對偶邊界元素法在疲勞破壞之工程應用

Abstract

洪與陳於 1986 年發展出對偶邊界元素法，已成功克服了含退化邊界（裂縫）以邊界元素法求解的困難。基於只對問題的邊界作離散，引入超奇異積分方程式，式中的發散積分則以阿達馬主值觀念求解，可對破壞力學與裂縫成長路徑預測進行分析。本文首先回顧對偶邊界積分方程理論，進而介紹對偶邊界元素法。最後以二維與三維含裂縫彈性體進行應力強度因子計算，並與解析解和有限元素法比較，驗證本法之可行性。據此，更實際應用在火箭發動機裂縫之破壞模式評估與裂縫成長路徑預測，並與有限元素法和實驗結果比較。另對飛彈連結結構 V 型環進行破壞力學與裂縫成長分析並與有限元素法比較，均能得到滿意的結果，真正落實產業界的實際應用。 Hong and Chen have derived the dual boundary integral equations (DBIE) in 1986 and solved the rank-deficiency problem of the conventional BEM for crack analysis. In numerical implementation, Hong and Chen introduced the hypersingular equation and interpreted the improper integral in the sense of Hadamard principal value. In this paper, we first review the theory of dual boundary integral equations, and introduce the dual boundary element method. In the numerical examples, two and three-dimensional cases are designed to verify the validity. The results are compared with analytical solutions, FEM and experimental data. Good agreement is obtained. In addition, the applications to solid rocket motor and V-band structures are successfully implemented and the results are compared well with FEM.