高低阶覆盖函数混合的数值流形方法

在数值流形方法中混合使用高、低阶覆盖函数可以使求解精度和求解效率之间得到协调。同时,高低阶覆盖函数混合使用也体现了数值流形方法本身的灵活性和对复杂问题的适应性。本文详细推导了混合使用高、低阶覆盖函数的流形单元的数值计算格式,有利于数值流形方法的程序实现和工程应用,并通过岩土工程中地基变形的计算证明了方法的可靠性和有效性。

The numerical manifold method using low-order and high-order cover functions

In solving rock mechanics problems,one may find solutions with a balanced performance of high accuracy and computational efficiency by using low-order and high-order cover functions together with the numerical manifold method.Moreover,the use of combined cover functions has shown the flexibility and adaptability of numerical manifold method for solving complex problems.This paper presents the finite element stiffness formulations based on the manifold method using both the low-order and high-order cover functions.A numerical example on footing is given to show the reliability and effectiveness of the proposed method.