Utilizing new spherical Hankel shape functions to reformulate the deection, free vibration, and buckling analysis of Mindlin plates based on finite element method

Abstract

In this study, a new class of shape functions, namely spherical Hankel shape functions, is derived and applied to reformulate the deection, free vibration, and buckling of Mindlin plates based on Finite Element Method (FEM). In doing so, the addition of polynomial terms to the functional expansion, in which only spherical Hankel Radial Basis Functions (RBFs) are used, leads to obtaining spherical Hankel shape functions. Accordingly, the application of polynomial and spherical Bessel function fields together results in achieving greater robustness and effectiveness. Spherical Hankel shape functions benefit from some useful properties including infinite piecewise continuity, partition of unity, and Kronecker delta property. In the end, the accuracy of the proposed formulation is investigated through several numerical examples for which the same degrees of freedom are selected in both of the presented formulation and the classical FEM. Finally, it can be concluded that the application of spherical Hankel shape functions ensures achieving higher accuracy than the Lagrangian FEM.