关键词: 数值流形方法, 高阶多项式覆盖函数, 大位移, 速度公式, 广义自由度

Abstract: Computational accuracy of structure deformation can be improved greatly by the high-order Numerical Manifold Method (NMM). However, poor accuracy or even incorrect velocity results were obtained in the dynamic analysis involved in large displacement. Based on 2-D triangular mathematical meshes and 1-order polynomial cover functions, the reason of the above cases is discussed through an example of rotation of a rigid bar in this paper. Three treatments and the corresponding equations for high-order velocities are presented for the first time, reflecting the change of configuration coordinates under large displacement. The high-order numerical manifold method is useful to other methods such as Generalized Finite Element Method (GFEM) which introduces generalized freedoms at nodes when solving geometric nonlinear problems.

Key words: Numerical Manifold Method(NMM), high-order polynomial cover function, large displacement, velocity equation, generalized degree of freedom