無元素法在平板問題之應用

研 究 生：高嘉坤
指導教授：潘誠平
時 間：94年6月

論 文 摘 要
本文主要將Mindlin Theory應用在無元素法去分析梁、板問題，且在分析懸臂梁及簡支梁之位移及應力後，可以得到良好之近似解，由此可驗證Mindlin Theory應用在無元素法之可行性及驗證程式之正確性。
之後再去分析四邊為簡支承平板問題，求解不同板厚狀況下之位移近似解，並加以分析，且由分析的結果得知，因為板之行為較複雜，所以需要比懸臂梁及簡支梁較多之節點數量，才可以得到良好之近似解。

The element-free Galerkin’s method is used to analyze a thick plate
problem based on Mindlin theory. After the successes of element free
Galerkin’s method applied in beam, plane stress, and solid problems.
This study proves that this method can solve plate problems well also.
The formulations of element free Galerkin’s method and Mindlin plate
theory are discussed in this thesis. A C++ program based on those
formulations was developed in this study. Verification problems were
shown to prove its accuracy. Comparisons between the element-free
Galerkin’s method and finite element method were given also. Some
parametric study for coefficients in weighting function was performed.
Generally speaking, the element-free Galerkin’s method can solve thick
plate problem very well.

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