The LSPIM-based numerical manifold method (NMM) for modeling transition elements

Abstract

In many structural applications, the transition region, where the solids connect to the shells, is of considerable interest. Due to the complex behavior of this area, accurate modeling is necessary in practical problems. A numerical manifold method (NMM) based on the least square point interpolation method (LSPIM) free from linear dependence, is proposed to simulate this region. First, the basic formulations of local approximation based on LSPIM and the method to construct composite shape function are briefly introduced. This new composite shape function possesses the Kronecker-delta, inter-element compatibility, and higher-order completeness properties. Then, the formulations of the hexahedral element, 3D shell and 3D transition elements are derived based on the proposed method. Several examples are carried out to validate the accuracy and robustness of the suggested method for simulation of transition regions.