The MLS based numerical manifold method for bending analysis of thin plates on elastic foundations

Abstract

Compared with the finite element method, H2-regularity in the Galerkin based approximation to the Kirchhoff thin plate model can be easily realized using either the moving least squares (MLS) or the generalized moving least squares (GMLS), which take the Lagrange form and the Hermite form, respectively. Coupling (G)MLS with the numerical manifold method (NMM) can greatly improve numerical properties of NMM in the treatment of plates of complicated shape, thereby denoted by MLS-NMM and GMLS-NMM. In the (G)MLS-NMM, the mathematical cover is composed of simply connected and partially overlapped mathematical patches that are the influence domains of (G)MLS nodes. GMLS-NMM appears to better fit to the Kirchhoff plate because it is equipped with rotation angle degrees of freedom. Through numerical tests and theoretical analysis in solving problems of thin plates on elastic foundations, however, this study shows that MLS-NMM is much more advantageous over GMLS-NMM from the aspects of both accuracy and memory usage.