Buckling and post-buckling analysis of a functionally graded material (FGM) plate by the Asymptotic Numerical Method. (June 2021) - Sitli, Yassir; Mhada, Khadija; Bourihane, Oussama; Rhanim, Hassan
Abstract: In this paper, a high order finite element model for buckling and post-buckling analysis of a functionally graded material (FGM) plate is proposed. The study is performed considering a functionally graded material plate under different loadings and solicitations. The analysis is based on the classical thin-plate kinematics of von Kármán by considering a quadrilateral finite element with four nodes and five degrees of freedom per node. Static equilibrium equations are obtained using the principle of potential energy. The resolution of the stability nonlinear equations is done using a high order algorithm so-called Asymptotic Numerical Method (ANM). This method is based on the Taylor series expansion and continuation techniques. The validity and accuracy of the proposed model is then tested by numerical comparisons of rectangular and perforated plates with the results obtained by the Abaqus industrial software and with those given in the literature