Institute of Fundamental Technological Research

We present a nonlinear finite element analysis to investigate the nonlinear behaviour of functionally graded materials (FGM) plates. The material properties are assumed to vary gradually across the thickness according to a power law distribution. The starting point of the investigation is the generalized third-order plate theory which is modified in the present analysis to include the position of the neutral surface and enhanced with additional terms to represent the distribution stresses better. The plates are subjected to bending and compression loads including buckling and post-buckling analysis.

FGM plate, Nonlinear finite element analysis, Bending, Post-buckling

In this paper, some of the displacement-based plate theories are used to investigate the elastic-plastic analysis of plates in the framework of the finite element method including the buckling and postbuckling effects with the focus on the general third-order plate theory (GTPT). The plate calculation results were compared with the results obtained using 64-nodes solid elements involving Lobatto integration scheme. The problem is solved using the Newton–Raphson method applying modified Crisfield constant arc-length procedure. The results show good agreement of results and the GTPT can be acknowledged to fulfill essential criteria for application to the elastic-plastic analysis of thin and thick plates.

buckling and postbuckling, elasto-plastic plates, third-order plate theory

We present a nonlinear finite element method to investigate the nonlinear stability of stiffened functionally graded materials (FGM) plates considered as a whole unit. The plates are subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and varied gradually across the thickness according to a power law distribution. The nonlinear equations of FGM plates are based on the first-order shear order plate theory. The influence of material, geometrical properties of stiffeners and initial deflections on the buckling and post-buckling response of the stiffened plates are studied in detail. Including the latest information no work has been oriented towards post-buckling analysis of stiffened FGM plates considered as a whole unit.

FGM stiffened plate, nonlinear finite element analysis, post-buckling

The geometrically nonlinear free vibration of functionally graded thick plates resting on the elastic Pasternak foundation is investigated. The motion equations are derived applying the Hamilton principle. We consider the first order shear deformation plate theory (FSDT), in which the modified shear correction factor is required. A 16-noded Mindlin plate element of the Lagrange family which is free from shear locking due to small thickness of the plate used. The material properties are assumed to be temperature-dependent and expressed as a nonlinear function of temperature. Because the FGM plates are not homogeneous, the basic equations are calculated in the equivalent physical neutral surface which differs from the geometric mid-plane. In the pre-buckling range natural frequencies decrease ultimately reaching zero for critical stress in the bifurcation point.

FGM plates, Two-parameter elastic foundation, Nonlinear free vibration, Finite element method

First, we discuss characteristics of functionally graded materials and describe methods of their manufacturing. Then, we provide an overview of analytical and numerical methods for calculating plates, with characteristics of functionally graded materials, resting on elastic foundation. The presented numerical results have been obtained by the finite elements method, referring to post-bifurcation problems of thermally loaded plates. The first-order shear deformation theory (FSDT) has been employed. In numerical calculations we have used a new 16-node plate element, free of problems related to shear locking.

Thick plates, Functionally graded materials, Finite elements method

The Pasternak elastic foundation model is employed to study the statics and natural frequencies of thick plates in the framework of the finite element method. A new 16-node Mindlin plate element of the Lagrange family and a 32-node zero-thickness interface element representing the response of the foundation are used in the analysis. The plate element avoids ill-conditioned behaviour due to its small thickness. In the case of the eigenvalue analysis, the equation of motion is derived by applying the Hamilton principle involving the variation of the kinetic and potential energy of the plate and foundation. Regarding the plate, the firstorder shear deformation theory is used. By employing the Lobatto numerical integration in which the integration points coincide with the element nodes, we obtain the diagonal form of the mass matrix of the plate. In practice, diagonal mass matrices are often employed due to their very attractive timeintegration schemes in explicit dynamic methods in which the inversion of the effective stiffness matrix as a linear combination of the damping and mass matrices is required. The numerical results of our analysis are verified using thin element based on the classical Kirchhoff theory and 16-node thick plate elements.

Mindlin plate, two-parameter elastic foundation, Lobatto integration, bending and eigenvalue analysis