Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory

Abstract

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi-three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

“…Recently, many quasi-3D theories have been established to capture the stretching effect on the response of the plates. The formulae and applications of these theories can be found in the works of Zenkour, 27 Mantari et al, 28,29 Adim et al 30 and Thai et al 31 On the other hand, quasi-3D theories have been combined with the Carrera unified formulation (CUF) to investigate a wide range of structures as shown in Neves et al, 32,33 Carrera et al 34 and so on. In these theories, the normal stress being the thickness direction does not neglect, so they can be applied to study thick and very thick plates.…”

Nano-Clay Platelet Integration for Enhanced Bending Performance of Concrete Beams Resting on Elastic Foundation: An Analytical Investigation

“…Afshari et al [ 43 ] conducted vibration analyses and investigated the size-dependent buckling of GNP-reinforced microplates based on the quasi-3D sinusoidal shear deformation theory. Additionally, Adim et al [ 44 ] studied the effects of thickness stretching in FGM plates using a quasi-3D higher-order shear deformation theory. These studies collectively highlight the reliability and applicability of the quasi-3D deformation theory in various structural analyses.…”

Mechanical analysis of shrink-fitted thick FG cylinders based on first order shear deformation theory and FE simulation

“…1 By this continuous transmuting in the volume fraction of the constituents, the properties vary smoothly which results in the elimination of interface problems and consequently, uniformity of stress and temperature distribution. [2][3][4][5] Typically for industrial and medical applications these materials are made from an amalgamation of metallic and ceramic constituents. [6][7][8] FG materials also could be found in biological systems with examples such as the spongy trabecular structures of bone or local tissue of some seashells and plants.…”