• Steel and Composite Structures
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• v.46 no.1
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• pp.1-13
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• 2023

Elastic bending of imperfect functionally graded sandwich plates (FGSPs) laying on the Winkler-Pasternak foundation and subjected to sinusoidal loads is analyzed. The analyses have been established using the quasi-3D sinusoidal shear deformation model. In this theory, the number of unknowns is condensed to only five unknowns using integral-undefined terms without requiring any correction shear factor. Moreover, the current constituent material properties of the middle layer is considered homogeneous and isotropic. But those of the top and bottom face sheets of the graded porous sandwich plate (FGSP) are supposed to vary regularly and continuously in the direction of thickness according to the trigonometric volume fraction's model. The corresponding equilibrium equations of FGSPs with simply supported edges are derived via the static version of the Hamilton's principle. The differential equations of the system are resolved via Navier's method for various schemes of FGSPs. The current study examine the impact of the material index, porosity, side-to-thickness ratio, aspect ratio, and the Winkler-Pasternak foundation on the displacements, axial and shear stresses of the sandwich structure.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.353-368
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• 2018

In this work, a high order hyperbolic shear deformation theory with four variables is presented to study the vibratory behavior of functionally graduated plates. The field of displacement of the theory used in this work is introduced indeterminate integral variables. In addition, the effect of porosity is studied. It is assumed that the material characteristics of the porous FGM plate, varies continuously in the direction of thickness as a function of the power law model in terms of volume fractions of constituents taken into account the homogeneous distribution of porosity. The equations of motion are obtained using the principle of virtual work. An analytical solution of the Navier type for free vibration analysis is obtained for a FGM plate for simply supported boundary conditions. A comparison of the results obtained with those of the literature is made to verify the accuracy and efficiency of the present theory. It can be concluded from his results that the current theory is not only accurate but also simple for the presentation of the response of free vibration and the effect of porosity on the latter.

• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.443-459
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• 2023

This study investigates the theoretical thermal buckling analyses of thick porous rectangular functionally graded (FG) plates with different geometrical boundary conditions resting on a Winkler-Pasternak elastic foundation using a new higher-order shear deformation theory (HSDT). This new theory has only four unknowns and involves indeterminate integral variables in which no shear correction factor is required. The variation of material properties across the plate's thickness is considered continuous and varied following a simple power law as a function of volume fractions of the constituents. The effect of porosity with two different types of distribution is also included. The current formulation considers the Von Karman nonlinearity, and the stability equations are developed using the virtual works principle. The thermal gradients are involved and assumed to change across the FG plate's thickness according to nonlinear, linear, and uniform distributions. The accuracy of the newly proposed theory has been validated by comparing the present results with the results obtained from the previously published theories. The effects of porosity, boundary conditions, foundation parameters, power index, plate aspect ratio, and side-to-thickness ratio on the critical buckling temperature are studied and discussed in detail.