A new analytical method for calculating the Stress Intensity Factor (SIF) under Mode II loading is presented in the framework of two-dimensional stationary elasticity. Starting from the linear elasticity equations, the crack problem is formulated as a system of Hamiltonian equations, solved based on a new method for determining eigensystems, called Exponential Matrix Method (EMM). The obtained eigensolutions satisfy the adjoint symplectic orthogonality by means of performing an angular stress variation with respect to the radial stress. The linear combination of these eigensolutions then allows a good description of the expected solution. Related to one of the asymptotic expansion coefficients, the SIF under Mode II Loading is calculated using the trapezoidal integration method (TIM). The implemented methodology validation is carried out by comparing the obtained results with those provided by the literature review.

在二维静态弹性的框架内，提出了一种新的分析方法，用于计算II型载荷下的应力强度因子（SIF）。从线性弹性方程开始，将裂纹问题公式化为哈密顿方程组，并基于一种确定特征系统的新方法（称为指数矩阵法（EMM））进行求解。通过相对于径向应力执行角应力变化，所获得的本征解满足伴随辛正交性。这些特征解的线性组合可以很好地描述期望的解。与渐近扩展系数之一相关，使用梯形积分法（TIM）计算模式II载荷下的SIF。