本論文主要探討的問題是對於二維全異向熱彈性體，處理全異向薄層複材之熱彈性體受熱效應力，而當在薄層幾何體上相對表面非常接近時，會發生源點逼近邊界元素的情形，也就是將產生眾所皆知的近似奇異積分問題(nearly singular integration)，造成無法正確計算數值積分，便無法分析薄層複材異相熱彈性體。對於熱彈性來說，由於熱效應的關係導致面積分存在於邊界積分方程式中，為了避免直接積分，面積分已經分析轉換為邊界積分，在論文中，近似奇異積分由分部積分的方法正規化，此外，在數值計算中出現了額外的困難就是與三角函數相關的被積函數，當近似奇異積分中的狀況下，被積函數在源點投影點附近產生劇烈的波動，所以會增加數值分析的難度，對於此問題由在投影點附近劃分子區域的方法來克服，並且需要增加高斯點的數量，最後再利用修改完成的BEM程式來分析幾種範例，比較邊界元素法與ANSYS也就是有限元素法的結果都完全一致。

The main study of the thesis is for applying the boundary element method (BEM) to study the two-dimensional anisotropic thermoelasticity of composites when layers of the structures are very thin. Under the circumference when the source point on one surface is very close to integration elements on the opposite surface of thin layers, the well known issue of “nearly singular integration” in the BEM will arise, causing instability in numerical integrations. As a result, the BEM will fail to properly analyze the thermoelaticity of thin anisotropic composites. For thermoelaticity, the thermal effect will lead to a domain integral in the boundary
integral equation. For avoiding direct integration, the domain integral has been analytically transformed to surface ones. In the thesis, the nearly singular integrals are regularized by the scheme of integration by parts. Furthermore, an additional numerical difficulty arises in numerically evaluating the transformed boundary
integrals whose integrands are associated with trigonometric functions. Under the condition of nearly singular integration, the integrands shall fluctuate drastically near the projection point of the source, posing difficulty in numerical evaluation. This
problem is overcome by the approach of domain sub-division near the projection point and moreover, increased numbers of Gauss points are required. A few
benchmark examples are investigated by the implemented BEM code. All BEM results turn out to agree with those obtained by ANSYS, based on the finite element method.

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