• Structural Engineering and Mechanics
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• v.53 no.6
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• pp.1215-1240
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• 2015

In this work, a novel simple first-order shear deformation plate theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded plates and supported by either Winkler or Pasternak elastic foundations. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The governing equations are derived by employing the Hamilton's principle and the physical neutral surface concept. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Numerical results of present theory are compared with results of the traditional first-order and the other higher-order theories reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of functionally graded plates.

• Journal of Korean Society of Steel Construction
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• v.15 no.2
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• pp.97-107
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• 2003

To obtain a more accurate response from larninated composite structures, the effect of transverse shear deformation, transverse normal strain/stress, and nonlinear variation of in-plane displacements vis-$\\grave{a}$-vis the thickness coordinate should be considered in the analysis. The improved higher-order theory was used to determine the critical buckling load and natural frequencies of laminated composite structures. Solutions of simply supported laminated composite plates and sandwiches were obtained in closed form using Navier's technique, with the results compared with calculated results using the first order and other higher-order theories. Numerical results were presented for fiber-reinforced laminates, which show the effects of ply orientation, number of layers, side-toithickness ratio, and aspects ratio.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.611-633
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• 2020

In this paper, a comprehensive review of nanostructures that exhibit piezoelectric behavior on all mechanical, buckling, vibrational, thermal and electrical properties is presented. It is firstly explained vast application of materials with their piezoelectric property and also introduction of other properties. Initially, more application of material which have piezoelectric property is introduced. Zinc oxide (ZnO), boron nitride (BN) and gallium nitride (GaN) respectively, are more application of piezoelectric materials. The nonlocal elasticity theory and piezoelectric constitutive relations are demonstrated to evaluate problems and analyses. Three different approaches consisting of atomistic modeling, continuum modeling and nano-scale continuum modeling in the investigation atomistic simulation of piezoelectric nanostructures are explained. Focusing on piezoelectric behavior, investigation of analyses is performed on fields of surface and small scale effects, buckling, vibration and wave propagation. Different investigations are available in literature focusing on the synthesis, applications and mechanical behaviors of piezoelectric nanostructures. In the study of vibration behavior, researches are studied on fields of linear and nonlinear, longitudinal and transverse, free and forced vibrations. This paper is intended to provide an introduction of the development of the piezoelectric nanostructures. The key issue is a very good understanding of mechanical and electrical behaviors and characteristics of piezoelectric structures to employ in electromechanical systems.

• Journal of Korean Society of Steel Construction
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• v.12 no.4 s.47
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• pp.363-374
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• 2000

An accurate method is presented for vibrations of rhombic plates having three different combinations of clamped, simply supported, and free edge conditions. A specific feature here is that the analysis explicitly considers the moment singularities that occur in the two opposite corners having obtuse angles of the rhombic plates. Stationary conditions of single-field Lagrangian functional are derived using the Ritz method. Convergence studies of frequencies show that the corner functions accelerate the convergence rate of solutions. In this paper, accurate frequencies and normalized contours of the vibratory transverse displacement are presented for highly skewed rhombic plates, so that a significant effect of corner stress singularities nay be understood.

• Structural Engineering and Mechanics
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• v.54 no.4
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• pp.693-710
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• 2015

This paper presents a nonlocal shear deformation beam theory for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The developed theory account for higher-order variation of transverse shear strain through the depth of the nanobeam, and satisfy the stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. In addition, this nonlocal nanobeam model incorporates the length scale parameter which can capture the small scale effect and it has strong similarities with Euler-Bernoulli beam model in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived from Hamilton's principle. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• Steel and Composite Structures
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• v.25 no.6
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• pp.649-661
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• 2017

This paper is motivated by the lack of studies in the technical literature concerning to the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) plate has smooth variation of CNT fraction based on the power-law distribution in the thickness direction, and the material properties are also estimated by the extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Parametric studies are carried out to highlight the influence of CNTs volume fraction, waviness and aspect ratio, boundary conditions and elastic foundation on vibrational behavior of FG-CNT thick sectorial plates. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. For an overall comprehension on 3-D vibration of annular sector plates, some mode shape contour plots are reported in this research work.

• Wind and Structures
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• v.23 no.6
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• pp.543-558
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• 2016

The response of functionally graded ceramic-metal plates is investigated using theoretical formulation, Navier's solutions, and a new displacement based on the high-order shear deformation theory are presented for static analysis of functionally graded plates. The theory accounts for a quadratic variation of the transverse shear strains across the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. Numerical results of the new refined plate theory are presented to show the effect of the material distribution on the deflections, stresses and fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the static and free vibration behavior of functionally graded plates.

• Structural Engineering and Mechanics
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• v.10 no.1
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• pp.81-92
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• 2000

This study is an investigation of the effect of cracks on the dynamical characteristics of a cantilever beam, having multiple open-edge transverse cracks. The flexibilities due to crack have been identified for several crack depths and locations. In the study the finite element method and component mode synthesis methods are used. Coupling the components is performed by a flexibility matrix taking into account the interaction forces. Each component is modelled by cantilever beam finite elements with two nodes and three degrees of freedom at each node. The results obtained lead to conclusion that, by using the drop in the natural frequencies and the change in the mode shapes, the presence and nature of cracks in a structure can be detected. There is some counter-evidence, however, that the effects due to multiple cracks may interact to make detection more difficult than for isolated cracks.

• Structural Engineering and Mechanics
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• v.31 no.3
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• pp.277-296
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• 2009

The paper investigates the dynamic behaviour of stiffened panels. The coupled differential equations for eccentric stiffening configuration are first derived. Then a semi-analytical procedure for dynamic analysis of stiffened panels is presented. Unlike finite element or finite strip methods, where the plate is discretized into a set of elements or strips, the plate in this procedure is treated as a single element. The potential energy of the structure is first expressed in terms generalized functions that describe the longitudinal and transverse displacement profiles. The resulting non-linear strain energy functions are then transformed into unconstrained optimization problem in which mathematical programming techniques are employed to determine the magnitude of the lowest natural frequency and the associated mode shape for pre-selected plate/stiffener geometric parameters. The described procedure is verified with other numerical methods for several stiffened panels. Results are then presented showing the variation of the natural frequency with plate/stiffener geometric parameters for various stiffening configurations.

• Journal of KSNVE
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• v.7 no.5
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• pp.819-826
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• 1997

The finite element analyses of a composite hingeless rotor blade in forward flight have been performed to investigate the influence of blade design parameters on the blade stability. The blade structure is represented by a single cell composite box-beam and its nonclassical effects such as transverse shear and torsion-related warping are considered. The nonlinear periodic differential equations of motion are obtained by moderate deflection beam theory and finite element method based on Hamilton principle. Aerodynamic forces are calculated using the quasi-steady strip theiry with compressibility and reverse flow effects. The coupling effects between the rotor blade and the fuselage are included in a free flight propulsive trim analysis. Damping values are calculated by using the Floquet transition matrix theory from the linearized equations perturbed at equilibrium position of the blade. The aeroelastic results were compared with an alternative analytic approch, and they showed good correlation with each other. Some parametric investigations for the helicopter design variables, such as pretwist and precone angles are carried out to know the aeroelastic behavior of the rotor.