On the optimal shape parameters of distinct versions of RBF meshless methods for the bending analysis of plates

Abstract

This study intends to computationally analyze single-layer plates. Reissner–Mindlin plate deformation theory was combined with the radial basis function (RBF) meshless method. Considering the first order shear deformation theory, the RBF meshless method formulation for isotropic plates analysis is presented. According to the motion equations in terms of displacement for isotropic homogeneous laminates, non-zero laminate stiffness is determined. Transverse displacement results are evaluated for various thickness values where the plate is simply supported in all edges. In this work, it is also shown that Wendland's RBF formulation with optimal values of the shape parameter formulation using several mesh densities produces deflections of single-layer laminate plates agreeing well with analytical solutions. The obtained RBF solution proves that the supporting numerical methodology is efficient and robust.