• Steel and Composite Structures
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• v.14 no.1
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• pp.85-104
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• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric 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. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

• Steel and Composite Structures
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• v.27 no.3
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• pp.311-325
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• 2018

This article presents the bending analysis of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment. Theoretical formulations are based on a recently developed refined shear deformation theory. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. The present theory satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modeled as non-uniform foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermo-mechanical behavior of functionally graded plates. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

• Advances in nano research
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• v.10 no.2
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• pp.101-114
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• 2021

An analytical investigation has been performed on the mechanical performance of waves propagated in a Single-Layered Graphene Sheet (SLGS) when an In-plane Varying Bending (IVB) load is interacted. It has been supposed that the Graphene Sheet (GS) is located on an elastic medium. Employing a two-parameter elastic foundation, the effects of elastic substrate on the GS behavior are modeled. Besides, the kinematic equations are derived by the means of a trigonometric two-variable refined plate theory. Moreover, in order to indicate the size-dependency of the SLGS, a Nonlocal Strain Gradient Theory (NSGT) was considered. The nonlocal governing differential equations are achieved in the framework of Hamilton's Principle (HP). Also, an analytical approach was used to detect the unknowns of the final eigenvalue equation. Finally, the effects of each parameters using some dispersion charts were determined.

• Advances in concrete construction
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• v.15 no.2
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• pp.97-114
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• 2023

The nonlocal strain gradient theory for the static bending analysis of graphene nanoplatelets (GPLs) reinforced the nanoplate is developed in this paper. The nanoplatelet is exposed to thermo-mechanical loads and is also supposed to stand on an elastic foundation. For computing impressive composite material characteristics, the Halpin-Tsai model is selected for various sectors. The various distributions are propounded including UD, FG-O, and FG-X. The represented equations are acquired based on the virtual work and sinusoidal shear and normal deformation theory (SSNDT). Navier's solution as the analytical method is applied to solve these equations. Furthermore, the effects of GPL weight fraction, temperature parameters, distribution pattern and parameters of the foundation are presented and discussed.

• Advances in nano research
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• v.8 no.4
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• pp.265-276
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• 2020

A study that primarily focuses on nonlocal strain gradient plate model for the sole purpose of vibration examination, for graphene sheets under linearly variable in-plane mechanical loads. To study a better or more precise examination on graphene sheets, a new advance model was conducted which carries two scale parameters that happen to be related to the nonlocal as well as the strain gradient influences. Through the usage of two-variable shear deformation plate approach, that does not require the inclusion of shear correction factors, the graphene sheet is designed. Based on Hamilton's principle, fundamental expressions in regard to a nonlocal strain gradient graphene sheet on elastic half-space is originated. A Galerkin's technique is applied to resolve the fundamental expressions for distinct boundary conditions. Influence of distinct factors which can be in-plane loading, length scale parameter, load factor, elastic foundation, boundary conditions, and nonlocal parameter on vibration properties of the graphene sheets then undergo investigation.

• Advances in nano research
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• v.9 no.4
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• pp.221-235
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• 2020

The following composition establishes a nonlocal strain gradient plate model that is essentially related to mass sensors laying on Winkler-Pasternak medium for the vibrational analysis from graphene sheets. To achieve a seemingly accurate study of graphene sheets, the posited theorem actually accommodates two parameters of scale in relation to the gradient of the strain as well as non-local results. Model graphene sheets are known to have double variant shear deformation plate theory without factors from shear correction. By using the principle of Hamilton, to acquire the governing equations of a non-local strain gradient graphene layer on an elastic substrate, Galerkin's method is therefore used to explicate the equations that govern various partition conditions. The influence of diverse factors like the magnetic field as well as the elastic foundation on graphene sheet's vibration characteristics, the number of nanoparticles, nonlocal parameter, nanoparticle mass as well as the length scale parameter had been evaluated.

• Advances in nano research
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• v.17 no.3
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• pp.257-274
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• 2024

This work aims to study and analyse the dynamic size dependent behvior of functionally graded carbon nanotubes (FGCNTs) nanoplates embedded in elastic media and subjected to moving point load. The non-classical effect is incorporated into the governing equations using the nonlocal strain gradient theory (NSGT). Four different reinforcement configurations of the carbon nanotubes (CNTs) are considered to show the effect of reinforcement configuration on the dynamic behvior of the FGCNTs nanoplates. The material characteristics of the functionally graded materials are assumed to be continuously distributed throughout the thickness direction according to the power law. The Hamiltonian principle is exploited to derive the dynamic governing equations of motion and the associated boundary conditions in the framework of the first order shear deformation plate theory. The Navier analytical approach is adopted to solve the governing equations of motion. The obtained solution is checked by comparing the obtained results with the available results in the literature and the comparison shows good agreement. Numerical results are obtained and discussed. Obtained results showed the significant impact of the elastic foundation parameters, the non-classical material parameters, the CNT configurations, and the volume fractions on the free and forced vibration behaviors of the FGCNT nanoplate embedded in two parameters elastic foundation and subjected to moving load.

• Steel and Composite Structures
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• v.28 no.1
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• pp.99-110
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• 2018

In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton's principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

• Geomechanics and Engineering
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• v.32 no.2
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• pp.159-177
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• 2023

In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.

• Structural Engineering and Mechanics
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• v.58 no.4
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• pp.613-625
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• 2016

Contact interaction of a beam (flexible element) with an elastic half-plane is considered, when a soft inhomogeneous (functionally graded) interlayer is present between them. The beam is bent under the action of a distributed load applied to the surface and a reaction of the elastic interlayer and the half-space. Solution of the contact problem is obtained for different values of thickness and parameters of inhomogeneity of the layer. The interlayer is assumed to be significantly softer than the underlying half-plane; case of 100 times difference in Young's moduli is considered as an example. The influence of the interlayer thickness and gradient of elastic properties on the distribution of the contact stresses under the beam is studied.