Bending of FGM plates by a sinusoidal plate formulation and collocation with radial basis functions

Bi-directional functionally graded materials (BDFGMs) for free and forced vibration of Timoshenko beams with various boundary conditions

“…Since material properties exhibit a smooth and continuous variation from one surface to another in FGMs, the main advantages of FGMs over the classical composites are that cracking and delamination phenomenon, stress concentrations and residual stresses can be avoided, and thus structural integrity can be maintained to a desirable level. Due to the wide applications of FGMs in engineering structures, static [1][2][3][4][5][6], buckling [7][8][9][10], free and forced [32][33][34][35][36] vibration behavior of FG structures have been examined extensively by several researchers. On the other hand, since the temperature field in advanced machines such as modern aerospace shuttles and craft develops in two or three directions, conventional FG materials may not be useful in the design of such structures [37].…”

A review of theories for the modeling and analysis of functionally graded plates and shells

“…The governing equations are solved for the bending and free vibration problems using the meshless collocation method with multiquadric RBFs. Neves et al [411][412] used the similar approach of Ferreira et al [410] to study the effect of thickness stretching on the static bending [411][412] and free vibration [412] responses of FG plates. However, their formulations are based on a hybrid quasi-3D theory in which the in-plane and transverse displacements are respectively assumed as sinusoidal and quadratic variations across the thickness.…”

Refined theories based on non-polynomial kinematics for the thermoelastic analysis of functionally graded plates

“…Neves et al [29,30] used a similar theory of Ferreira to study the bending and free vibration of functionally graded plates (FGPs). Their formulations are based on hybrid quasi-3D SSDT with a quadratic variation across the thickness.…”

“…Their formulations are based on hybrid quasi-3D SSDT with a quadratic variation across the thickness. A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of FGPs, similar to the previous theory [29,30], was developed by Neves et al [31,32]. Static analysis for several theories based on trigonometric, hyperbolic, exponential, and zig-zag function was developed by Carrera et al [33] for laminated beams and Filippi et al [34] for FGM beams.…”