非协调数值流形方法的稳定性和收敛性分析

在流形元的基础上，提出了非协调数值流形方法，非协调数值流形方法的优点是在不增加广义节点自由度的前提下，大大提高数值流形方法的计算精度和计算效率.利用内部自由度静力凝聚处理，推导了消除内参后的单元应变矩阵和单元刚度矩阵.在Hilbert空间内，从最小势能原理出发对非协调数值流形方法的稳定性和收敛性进行了分析和讨论，得到了保证非协调流形元解唯一存在和收敛的基本条件，完善了非协调数值流形方法的理论基础.数值试验表明，新单元构造过程简单，有较高的精度，从而证明了本方法的可行性. 关键词： 数值流形方法 非协调元 稳定性分析 收敛性分析

Stability and convergence analysis of incompatible numerical manifold method

The incompatible numerical manifold method (INMM) is developed on the basis of numerical manifold method (NMM). The advantages of INMM are that the calculation accuracy and computing efficiency can be greatly increased without adding generalized degrees of freedom. The expressions of element strain matrix and element stiffness matrix are given based on eliminating the internal parameters. On the basis of least potential energy theory the stability and convergence are analyzed and discussed in Hilbert space, and the basic condition ensuring uniqueness and convergence of solution is given. The theorization of INMM is perfected. To illustrate the stability and convergence of the present approach, numerical examples are provided. It is shown that this method produces highly accurate and convergent results.