以邊界元素法分析含 雙橢圓孔洞異向性彈板受彎矩作用之應力集中現象

Abstract

本文使用一個新的邊界積分方程式分析含雙孔洞的異向彈性平板承受遠端彎曲或扭轉力矩之應力集中的問題。該邊界積分方程式是以柯西積分式配合古典版理論與異向彈性力學問題之Stroh方法而得。除運用此邊界積分方程式外，另亦使用有限元素分析軟體ABAQUS，計算孔壁之曲率與力矩。兩種方法比較之結果顯示出以位移為基礎的有限元素求得的力矩有較大的誤差，而邊界元素法則可以直接求得力矩，因此準確度較高；但對位移而言，邊界元素法之誤差與有限元素軟體相去不遠。

This work uses a new boundary integral equation (BIE) and finite element method (FEM) to analyze an infinite anisotropic plate containing two elliptic/circular holes subjected to remote bending or twisting moments. The foundation of the boundary integral equation is the classical plate theory with Cauchy integral formula. The BIE is used to calculate the curvatures and moments on the boundaries directly. Numerical examples are given for orthotropic and isotropic plates with circular or elliptic holes under uniform bending and twisting moments. Comparison of the numerical results with the analytic solution for one hole shows that in general BIE can achieve higher accuracies in evaluating moments while BIEs and FEM have comparable accuracies for computing deflections.