• Steel and Composite Structures
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• v.25 no.3
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• pp.257-270
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• 2017

In this article, an efficient and simple refined theory is proposed for buckling analysis of functionally graded plates by using a new displacement field which includes undetermined integral variables. This theory contains only four unknowns, with is even less than the first shear deformation theory (FSDT). Governing equations are obtained from the principle of virtual works. The closed-form solutions of rectangular plates are determined. Comparison studies are carried out to check the validity of obtained results. The influences of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are examined and discussed.

• Steel and Composite Structures
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• v.22 no.3
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• pp.473-495
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• 2016

This work presents a bending, buckling, and vibration analysis of functionally graded plates by employing a novel higher-order shear deformation theory (HSDT). This theory has only four unknowns, which is even less than the first shear deformation theory (FSDT). A shear correction coefficient is, thus, not needed. Unlike the conventional HSDT, the present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Steel and Composite Structures
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• v.46 no.6
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• pp.839-856
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• 2023

This work presents a simple four-unknown refined integral plate theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on Visco-Pasternak foundations. The proposed refined high order shear deformation theory has a new displacement field which 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). Governing equations are deduced from the principle of minimum total potential energy and a Navier type analytical solution is adopted for simply supported FG plates. The Visco-Pasternak foundations is considered by adding the impact of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The accuracy of the present model is demonstrated by comparing the computed results with those available in the literature. Some numerical results are presented to show the impact of material index, elastic foundation type, and damping coefficient of the foundation, on the mechanical and thermal buckling behaviors of FG plates.

• Steel and Composite Structures
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• v.33 no.6
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• pp.805-822
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• 2019

In this work, a simple four-variable integral plate theory is employed for examining the thermal buckling properties of functionally graded material (FGM) sandwich plates. The proposed kinematics considers integral terms which include the effect of transverse shear deformations. Material characteristics and thermal expansion coefficient of the ceramic-metal FGM sandwich plate faces are supposed to be graded in the thickness direction according to a "simple power-law" variation in terms of the "volume fractions" of the constituents. The central layer is always homogeneous and consists of an isotropic material. The thermal loads are supposed as uniform, linear, and nonlinear temperature rises within the thickness direction. The influences of geometric ratios, gradient index, loading type, and type sandwich plate on the buckling properties are examined and discussed in detail.

• Steel and Composite Structures
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• v.27 no.1
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• pp.109-122
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• 2018

In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Geomechanics and Engineering
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• v.15 no.1
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• pp.711-719
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• 2018

The present work presents a free vibration and buckling analysis of orthotropic plates by proposing a novel two variable refined plate theory. Contrary to the conventional higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed theory utilizes a novel displacement field which incorporates undetermined integral terms and involves only two unknowns. The governing equations are obtained from the dynamic version of principle of virtual works. The analytical solution of a simply supported orthotropic plate has been determined by using the Navier method. Numerical investigations are performed by employing the proposed model and the obtained results are compared with the existing HSDTs.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.719-724
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• 2017

We consider an elastic isotropic plate reinforced by stringers and weakened by a periodic system of rectilinear slots of variable width. The variable width of the slots is comparable with elastic deformations. We study the case when the slots faces get in contact at some area. Determination of parameters characterizing the partial closure of variable width slots is reduced to the solution of a singular integral equation. The action of the stringers is replaced with unknown equivalent concentrated forces at the points of their connection with the plate. The contact stresses and contact zone sizes are found from the solution of the singular integral equation.

• Structural Engineering and Mechanics
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• v.72 no.5
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• pp.653-673
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• 2019

This work investigates a novel quasi-3D hyperbolic shear deformation theory is presented to discuss the buckling of new type of sandwich plates. This theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of all displacements through the thickness. The enhancement of this formulation is due to the use of only five unknowns by including undetermined integral terms, contrary to other theories where we find six or more unknowns. It does not require shear correction factors and transverse shear stresses vary parabolically across the thickness. A new type of FGM sandwich plates, namely, both FGM face sheets and FGM hard core are considered. The governing equations and boundary conditions are derived using the principle of virtual displacements. Analytical solutions are obtained for a simply supported plate. The accuracy of the present theory is verified by comparing the obtained results with quasi-3D solutions and those predicted by higher-order shear deformation theories. The comparison studies show that the obtained results are not only more accurate than those obtained by higher-order shear deformation theories, but also comparable with those predicted by quasi-3D theories with a greater number of unknowns.

• Structural Engineering and Mechanics
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• v.82 no.6
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• pp.725-734
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• 2022

This work presents a simple exponential shear deformation theory for the flexural and free vibration responses of thick bridge deck. Contrary to the existing higher order shear deformation theories (HSDT) and the first shear deformation theory (FSDT), the proposed model uses a new displacement field which incorporates undetermined integral terms and involves only two variables. Governing equations and boundary conditions of the theory are derived by the principle of virtual work. The simply supported thick isotropic square and rectangular plates are considered for the detailed numerical studies. Results of displacements, stresses and frequencies are compared with those of other refined theories and exact theory to show the efficiency of the proposed theory. Good agreement is achieved of the present results with those of higher order shear deformation theory (HSDT) and elasticity theory. Moreover, results demonstrate that the developed two variable refined plate theory is simple for solving the flexural and free vibration responses of thick bridge deck and can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Smart Structures and Systems
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• v.19 no.6
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• pp.601-614
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• 2017

In this work, free vibration analysis of size-dependent functionally graded (FG) nanoplates resting on two-parameter elastic foundation is investigated based on a novel nonlocal refined trigonometric shear deformation theory for the first time. This theory includes undetermined integral variables and contains only four unknowns, with is even less than the conventional first shear deformation theory (FSDT). Mori-Tanaka model is employed to describe gradually distribution of material properties along the plate thickness. Size-dependency of nanosize FG plate is captured via the nonlocal elasticity theory of Eringen. By implementing Hamilton's principle the equations of motion are obtained for a refined four-variable shear deformation plate theory and then solved analytically. To show the accuracy of the present theory, our research results in specific cases are compared with available results in the literature and a good agreement will be demonstrated. Finally, the influence of various parameters such as nonlocal parameter, power law indexes, elastic foundation parameters, aspect ratio, and the thickness ratio on the non-dimensional frequency of rectangular FG nanoscale plates are presented and discussed in detail.