关键词: 数值流形方法, 独立覆盖, Timoshenko梁, Euler-Bernoulli梁, 梁板壳分析

Abstract: Using Numerical Manifold Method (NMM) based on independent covers proposed in previous studies, a numerical method for beam analysis based on independent covers is presented. The solution process is almost the same with solid analysis: complete polynomials can be used as cover functions to analyze beams as solids; or, with some polynomial terms not involved in the computation, the fundamental beam assumptions, such as the assumption for Timoshenko beam, or the assumption for Euler-Bernoulli beam, are implemented. The approximate field functions with only C₀ continuity are needed. In the meantime, the “shear locking” problem for Timoshenko beam is avoided when dealing with long beams with small cross-sections. Even for totally solid analysis, the numerical ill-conditioning problem due to very small ratio of height to length does not exist in general situations. With two-dimensional beams with rectangular cross-sections as a case study, the formulae of independent covers in the local coordinate system are given to reflect the features of beams, together with the integration approach of “firstly along the cross-section, and then along the axial direction”. Some numerical examples demonstrate the validity of the method. The idea of the paper can be directly expanded to solve three-dimensional problems, and to provide a new approach for analysis of beams, plates and shells.

Key words: Numerical Manifold Method (NMM), independent covers, Timoshenko beam, Euler-Bernoulli beam, beam, plate and shell analysis