A meshfree Hermite point interpolation method for buckling and post-buckling analysis of thin plates

This paper aims to develop a meshfree approach based on the coupling of the Hermite-type point interpolation method (HPIM) and a high order continuation (HOC) Solver for numerical simulation of the geometrically nonlinear problems that require higher order continuity shape functions such as the buckling of a thin plate. The point interpolation method (PIM) and Hermite-type point interpolation method (HPIM) shape functions construction procedure is presented in detail. The first type is used to approximate the in-plane displacements, while the second one is used for the transverse component and its derivatives. The standard Galerkin method is adopted to discretize the governing partial differential equations which were derived from using the Kirchhoff’s plate theory. The resolution of the considered problem is performed thanks to a solver that combines a Taylor series expansion with a continuation procedure. Numerical examples with different geometric shapes, various boundary conditions and loadings are given to verify the efficiency, accuracy, and robustness of the proposed approach.