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
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