目前邊界元素法能利用直接轉換體積分來處理三維異向性含等效應力之靜彈問題，不過若要分析薄層幾何體，基本解會遇到奇異性問題造成誤差過大結果不夠準確。為了降低誤差，可先將基本解的被積元素轉換為高斯積分，再增加積分的高斯積分點。透過模擬的數值結果可得知幾何體越薄需要越多的高斯點，而增加積分的高斯點會大量增加程式計算時間，所以本論文也將格林函數的傅立葉級數進行公式簡化，利用格林函數的係數奇偶性與共軛複數的性質，將傅立葉級數的計算範圍縮小，避免重複計算，提高公式計算效率，從而減少計算時間。而將優化後的公式改寫入程式，與有限元素法ANSYS比對數個範例後，確實比起先前的結果誤差更小，答案較為精確。而為了降低在分析上的操作複雜性，利用軟體程式語法設計出一個視窗頁面，輸入所需的參數後便可由執行檔進行分析，在操作分析頁面上更為清楚且簡單。

As present, the boundary element method can analize three-dimensional anisotropic elastostatics with equivalent body force by direct transformation of the volume integral. However, when analizing a thin layer geometry model, the basic solution will encounter singularity problem. It will casue the excessive error and imprecise result. In order to reduce the error, the element of basic solution can convert into Gauss integration first, then increasing the Gauss points.Through the numerical results of the simulation, it can be known that the thinner the geometry model, the more Gauss points will be needed. Because increase the Gauss points will greatly raise the calculate time, therefore the thisis also simplified the Fourier series of Green’s function. By using the properties of odd number with even nember and the properties of conjugate complex numbers, it can reduce the calculation range of the Fourier series, aviod repeated calculation, improve formula calculation efficency, and decrease the computing time.After the optimized formula results were changed into programs, and compared with several examples of the finite element method ANSYS, the error was indeed smaller than the previous results.In other words, the answers got more accurate.At last for reducing the complexity of analysis operation, a visual page was designed by a software program.After entering some required parameters, the file can analize the model.It is clearer and more simplified for opertion anlysis pages.

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