摘要 無元素法( Element Free method，EFM)處理網格邊界與材料邊界不一致的不規則邊界問題，常以高斯積分點在材料邊界內外做為取捨標準，容易造成數值誤差。 本論文提出積分權值調整觀念，由高斯積分的幾何意義著手，將積分網格中積分點與權的值拓展成積分面積的觀念，處理邊界網格積分時直接估算材料邊界內的高斯積分面積，使能量計算誤差降低，取代以往以高斯積分點點位座落於介質體內外為取捨的積分觀念。數值範例顯示積分權值調整觀念處理網格邊界與材料邊界不一致的邊界積分，不必細分網格也可以達到相當的分析精度，不論處理傾斜邊界或曲線邊界均呈現出穩定而且良好的分析結果。運用本法結合J積分計算版裂縫應力強度因子與運用完整高斯積分法情況所得相近。積分權值調整觀念使用於裂縫拓展分析中也相當便利，由彈性樑垂直邊裂縫拓展與版雙裂縫拓展分析顯示本法可以在處理移動性邊界問題時真正做到不必網格重建。此一新的積分法以簡單有效的權值調整觀念處理複雜的邊界網格積分問題，不僅符合無元素法的原創精神，也確保了無元素法能量積分的正確性。 A Weighting Adjustment Scheme of Gauss Integration in Element Free Method In this thesis, a modified numerical integration scheme is presented that improves the accuracy of the numerical integration of the Galerkin weak form, within the integration cells of the analyzed domain in the element-free methods. A geometrical interpretation of the Gaussian quadrature rule is introduced to map the effective weighting territory of each quadrature point in an integration cell. Then, the conventional quadrature rule is extended to cover the overlapping area between the weighting territory of each quadrature point and the physical domain. This modified numerical integration scheme can lessen the errors due to misalignment between the integration cell and the boundary or interface of the physical domain. Numerical examples illustrate that this proposed integration scheme for element-free methods does effectively improve the accuracy of solving solid mechanics problems, and is easy to handle the crack propagation problems of solids than it does in the finite element method.
