A comprehensive analysis of in-plane functionally graded plates using improved first-order mixed finite element model

Influence of Applied Loads on Free Vibrations of Functionally Graded Material Plate–Shell Panels

“…The critical buckling parameters, defined as λ cr = N xx a 2 /D 0 , with D 0 = E m h 3 /12 1 − ν 2 , are shown in Table 1. From this table, an excellent agreement between the results (for the first mode) obtained is observed with the present model (PM) compared with those obtained by Nguyen-Xuan et al [21] using the MITC4 model and by Pham et al [13]. For benchmarking purposes, the eigenvalues of some higher modes are also presented.…”

“…2024, 14, x FOR PEER REVIEW 2 of 26 geometrically nonlinear analysis of FGM plates and shells. Phan et al [13] studied the buckling of FGM plates and shells. In this paper, the influence of the applied loads on the natural frequencies of functionally graded material plate/shell panels subjected to general loadings is analyzed.…”

“…More recently, a great number of works have also been published in functionally graded material (FGM) structures. Here, some representative works involving plate/shell panels and continuous variation of the material properties through the thickness direction, used to validate the static nonlinear and linear buckling and free vibrations analyses, are mentioned [1][2][3][4][5][6][7][8][9][10][11][12][13]. The aim and the novelty of this paper is to study the influence of external applied loads, which give the panels a state of stress and a slightly different geometry in comparison with the initial panel on the free vibration analysis of the FGM plates-shells, considering the geometrically nonlinear behavior.…”

“…Yin et al [9], Moita et al [10,11], and Long et al [12] presented models for a geometrically nonlinear analysis of FGM plates and shells. Phan et al [13] studied the buckling of FGM plates and shells.…”

Dynamic Analysis of Non-Uniform Functionally Graded Beams on Inhomogeneous Foundations Subjected to Moving Distributed Loads

“…By using the Chebyshev spectral method, the discretization of a system of partial differential equations with variable coefficients can be more easily performed and implemented. Moreover, compared with the finite element method and finite difference method, the Chebyshev spectral method adopts high-order shape functions, and can give a better approximation of the gradually varying material properties by setting fewer nodes, so it is accurate and has fast convergence compared to the FEM [30][31][32]. Finally, the discrete equations governing the bending and vibration of the beams are derived from Lagrange's equation, and a projection matrix method is introduced to apply boundary conditions.…”