插值矩阵法分析与复合材料界面相交的平面裂纹奇异应力场  

Analysis of the stress singularity of the plane cracks terminating at the interface in bonded dissimilar composite materials by the interpolating matrix method

作　　者：王静平[1] 程长征[2] 韩有民[1] 张金轮[1] 葛仁余[1] 

机构地区：[1]安徽工程大学汽车新技术安徽省工程技术研究中心,芜湖241000 [2]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《计算力学学报》2016年第1期89-94,共6页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(11372094)资助项目

摘　　要：提出了用插值矩阵法分析与各向异性材料界面相交的平面裂纹应力奇异性。基于V形切口尖端附近区域位移场渐近展开,将位移场的渐近展开式的典型项代入线弹性力学基本方程,得到关于平面内与复合材料界面相交的裂纹应力奇异性指数的一组非线性常微分方程的特征值问题,运用插值矩阵法求解,获得了平面内各向异性结合材料中与界面以任意角相交的裂纹尖端的应力奇异性指数随裂纹角的变化规律,数值计算结果与已有结果比较表明,本文方法具有很高的精度和效率。In this paper,a method for calculating the singularity orders of the crack terminating at the interface in the anisotropic planes by the interpolating matrix method is proposed.Based on the asymptotic expansion of the generalized displacement fields at the notch tip,and by introducing the generalized displacement functions in the asymptotic expansion into the linear elasticity equilibrium equation,the governing equations of a crack terminating at the interface of the bonded dissimilar materials are transformed into a set of nonlinear characteristic ordinary differential equations（ODEs）with the singularity orders.Then the interpolating matrix method is introduced to solve the derivative ODEs.The relation between the stress singularity and the ply angle of the crack terminating at the interface of bonded dissimilar anisotropic materials can be easily obtained by this method.The numerical results show that the method is efficient and has very high accuracy while comparing with the existent solutions.

关 键 词：正交各向异性材料 应力奇异性 插值矩阵法 与界面相交的裂纹 渐近展开 

分 类 号：O343.4[理学—固体力学]