiewicz and Zhu error estimator for predicting the error of the finite element solution. A new algorithm, based on the strain energy density concentration concept for automatically locating any singular points in the problem domain, is developed for defining the optimal mesh pattern for the refinement process. Three new automatic mesh generators which are capable of generating either pure triangular, mixed or pure quadrilateral meshes are developed iv for generating high quality, well-graded finite element meshes with node spacing closely compatible with the required pattern for optimal convergence of the solution. The performance and robustness of the proposed adaptive refinement scheme are tested by applying it to solve practical engineering problems with different geometrical complexity and difficulty. Finally, potential and possible areas for further extension of the current research work in different aspects of finite element applications will be suggested. DOI: 10.5353/th_b3101931 Subjects: Finite element methodElasticity - Mathematical models

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