Circular thin plates buckling analysis with HRPIM method

¹ Mechanical Engineering Laboratory, Faculty of Science and Technology, Sidi Mohamed Ben Abdellah University, Fez, Morocco
² Faculty of Science and Technology, Hassan First University, Settat, Morocco
³ LISA Laboratory, National School of Applied Sciences, Hassan First University, Berrechid, Morocco

^* Corresponding author:soukabaid@gmail.com

Abstract

This paper aims to introduce a new approach to simulate geometrically nonlinear problems that require shape functions with higher order continuity such as the buckling analysis of circular thin and thick plates based on two theories; Classical plate theory (CPT) and Third order Shear Deformation Theory (TSDT). The algorithm integrates high-order continuation (HOC) solver and the Hermite-type radial point interpolation method (HRPIM). The in-plane displacement is approximated with RPIM method, while the HRPIM approach is used to compute the transverse component and its derivatives. The governing partial differential equations are discretized using the Galerkin method and solved by combining a Taylor series expansion with a continuation procedure. The paper includes two numerical examples of clamped and simply supported circular plates subjected to radial compression. The critical buckling loads have been calculated for different values of h/R ratio and compared with Finite Elements Method to illustrate the efficiency, robustness and accuracy of this approach across various boundary conditions.