GMLS-based numerical manifold method in mechanical analysis of thin plates with complicated shape or cutouts

Abstract

We proposed a generalized moving least squares (GMLS) based numerical manifold method (NMM) and applied to investigate mechanical behaviors of thin plates with various shape and cutouts. The influence domains of nodes in generalized moving least squares (GMLS) interpolation are employed to construct the mathematical cover, which is specifically fitted for the fourth-order problems with rotational degrees of freedom. Moreover, the GMLS-based NMM can naturally treat plates with arbitrary complex geometry and openings without resorting to those complicated criteria and tailored operations while simplifying the physical cover generation process. In numerical study, a suitable mass lumping scheme is formulated and advised for transverse vibration analysis. Bending, vibration and buckling behaviors of thin plates with different shapes and cutouts are studied. Numerical results manifest that GMLS-based NMM can accurately model transverse mechanical behaviors.