高阶流形方法及其应用

FUNDAMENTALS AND APPLICATIONS OF HICH-ORDER MANIFOLD METHOD

流形方法是一种可进行连续与非连续变形问题分析的灵活而有效的数值计算方法。本文详细地推导了二阶流形方法的具体计算列式，分别开发了一阶流形方法与二阶流形方法的计算程序．通过实例计算表明：提高覆盖函数的阶次可有效地提高流形方法的计算精度。

Manifold Method (MM) developed by Dr. Shi is a novel and very versatile numerical method, which is applicable to both continuous deformation problems and discontinuous deformation problems in structural and geotechnical engineering in a unified framework. In this paper, the generalized mathematical formulations of the manifold method using polynomial cover functions with high orders are presented. Accordingly, the manifold method using the second-order polynomial cover functions is given in detail. Afterwards, the Visual C++ computer programs of the MM using the second- and first-order polynomial cover functions have been developed respectively, and applied to the analysis of a purely-bending beam subjected to bending moment. The calculated results with use of the 2nd-order MM agree fairly well with theoretical solutions. However, the results computed for the same model using the 1st-order MM have marked deviation from the theoretical values. The comparison between the calculated results for this numerical example indicates that the computational accuracy of the MM can be greatly improved if a higher order cover function is employed. Therefore, it is practically necessary and important to develop a higher order manifold method for complicated deformation problems.