• Steel and Composite Structures
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• 제22권1호
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• pp.91-112
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• 2016

In this paper, post-buckling behavior of sandwich plates with functionally graded (FG) face sheets under uniform temperature rise loading is examined based on both sinusoidal shear deformation theory and stress function. It is supposed that the sandwich plate is in contact with an elastic foundation during deformation, which acts in both compression and tension. Thermo-elastic non-homogeneous properties of FG layers change smoothly by the variation of power law within the thickness, and temperature dependency of material constituents is considered in the formulation. In the present development, Von Karman nonlinearity and initial geometrical imperfection of sandwich plate are also taken into account. By employing Galerkin method, analytical solutions of thermal buckling and post-buckling equilibrium paths for simply supported plates are determined. Numerical examples presented in the present study discuss the effects of gradient index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation parameters.

• Computers and Concrete
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• 제25권4호
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• pp.311-325
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• 2020

In this research work, the hygrothermal and mechanical buckling responses of simply supported FG sandwich plate seated on Winkler-Pasternak elastic foundation are investigated using a novel shear deformation theory. The current model take into consideration the shear deformation effects and ensures the zero shear stresses on the free surfaces of the FG-sandwich plate without requiring the correction factors "Ks". The material properties of the faces sheets of the FG-sandwich plate are assumed varies as power law function "P-FGM" and the core is isotropic (purely ceramic). From the virtual work principle, the stability equations are deduced and resolved via Navier model. The hygrothermal effects are considered varies as a nonlinear, linear and uniform distribution across the thickness of the FG-sandwich plate. To check and confirm the accuracy of the current model, a several comparison has been made with other models found in the literature. The effects the temperature, moisture concentration, parameters of elastic foundation, side-to-thickness ratio, aspect ratio and the inhomogeneity parameter on the critical buckling of FG sandwich plates are also investigated.

• Structural Engineering and Mechanics
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• 제85권3호
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• pp.289-304
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• 2023

The main objective of this paper is to study the effect of porosity on the buckling behavior of thick functionally graded sandwich plate resting on various boundary conditions under different in-plane loads. The formulation is made for a newly developed sandwich plate using a functional gradient material based on a modified power law function of symmetric and asymmetric configuration. Four different porosity distribution are considered and varied in accordance with material propriety variation in the thickness direction of the face sheets of sandwich plate, metal foam also is considered in this study on the second model of sandwich which containing metal foam core and FGM face sheets. New quasi-3D high shear deformation theory is used here for this investigate; the present kinematic model introduces only six variables with stretching effect by adopting a new indeterminate integral variable in the displacement field. The stability equations are obtained by Hamilton's principle then solved by generalized solution. The effect of Pasternak and Winkler elastic foundations also including here. the present model validated with those found in the open literature, then the impact of different parameters: porosities index, foam cells distribution, boundary conditions, elastic foundation, power law index, ratio aspect, side-to-thickness ratio and different in-plane axial loads on the variation of the buckling behavior are demonstrated.

• Steel and Composite Structures
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• 제15권2호
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• pp.221-245
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• 2013

This paper presents an analytical solution to the thermomechanical bending analysis of functionally graded sandwich plates by using a new hyperbolic shear deformation theory in which the stretching effect is included. The modulus of elasticity of plates is assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio and aspect ratio on the deflections and stresses of functionally graded sandwich plates are investigated.

• Structural Engineering and Mechanics
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• 제61권1호
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• pp.49-63
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• 2017

This paper presents an original hyperbolic (first present model) and parabolic (second present model) shear and normal deformation theory for the bending analysis to account for the effect of thickness stretching in functionally graded sandwich plates. Indeed, the number of unknown functions involved in these presents theories 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. It is evident from the present analyses; the thickness stretching effect is more pronounced for thick plates and it needs to be taken into consideration in more physically realistic simulations. The numerical results are compared with 3D exact solution, quasi-3-dimensional solutions and with other higher-order shear deformation theories, and the superiority of the present theory can be noticed.

• Smart Structures and Systems
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• 제18권2호
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• pp.267-291
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• 2016

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) sandwich plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present refined theory. The non-linear governing equations are solved for plates subjected to simply supported and clamped boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.

• Computers and Concrete
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• 제25권3호
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• pp.225-244
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• 2020

The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton's principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin's approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

• Computers and Concrete
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• 제32권1호
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• pp.61-74
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• 2023

This article investigates the wave propagation analysis of the imperfect functionally graded (FG) sandwich plates based on a novel simple four-variable integral quasi-3D higher-order shear deformation theory (HSDT). The thickness stretching effect is considered in the transverse displacement component. The presented formulation ensures a parabolic variation of the transverse shear stresses with zero-stresses at the top and the bottom surfaces without requiring any shear correction factors. The studied sandwich plates can be used in several sectors as areas of aircraft, construction, naval/marine, aerospace and wind energy systems, the sandwich structure is composed from three layers (two FG face sheets and isotropic core). The material properties in the FG faces sheet are computed according to a modified power law function with considering the porosity which may appear during the manufacturing process in the form of micro-voids in the layer body. The Hamilton principle is utilized to determine the four governing differential equations for wave propagation in FG plates which is reduced in terms of computation time and cost compared to the other conventional quasi-3D models. An eigenvalue equation is formulated for the analytical solution using a generalized displacements' solution form for wave propagation. The effects of porosity, temperature, moisture concentration, core thickness, and the material exponent on the plates' dispersion relations are examined by considering the thickness stretching influence.

• Steel and Composite Structures
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• 제25권6호
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• pp.693-704
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• 2017

In this research, a simple hyperbolic shear deformation theory is developed and applied for the bending, vibration and buckling of powerly graded material (PGM) sandwich plate with various boundary conditions. The displacement field of the present model is selected based on a hyperbolic variation in the in-plane displacements across the plate's thickness. By splitting the deflection into the bending and shear parts, the number of unknowns and equations of motion of the present formulation is reduced and hence makes them simple to use. Equations of motion are obtained from Hamilton's principle. Numerical results for the natural frequencies, deflections and critical buckling loads of several types of powerly graded sandwich plates under various boundary conditions are presented. The accuracy of the present formulation is demonstrated by comparing the computed results with those available in the literature. As conclusion, this theory is as accurate as other theories available in the literature and so it becomes more attractive due to smaller number of unknowns.

• Geomechanics and Engineering
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• 제21권5호
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• pp.471-487
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• 2020

In this work, the buckling analysis of material sandwich plates based on a two-parameter elastic foundation under various boundary conditions is investigated on the basis of a new theory of refined trigonometric shear deformation. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Applying the principle of virtual displacements, the governing equations and boundary conditions are obtained. To solve the buckling problem for different boundary conditions, Galerkin's approach is utilized for symmetric EGM sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of plate aspect ratio, elastic foundation coefficients, ratio, side-to-thickness ratio and boundary conditions on the buckling response of FGM sandwich plates. A good agreement between the results obtained and the available solutions of existing shear deformation theories that have a greater number of unknowns proves to demonstrate the precision of the proposed theory.