关键词: 数值流形方法, 独立覆盖, 本质边界条件, 多项式覆盖函数, 罚函数法

Abstract: At present, some new numerical methods such as Numerical Manifold Method (NMM) and Meshless Method are facing with the difficulty of strictly applying essential boundary conditions. Through a case study of a cantilever beam, the application of essential boundary conditions is systematically analyzed in NMM based on independent covers previously proposed by the authors. On the basis of polynomial cover functions, two methods are presented: one is the improved method of boundary cover functions; and the other is the method of setting independent cover functions. The boundary conditions are strictly satisfied, and the approximate functions near the boundaries are guaranteed to approach the real solutions. The proposed methods are refrained from the influence of penalty number in common penalty method on computational results and linear equation conditions. Moreover, the implementation is very simple, for it just needs some degrees of freedom not involved in the computation.The proposed approach of applying boundary conditions by setting cover functions has a reference value for other new methods.

Key words: Numerical Manifold Method (NMM), independent covers, essential boundary conditions, polynomial cover functions, penalty function method