The aim of this study is to determine the complete elastic–plastic stress asymptotic solutions at the plane V-notch tip with the two edges being clamped–clamped, free-clamped and free-friction. Firstly, the displacement and stress fields around the notch tip are expressed as asymptotic expansions, and then, these asymptotic expansions are substituted into the displacement–strain relation and the equilibrium equations to establish the ordinary differential equations (ODEs). Finally, the interpolating matrix method is employed to solve the eigenvalue problem of the ODEs, and consequently, the leading-order and higher-order stress and displacement eigen-solutions at the notch tip are obtained. Numerical examples demonstrate that the presented method has the advantages of great versatility and high accuracy.

这项研究的目的是确定平面V形缺口尖端处的完整弹塑性应力渐近解，并且将两个边缘分别进行夹紧，夹紧，自由夹紧和自由摩擦。首先，将切口尖端周围的位移和应力场表示为渐近展开，然后将这些渐近展开代入位移-应变关系和平衡方程，以建立常微分方程（ODE）。最后，采用插值矩阵法求解ODE的特征值问题，从而获得了缺口尖端的前阶和高阶应力和位移本征解。数值算例表明，该方法具有通用性强，准确性高的优点。