Mesh-free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in-plane point loads

In this paper, a mesh-free approach is employed for buckling analysis of Mindlin plates that are subjected to in-plane point loads. The radial point interpolation method (RPIM) is used to approximate displacements based on nodes. Variational forms of the system equations are established. Two-step solution procedures are implemented. The non-uniform pre-stress distribution of plate is first obtained using the RPIM based on a two-dimensional (2D) elastic plane stress problem. This predetermined non-uniform pre-stress distribution is then used to compute buckling loads of plate using the RPIM based on Mindlin’s plate assumption. The RPIM can easily handle any number and location of nodes in the plate domain for a desired computational accuracy without major difficulties in solving the initial stresses and buckling loads. Numerical examples considered here include circular and rectangular Mindlin plates that are subjected to in-plane uniform and point loads with different aspect ratios and boundary conditions. The present results are validated against the available analytical and numerical solutions