正交异性多材料三维接头应力奇异性分析  

Evaluation of stress singularities of multi-material 3D junctions in orthotropic materials

作　　者：葛仁余[1] 牛忠荣[2] 程长征[2] 韩有民[1] 张金轮[1] 

机构地区：[1]安徽工程大学力学重点实验室,芜湖241000 [2]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《应用力学学报》2017年第2期237-242,共6页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(11272111;11372094);安徽省高校自然科学研究重点项目(KJ2016A055)

摘　　要：不同材料组成的接头结构在实际工程中是很常见的,这些应力集中较高的接头常常是工程结构断裂失效所处的最关键位置。基于正交异性多材料接头端部物理场的幂级数渐近展开假设,由弹性力学理论导出了关于正交异性多材料接头端部应力奇性指数的特征微分方程组,并将接头端部的力学交界和边界条件表达为奇性指数和特征角函数的组合,从而将正交异性多材料接头端部应力奇性指数的计算转化为相应边界条件下常微分方程组特征值的求解问题,运用插值矩阵法求解可以获得多材料接头端部若干阶应力奇性指数和相应的特征角函数。数值计算结果与现有结果对比表明了该方法的有效性和具有较高的计算精度;同时计算结果还表明多材料接头结构发生断裂失效的主要原因是位移场特征角函数的一阶导函数在不同材料粘结界面发生了突变。Junctions of different materials are very common in many practical applications,these regions with high stress concentrations are usually the most critical locations for mechanical failures.Based on the asymptotic assumption for the physical field near the orthotropic multi-material junction tip,and according to the theory of elastic mechanics,the characteristic differential equations with respect to the stress singularities of junctions that contain bonded orthotropic/orthotropic materials are built.At the same time,the mechanical boundaries and interface conditions are expressed by the combination of the singularity orders and displacement characteristic angle functions.Thus,the evaluation of the singularity orders is transformed into the problem of solving the ordinary differential equations(ODEs)under the designated boundary conditions.Then the interpolating matrix method is introduced to solve the derivative ODEs.The stress singularity orders and the associated eigenfunctions in multi-material junction that comprise three bonded orthotropic materials are obtained.Numerical results obtained show that the validity of this method and the calculation accuracy are very high while compared with the existent results,and the results also show that there is a sharp variation for the first order derivative displacement characteristic angle function at the bonded interface,which is one of the major modes of failures for multi-junctions in bonded dissimilar materials.

关 键 词：奇异性 正交异性材料 渐近展开 特征角函数 插值矩阵法 

分 类 号：O343.4[理学—固体力学]