数值流形法中覆盖函数的改进形式及其应用

采用高阶覆盖函数可以提高数值流形法的计算精度，但常用的基于全局坐标的高阶函数会导致刚度矩阵病态，并且影响物体边界上占据部分数学网格的小单元的计算精度。在其他研究者建议的基于局部坐标的覆盖函数基础上，提出了改进的局部覆盖函数，使刚度矩阵的性态得到有效改善，并提高了边界上小单元的应力精度；建立了局部覆盖函数与全局覆盖函数间的关系式，方便了公式推导。

Improved Local Cover Function of Numerical Manifold Method and Its Application

Adopting high-order global cover function can enhance the calculation precision of the numerical manifold method, but the high-order function in common use related to global coordinate may cause ill-condition of stiffness matrix in the numerical manifold method and affect the computational precision of the small boundary blocks that occupy a part of mathematical meshes. Based on the local cover function proposed by orther researchers, an improved local cover function is presented, resulting in effective improvement of the quality of stiffness matrix and the stress precision of small blocks on model boundary. A relationship between the improved local cover function and the global cover function is also established and this improved function can simplify the derivation of formulation.