• Advances in nano research
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• v.4 no.3
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• pp.229-249
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• 2016

In this paper, buckling characteristics of nonhomogeneous functionally graded (FG) nanobeams embedded on elastic foundations are investigated based on third order shear deformation (Reddy) without using shear correction factors. Third-order shear deformation beam theory accounts for shear deformation effects by a parabolic variation of all displacements through the thickness, and verifies the stress-free boundary conditions on the top and bottom surfaces of the FG nanobeam. A two parameters elastic foundation including the linear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The material properties of FG nanobeam are supposed to vary gradually along the thickness and are estimated through the power-law and Mori-Tanaka models. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. Nonlocal equations of motion are derived through Hamilton's principle and they are solved applying analytical solution. Comparison between results of the present work and those available in literature shows the accuracy of this method. The obtained results are presented for the buckling analysis of the FG nanobeams such as the effects of foundation parameters, gradient index, nonlocal parameter and slenderness ratio in detail.

• Smart Structures and Systems
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• v.21 no.1
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• pp.113-122
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• 2018

In this article, an exact analytical solution for mechanical buckling analysis of magnetoelectroelastic plate resting on pasternak foundation is investigated based on the third-order shear deformation plate theory. The in-plane electric and magnetic fields can be ignored for plates. According to Maxwell equation and magnetoelectric boundary condition, the variation of electric and magnetic potentials along the thickness direction of the plate is determined. The von Karman model is exploited to capture the effect of nonlinearity. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical results reveal the effects of (i) lateral load, (ii) electric load, (iii) magnetic load and (iv) higher order shear deformation theory on the critical buckling load have been investigated. These results must be the analysis of intelligent structures constructed from magnetoelectroelastic materials.

• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1143-1165
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• 2015

In this work, various higher-order shear deformation plate theories for wave propagation in functionally graded plates are developed. Due to porosities, possibly occurring inside functionally graded materials (FGMs) during fabrication, it is therefore necessary to consider the wave propagation in plates having porosities in this study. The developed refined plate theories have fewer number of unknowns and equations of motion than the first-order shear deformation theory, but accounts for the transverse shear deformation effects without requiring shear correction factors. The rule of mixture is modified to describe and approximate material properties of the functionally graded plates with porosity phases. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and porosity volume fraction on wave propagation of functionally graded plate are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.625-644
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• 2015

In this paper, a two-layer partial interaction composite beams model considering the higher order shear deformation of sub-elements is built. Then, the governing differential equations and boundary conditions for static analysis of linear elastic higher order composite beams are formulated by means of principle of minimum potential energy. Subsequently, analytical solutions for cantilever composite beams subjected to uniform load are presented by Laplace transform technique. As a comparison, FEM for this problem is also developed, and the results of the proposed FE program are in good agreement with the analytical ones which demonstrates the reliability of the presented exact and finite element methods. Finally, parametric studies are performed to investigate the influences of parameters including rigidity of shear connectors, ratio of shear modulus and slenderness ratio, on deflections of cantilever composite beams, internal forces and stresses. It is revealed that the interfacial slip has a major effect on the deflection, the distribution of internal forces and the stresses.

• Steel and Composite Structures
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• v.25 no.4
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• pp.389-401
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• 2017

In this work, a new higher shear deformation theory (HSDT) is developed for the free vibration and buckling of functionally graded (FG) sandwich plates. The proposed theory presents a new displacement field by using undetermined integral terms. Only four unknowns are employed in this theory, which is less than the classical first shear deformation theory (FSDT) and others HSDTs. Equations of motion are obtained via Hamilton's principle. The analytical solutions of FG sandwich plates are determined by employing the Navier method. A good agreement between the computed results and the available solutions of existing HSDTs is found to prove the accuracy of the developed theory.

• Steel and Composite Structures
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• v.38 no.1
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• pp.47-66
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• 2021

This work addresses the free vibration analysis of Functionally Graded Porous (FGP) nanocomposite truncated conical shells with Graphene PLatelet (GPL) reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin-Tsai equations are used to find the effective material properties of the graphene platelet reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders's theory. The Fourier Differential Quadrature (FDQ) technique is implemented to solve the governing equations of the problem and to obtain the natural frequencies of the truncated conical shell. The combination of FDQ with higher-order shear deformation theory allows a very accurate prediction of the natural frequencies. The precision and reliability of the proposed method are verified by the results of literature. Moreover, a wide parametric study concerning the effect of some influential parameters, such as the geometrical parameters, porosity distribution, circumferential wave numbers, GPLs dispersion as well as boundary restraint conditions on free vibration response of FGP-GPL truncated conical shell is also carried out and investigated in detail.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.426-431
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• 2000

A decoupled thermo-piezoelectric-mechanical model of composite laminates with surface bonded piezoelectric actuators, subjected to externally applied load, temperature change load, electric field load is developed. The governing differential equations are obtained by applying the principle of free energy and variational techniques. A higher order zigzag theory displacement field is employed to accurately capture the transverse shear and normal effects in laminated composite plates of arbitrary thickness.

• Steel and Composite Structures
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• v.26 no.2
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• pp.125-137
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• 2018

In this work, the bending and free vibration analysis of multilayered plates and shells is presented by utilizing a new higher order shear deformation theory (HSDT). The proposed involves only four unknowns, which is even less than the first shear deformation theory (FSDT) and without requiring the shear correction coefficient. Unlike the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral variables. The equations of motion are derived by using the Hamilton's principle. These equations are then solved via Navier-type, closed form solutions. Bending and vibration results are found for cylindrical and spherical shells and plates for simply supported boundary conditions. Bending and vibration problems are treated as individual cases. Panels are subjected to sinusoidal, distributed and point loads. Results are presented for thick to thin as well as shallow and deep shells. The computed results are compared with the exact 3D elasticity theory and with several other conventional HSDTs. The proposed HSDT is found to be precise compared to other several existing ones for investigating the static and dynamic response of isotropic and multilayered composite shell and plate structures.

• Steel and Composite Structures
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• v.48 no.6
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• pp.693-708
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• 2023

Composite beams, two materials joined together, have become more common in structural engineering over the past few decades because they have better mechanical and structural properties. The shear connectors between their layers exhibit some deformability with finite stiffness, resulting in interfacial shear slip, a phenomenon known as partial shear interaction. Such a partial shear interaction contributes significantly to the composite beams. To provide precise predictions of the geometric nonlinear behavior shown by two-layered composite beams with interfacial shear slips, a robust analytical model has been developed that incorporates the influence of significant displacements. The application of a higher-order beam theory to the two material layers results in a third-order adjustment of the longitudinal displacement within each layer along the depth of the beam. Deformable shear connectors are employed at the interface to represent the partial shear interaction by means of a sequence of shear connectors that are evenly distributed throughout the beam's length. The Von-Karman theory of large deflection incorporates geometric nonlinearity into the governing equations, which are then solved analytically using the Navier solution technique. Suggested model exhibits a notable level of agreement with published findings, and numerical outputs derived from finite element (FE) model. Large displacement substantially reduces deflection, interfacial shear slip, and stress values. Geometric nonlinearity has a significant impact on beams with larger span-to-depth ratio and a greater degree of shear connector deformability. Potentially, the analytical model can accurately predict the geometric nonlinear responses of composite beams. The model has a high degree of generality, which might aid in the numerical solution of composite beams with varying configurations and shear criteria.

• International Journal of Aeronautical and Space Sciences
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• v.18 no.2
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• pp.255-269
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• 2017

Free vibration analysis is presented for a simply-supported, functionally graded piezoelectric (FGP) nanobeam embedded on elastic foundation in the framework of third order parabolic shear deformation beam theory. Effective electro-mechanical properties of FGP nanobeam are supposed to be variable throughout the thickness based on power-law model. To incorporate the small size effects into the local model, Eringen's nonlocal elasticity theory is adopted. Analytical solution is implemented to solve the size-dependent buckling analysis of FGP nanobeams based upon a higher order shear deformation beam theory where coupled equations obtained using Hamilton's principle exist for such beams. Some numerical results for natural frequencies of the FGP nanobeams are prepared, which include the influences of elastic coefficients of foundation, electric voltage, material and geometrical parameters and mode number. This study is motivated by the absence of articles in the technical literature and provides beneficial results for accurate FGP structures design.