正交异性材料V型切口反对称变形下的尖端场  

Singular Stress Field near Tip of V-notch with Anti-Symmetric Deformation in Orthotropic Materials

作　　者：吴枝根[1] 刘一华[1] 

机构地区：[1]合肥工业大学,合肥230009

出　　处：《应用力学学报》2007年第4期664-668,共5页Chinese Journal of Applied Mechanics

基　　金：基金项目国家自然科学基金(10372028);安徽省教育厅自然科学重点科研计划项目(2003kj045zd)

摘　　要：基于正交各向异性材料弹性平面问题的通解,导出了正交各向异性材料奇异点附近的位移场和奇异应力场的解析表达式,由此给出了反对称变形模态下V型切口尖端附近的位移场和奇异应力场的解析解,通过算例难证,解析解与有限元解吻合得非常好。研究结果表明,正交各向异性材料V型切口尖端附近的应力奇异性不仅与切口的张角有关,还与材料的弹性常数有关。In the general solutions of two-dimensional linear elasticity for orthotropic materials, the displacement and stress fields can be expressed in terms of two quasi-harmonic functions ψi(x, y)(i=1, 2). Adopting coordinate transformation, the quasi-harmonic functions are transformed into the corresponding harmonic functions. The related displacement and singular stress fields near the tip of a V-notch with antisymmetric defomation in orthotropic materials are obtained subsequently, and verified by comparing the numerical results with theoretical ones. It is found that the stress singularity depends on both V-notch angle and elastic constants.

关 键 词：正交各向异性 V型切口 反对称 奇异应力场 准调和函数 

分 类 号：O343.8[理学—固体力学]