数值流形位移法在岩体裂缝扩展中的应用

基于三角形网格，对裂缝扩展过程中流形单元变化情况进行了深入研究，从几何网格的角度对数值流形方法的连续与非连续统一处理方式进行解读.采用一阶覆盖函数，推导出数值流形算法的权函数表达式，建立局部位移函数.通过数值流形计算程序，得出裂缝尖端位移，并计算尖端应力强度因子.通过经典的中心裂纹板模型，对数值流形位移法求得的尖端应力强度因子进行验证，算例的数值解和解析解吻合度较高，证明数值流形法计算裂缝扩展的准确性，为裂纹扩展过程中尖端应力强度因子的求解提供了新的数值解法.

Application of Numerical Manifold Displacement Method in Crack Propagation of Rock Mass

Based on the finite element triangle mesh， the changing of manifold elements in crack propagation process was studied in depth， and the continuous and discontinuous unified processing of the numerical manifold method are interpreted from the perspective of geometric mesh. The first-order coverage function was used to derive the weight function expression of numerical manifold algorithm， so that the local displacement function can be established. Through the numerical manifold calculation program， the crack tip displacement was obtained， and the tip stress intensity factor was calculated and verified by the classical cracked plate model. The numerical result is in good agreement with the analytical solution， which proves the numerical manifold method is accuracy and can be used as a new numerical solution for solving the tip stress intensity factor in the crack propagation process.