复合材料切口应力奇性指数计算

Evaluation of the stress singularity orders for the composite material notch

提出一种计算广义平面应变状态下复合材料切口应力奇性指数的新方法。在切口尖端的位移幂级数渐近展开式被引入正交各向异性材料的物理方程后,将用位移表示的应力分量代入切口端部柱状邻域的线弹性理论控制方程,切口应力奇性指数的计算被转化为常微分方程组特征值的求解。采用插值矩阵法求解该常微分方程组,可一次性地获取切口尖端多阶应力奇性指数。本法适合平面和反平面应力场耦合或解耦的情形,并可退化计算裂纹或各向同性材料切口的应力奇性指数。算例表明,所提方法对分析复合材料切口应力奇性指数是一种准确有效的手段。

The presentation was mainly devoted to the study on the evaluation for the stress singularity orders of composite notch under the generalized plane strain state. Basing on a power series asymptotic extension for the displacement field in terms of radial coordinates at the notch tip, the governing equa- tions of the elastic theory at the vicinity of prismatic notch were transformed into an eigenvalue problem of ordinary differential equations. Then, the interpolating matrix method was introduced to solve the es- tablished ordinary differential equations for obtaining the eigenvalue. All the singularity orders of the prismatic notch in composite material can be determined at one time. The proposed method can be used to solve the generalized plane deformation problem in which the inplane and antiplane stress fields are cou- pled or decupled,respectively. The present method is versatile which can be degenerated to calculate the stress singularity orders for a crack or an isotropic notch. The accuracy of the proposed algorithm is in- vestigated and compared for several numerical examples, demonstrating that the presented method is an effective and accurate way to analyze the stress singularity orders for the generalized plane strain notch in composite material.