A mixed MLS and Hermite-type MLS method for buckling and postbuckling analysis of thin plates

Abstract

In the present paper, a new procedure, that combines the Asymptotic Numerical Method (ANM) with the Hermite-Type Moving Least Squares (HMLS) meshless method, is proposed to study the bending, buckling and postbuckling behaviors of Kirchhoff–Love thin plate model. The MLS shape functions are used to approximate the in-plane displacements, while Hermite-type MLS shape functions are used to approximate the transversal displacement and its derivatives. To overcome the difficulty in the imposition of the essential boundary conditions, we use the Lagrange multiplier method. The ANM is adopted in order to derive the results from the global nonlinear system of equations obtained from the principle of the stationarity condition of the total potential energy. This algorithm is based on the coupling of the Taylor series expansion and a continuation process. This approach allows the construction of the solution curve step by step thanks to a piecewise continuous representation. The continuation technique is performed by using the arc-length method. The effectiveness of the proposed coupling is brought out through illustrative examples which concern rectangular plate subjected to different load cases with various boundary conditions. The obtained results through this numerical investigation are compared with those obtained by the Finite Element Method (FEM) or the analytic formulas.