| Summary: | 博士 === 國立中正大學 === 機械系 === 92 === As a result of computer advancement in the last three decades, the finite element method (FEM) is now widely used in solving many engineering problems. However, the direct application of the FEM to the modeling of problems involving geometric singularities, infinite medium, etc., has limitations. Finer meshes and round-off errors are inevitable, making the FEM prohibitively expensive in terms of computational effort. In this thesis, the mathematical foundation for a two- and three-dimensional thermo-elastic infinite element method (IEM) is proposed as a viable alternative. The IEM is based on the conventional FEM and uses the similarity characteristic of element stiffness and the matrix condensing procedures. A series of layer-wise elements with similar shape are virtually generated within the problem domain. The resultant numerous degrees of freedom (DOFs) are condensed and transformed to those on the boundary master nodes only by means of derived recurrence formulas. A generalized superelement in which the dimension is reduced by one is formed; we designate it as the infinite element (IE). The convergence analysis of the combined element stiffness for the IE is proposed. A program framework taking advantage of matrix manipulation was constructed using the MATLAB language. The IE-FE coupling scheme was addressed and its implementation was accomplished by employing the commercial software ABAQUS to enhance the convenience and capability of the IEM. With the proposed approach, the execution time in the modeling stage, the number of DOFs, and PC memory storage were significantly reduced. Consistent formulation was used so that no prior governing assumptions and no special treatments were required to be incorporated. Three types of the elasto-static problems concerned with the geometric singularity, unbounded domain, and heterogeneous composite materials were investigated. The proposed approach provides another simple, efficient, and accurate numerical analysis tool for elasto-static problems, as demonstrated in the numerical examples presented in this dissertation.
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