• Steel and Composite Structures
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• 제26권1호
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• pp.89-102
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• 2018

This work investigates a novel plate formulation and a modified couple stress theory that introduces a variable length scale parameter is presented to discuss the static and dynamic of functionally graded (FG) micro-plates. A new type of third-order shear deformation theory of Reddy that use only 4 unknowns by including undetermined integral variables is proposed in this study. The equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for a simply supported micro-plate. Numerical examples are presented to examine the effect of the length scale parameter on the responses of micro-plates. The obtained results are compared with the previously published results to demonstrate the correctness of the present formulation.

• Smart Structures and Systems
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• 제19권6호
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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.

• Smart Structures and Systems
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• 제25권4호
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• pp.409-422
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• 2020

This article deals with the flexural analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal loading using a refined plate theory with four variables. In this theory, the undetermined integral terms are used and the number of variables is reduced to four, instead of five or more in other higher-order theories. The boundary conditions on the top and the bottom surfaces of the plate are satisfied; hence the use of the transverse shear correction factors is avoided. The principle of virtual work is used to obtain governing equations and boundary conditions. Navier solution for simply supported plates is used to derive analytical solutions. For the validation of the present theory, numerical results for displacements and stresses are compared with those of classical, first-order, higher-order and trigonometric shear theories reported in the literature.

• Steel and Composite Structures
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• 제19권1호
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• pp.93-110
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• 2015

The thermomechanical bending response of anti-symmetric cross-ply composite plates is investigated by the use of the simple four variable sinusoidal plate theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. The validity of the present theory is demonstrated by comparison with solutions available in the literature. Numerical results are presented to demonstrate the behavior of the system. The influences of aspect ratio, side-to-thickness ratio, thermal expansion coefficients ratio and stacking sequence on the thermally induced response are studied. The present study is relevant to aerospace, chemical process and nuclear engineering structures which may be subjected to intense thermal loads.

• Geomechanics and Engineering
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• 제13권3호
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• pp.385-410
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• 2017

This work presents a simple and refined nth-order shear deformation theory for mechanical and thermal buckling behaviors of functionally graded (FG) plates resting on elastic foundation. The proposed refined nth-order shear deformation theory has a new displacement field which includes undetermined integral terms and contains only four unknowns. Governing equations are obtained from the principle of minimum total potential energy. A Navier type analytical solution methodology is also presented for simply supported FG plates resting on elastic foundation which predicts accurate solution. The accuracy of the present model is checked by comparing the computed results with those obtained by classical plate theory (CPT), first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Moreover, results demonstrate that the proposed theory can achieve the same accuracy of the existing HSDTs which have more number of variables.

• Structural Engineering and Mechanics
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• 제72권1호
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• pp.113-129
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• 2019

A four-variable shear deformation refined plate theory has been proposed for dynamic characteristics of smart plates made of porous magneto-electro-elastic functionally graded (MEE-FG) materials with various boundary conditions by using an analytical method. Magneto-electro-elastic properties of FGM plate are supposed to vary through the thickness direction and are estimated through the modified power-law rule in which the porosities with even and uneven type are approximated. Pores possibly occur inside functionally graded materials (FGMs) due the result of technical problems that lead to creation of micro-voids in these materials. The variation of pores along the thickness direction influences the mechanical properties. The governing differential equations and boundary conditions of embedded porous FGM plate under magneto-electrical field are derived through Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factors. An analytical solution procedure is used to achieve the natural frequencies of embedded porous FG plate supposed to magneto-electrical field with various boundary condition. A parametric study is led to carry out the effects of material graduation exponent, coefficient of porosity, magnetic potential, electric voltage, elastic foundation parameters, various boundary conditions and plate side-to-thickness ratio on natural frequencies of the porous MEE-FG plate. It is concluded that these parameters play significant roles on the dynamic behavior of porous MEE-FG plates. Presented numerical results can serve as benchmarks for future analyses of MEE-FG plates with porosity phases.

• Smart Structures and Systems
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• 제19권4호
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• pp.441-448
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• 2017

This paper uses the four-variable refined plate theory for the free vibration analysis of functionally graded material (FGM) rectangular plates. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from the Hamilton's principle. The closed-form solutions of functionally graded plates are obtained using Navier solution. Numerical results of the refined plate theory are presented to show the effect of the material distribution, the aspect and side-to-thickness ratio on the fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of functionally graded plates.

• Coupled systems mechanics
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• 제13권2호
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• pp.95-113
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• 2024

In this paper, we will analyse the thermo-elastic behavior of the plate element of a structure arranged in a climatically aggressive environment (extreme temperature), we use a refined four-variable thick plate theory to take the shear effect into consideration, the proposed theory less computationally expensive and more accurate so that it incorporates the shear effect into the formulation. The plate is assumed to be simply supported on its four edges, so exact (closed-form) solutions are found according to the Navier expansion, and the governing stability equations and associated boundary conditions of the problem are obtained via the virtual works principle. The plate studied ismade of laminated composite materials, so a parametric study is needed to see the effect of different types of parameters and coupling on the critical temperature value causing thermo-elastic instability of the plate and also on the natural frequency of free vibration, as well as for other parameters such as anisotropy, slenderness and aspect ratio of the plate and finally the lamination angle. Numerical results are obtained for specially orthotropic and antisymmetrical plates and are compared with those obtained by othertheoriesin the literature to validate the analysis approach used.

• Steel and Composite Structures
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• 제24권5호
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• pp.603-613
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• 2017

In this research, the free vibration response of laminated composite plates is investigated using a novel and simple higher order shear deformation plate theory. The model considers a non-linear distribution of the transverse shear strains, and verifies the zero traction boundary conditions on the surfaces of the plate without introducing shear correction coefficient. The developed kinematic uses undetermined integral terms with only four unknowns. Equations of motion are obtained from the Hamilton's principle and the Navier method is used to determine the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical examples studied using the present formulation is compared with three-dimensional elasticity solutions and those calculated using the first-order and the other higher-order theories. It can be concluded that the present model is not only accurate but also efficient and simple in studying the free vibration response of laminated composite plates.

• Advances in aircraft and spacecraft science
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• 제7권2호
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• pp.169-186
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• 2020

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.