A high-order continuation for bifurcation analysis of functionally graded material sandwich plates

This work deals with nonlinear geometric functionally graded material (FGM) sandwich plates under various nonuniform compressions in the context of the high-order shear deformation theory. To do so, an efficient numerical model named a High Order Continuation with Finite Element Method (HOC-FEM) is used. The HOC-FEM has become an important tool to study and predict the behavior of an FGM sandwich plates, especially to analyze the nonlinear buckling and post-buckling phenomena. This numerical tool has an adaptive step length, which is effective especially for solving nonlinear problems and detecting bifurcation points. Thereafter, the procedure of numerical technique is based on the use of a Taylor series expansion, a finite element method, and a continuation procedure. Indeed, the Taylor series expansion permits to transform the nonlinear problem into a sequence of linear ones. Then, the use of the finite element method consists of interpolating the unknown of the obtained linear systems. The continuation procedure is introduced to compute the whole solution step by step manner. The accuracy and efficiency of the HOC-FEM are illustrated on numerical examples of an FGM plate and then an FGM sandwich-type.

Automated summary

This work utilizes a numerical model called the High Order Continuation with Finite Element Method (HOC-FEM) to study the behavior of nonlinear geometric functionally graded material (FGM) sandwich plates under various nonuniform compressions. HOC-FEM is an efficient tool for analyzing nonlinear buckling and post-buckling phenomena.