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題名 | A Dislocation and Point Force Approach to the Boundary Element Method for Mixed Mode Crack Analysis of Plane Anisotropic Solids=以差排與點作用力之模式的邊界元素法進行異向性的平面混合模式裂縫分析 |
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作者 | Denda,Mitsunori; | 書刊名 | 中國工程學刊 |
卷期 | 22:6 1999.11[民88.11] |
頁次 | 頁677-693 |
分類號 | 440.135 |
關鍵詞 | 邊界元素法; 平面的異向性彈性問題; 差排與點作用力的分佈法; 混合模式的裂縫分析; Boundary element method; Plane anisotropic elasticity; Dislocation and point force approach; Mixed mode crack analysis; |
語文 | 英文(English) |
中文摘要 | 本文推導平面異向性彈力問題的邊界元素法(即:將面內變形與面外變形分開討 論),基於差排偶極與點作用力的分佈,根據Somigliana掇恆等式的物理解釋,在一個有限 體R的位移場可表示為沿著埋藏於有限域中的虛邊界(R)來分配選擇差排偶極與點作用力, 我們採用異向性彈性的Stroh複數形式,來代表差排與點作用力、及其偶極,與有系統地利 用差排解與點作用力的對偶性關係之連續分佈。利用公式可得到位移和曳引力(位移的法向 微分)在邊界積分方程的解析解,應用這些公式可針對在多連通裂縫異向體中之混合模式的 裂縫問題,以Somigliana恆等式來擴展物理的解釋與表示裂縫的差排偶極之連續分佈,藉 著異向性彈性的積分值守恆,以驗證其可行性,並正確地決定此混合模式的應力強度因子(K□ and K□)。 |
英文摘要 | In this paper we formulate a direct boundary element method (BEM) for plane anisotropic elasticity (i.e., the in-plane deformation decoupled from the out-of-plane deformation) based on distributions of point forces and dislocation dipoles. According to a physical interpretation of Somigliana's identity the displacement field in a finite body R is represented by the continuous distributions of point forces and dislocation dipoles along the imaginary boundary □R of the finite domain R embedded in an infinite body. We adopt Stroh's complex variable formalism for anisotropic elasticity and represent the point force and the dislocation, their dipoles, and continuous distributions system atically exploiting the duality relations between the point force and the dislocation solutions. Explicit formulas for the displacement and the traction formulations, obtained by analytical integration of the boundary integrals, are given. We apply these formulas to mixed mode crack problems for multiply cracked anisotropic bodies by extending the physical interpretation of Somigliana's identity to cracked bodies and representing the crack by the continuous distributioin of dislocation dipoles. With the help of the conservation integrals of anisotropic elasticity. We will demonstrate the capability of the method to determine the mixed mode stress intensity factors (K□ and K□) accurately. |
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