• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.313-323
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• 2018

A numerical study is performed to investigate the impacts of thermal loading on the vibration and buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical shells. Thermo-mechanical properties of constituents are considered to be temperature-dependent. Considering the shear deformation theory, the energy functional is derived, and applying the variational differential quadrature (VDQ) method, the mass and stiffness matrices are obtained. The shear correction factors are accurately calculated by matching the shear strain energy obtained from an exact three-dimensional distribution of the transverse shear stresses and shear strain energy related to the first-order shear deformation theory. Numerical results reveal that considering temperature-dependent material properties plays an important role in predicting the thermally induced vibration of FG-CNTRC conical shells, and neglecting this effect leads to considerable overestimation of the stiffness of the structure.

• Smart Structures and Systems
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• v.1 no.3
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• pp.309-324
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• 2005

This paper presents an efficient and accurate coupled beam model for piezoelectric bimorphs based on improved first-order shear deformation theory (FSDT). The model combines the equivalent single layer approach for the mechanical displacements and a layerwise modeling for the electric potential. General electric field function is proposed to reasonably approximate the through-the-thickness distribution of the applied and induced electric potentials. Layerwise defined shear correction factor (k) accounting for nonlinear shear strain distribution is introduced into both the shear stress resultant and the electric displacement integration. Analytical solutions for free vibrations and forced response under electromechanical loads are obtained for the simply supported piezoelectric bimorphs with series or parallel arrangement, and the numerical results for various length-to-thickness ratios are compared with the exact two-dimensional piezoelasticity solution. Excellent predictions with low error estimates of local and global responses as well as the modal frequencies are observed.

• Journal of Mechanical Science and Technology
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• v.20 no.6
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• pp.748-758
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• 2006

In this paper, we have revisited the estimation of the rotational stiffness of sidewall of radial tire and have suggested a new method for evaluation of the rotational stiffness. Since thicknesses, and volume fractions of the constituents of sidewall are varied depending on radial position, the equivalent shear modulus of the sidewall also depends on radial position. For the estimation of rotational stiffness of sidewall's rubber, we have divided its cross-section into sufficient numbers of small parts and have calculated the equivalent shear modulus of each part of sidewall. Using the shear moduli of divided parts, we have obtained the rotational stiffness by employing in-plane shear deformation theory. This method is expected to be a useful tool in tire design since it relates such basic variables to the global stillness of tire. Applying the calculation method to a radial tire of P205/60R15, we have compared its rotational stiffness with experimental one.

• 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.19 no.2
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• pp.369-384
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• 2015

This work presents a free vibration analysis of functionally graded metal-ceramic (FG) beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a simple displacement field based on higher order shear deformation theory is implemented. The proposed theory is based on the assumption that the transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The most interesting feature of this theory is that it 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 beam without using shear correction factors. In addition, it has strong similarities with Euler-Bernoulli beam theory in some aspects such as equations of motion, boundary conditions, and stress resultant expressions. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. By employing the Hamilton's principle, governing equations of motion for coupled axial-shear-flexural response are determined. The validity of the present theory is investigated by comparing some of the present results with those of the first-order and the other higher-order theories reported in the literature. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Steel and Composite Structures
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• v.18 no.5
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• pp.1119-1127
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• 2015

A finite-element model for beams with partially delaminated layers is used to investigate their behavior. In this formulation account is taken of lateral strains and the first-order shear deformation theory is used. Both displacement continuity and force equilibrium conditions are imposed between the regions with and without delamination. Numerical results of the present model are presented and its performance is evaluated for static and dynamic problems.

• Structural Engineering and Mechanics
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• v.11 no.1
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• pp.89-104
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• 2001

This paper reviews the author's work on the development of relationships between solutions of the Kirchhoff (classical thin) plate theory and the Mindlin (first order shear deformation) thick plate theory. The relationships for deflections, stress-resultants, buckling loads and natural frequencies enable one to obtain the Mindlin plate solutions from the well-known Kirchhoff plate solutions for the same problem without much tedious mathematics. Sample thick plate solutions, deduced from the relationships, are presented as benchmark solutions for researchers to use in checking their numerical thick plate solutions.

• Steel and Composite Structures
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• v.20 no.4
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• pp.889-911
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• 2016

Using the hyperbolic shear deformation plate model and including plate-foundation interaction (Winkler and Pasternak model), an analytical method in order to determine the deflection and stress distributions in simply supported rectangular functionally graded plates (FGP) subjected to a sinusoidal load, a temperature and moisture fields. The present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. No transversal shear correction factors are needed because a correct representation of the transversal shearing strain is given. Materials properties of the plate (elastic, thermal and moisture expansion coefficients) are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Numerical examples are presented and discussed for verifying the accuracy of the present theory in predicting the bending response of FGM plates under sinusoidal load and a temperature field as well as moisture concentration. The effects of material properties, temperature, moisture, plate aspect ratio, side-to-thickness ratio, ratio of elastic coefficients (ceramic-metal) and three distributions for both temperature and moisture on deflections and stresses are investigated.

• Steel and Composite Structures
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• v.19 no.3
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• pp.521-546
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• 2015

A new refined hyperbolic shear and normal deformation beam theory is developed to study the free vibration and buckling of functionally graded (FG) sandwich beams under various boundary conditions. The effects of transverse shear strains as well as the transverse normal strain are taken into account. Material properties of the sandwich beam faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending, free vibration and buckling analyses are obtained for simply supported sandwich beams. Illustrative examples are given to show the effects of varying gradients, thickness stretching, boundary conditions, and thickness to length ratios on the bending, free vibration and buckling of functionally graded sandwich beams.

• Earthquakes and Structures
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• v.10 no.6
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• pp.1429-1449
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• 2016

The effect of porosity on bending and free vibration behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper. The modified rule of mixture covering porosity phases is used to describe and approximate material properties of the FGM plates with porosity phases. The effect due to transverse shear is included by using a new refined shear deformation theory. The number of unknown functions involved in the present theory is only four as against five or more in case of other shear deformation theories. The Poisson ratio is held constant. Based on the sinusoidal shear deformation theory, the position of neutral surface is determined and the equation of motion for FG rectangular plates resting on elastic foundation based on neutral surface is obtained through the minimum total potential energy and Hamilton's principle. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for both isotropic and functionally graded material (FGM). The effect of porosity volume fraction on Al/Al2O3 and Ti-6Al-4V/Aluminum oxide plates are presented in graphical forms. The roles played by the constituent volume fraction index, the foundation stiffness parameters and the geometry of the plate is also studied.