微分求积法分析平面接头应力奇异性

Analysis on Stress Singularity of Plane Joints With the Differential Quadrature Method

对于双材料平面接头问题提出了一个分析应力奇性指数的新方法:微分求积法(DQM).首先,将平面接头连接点处位移场的径向渐近展开格式代入平面弹性力学控制方程,获得了关于应力奇性指数的常微分方程组(ODEs)特征值问题.然后,基于DQM理论,将ODEs的特征值问题转化为标准型广义代数方程组特征值问题,求解之可一次性地计算出双材料平面接头连接点处应力奇性指数,同时,一并求出了接头连接点处相应的位移和应力特征函数.数值计算结果说明该文DQM计算平面接头连接点处应力奇性指数的结果是正确的.

A novel differential quadrature method(DQM) for analysis of the stress singularity index was proposed. Firstly,the radial asymptotic expansion scheme of the displacement field at the connection point of the plane joint was substituted into the governing equation of plane elasticity, and the eigenvalue problem of ordinary differential equations(ODEs) about the stress singularity index was obtained. Then, based on the DQM theory, the eigenvalue problem of ordinary differential equations was transformed into the eigenvalue problem of standard generalized algebraic equations. The stress singularity index at the connection point of the bi-material plane joint was calculated at one time, and the corresponding displacement and stress characteristic functions at the connection point were obtained at the same time. The numerical results show that,the DQM is correct in calculation of the stress singularity index at the connection point of the plane joint.