• Computers and Concrete
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• v.26 no.2
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• pp.185-201
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• 2020

This research is devoted to investigate the bending and free vibration behaviour of laminated composite/sandwich plates and shells, by applying an analytical model based on a generalized and simple refined higher-order shear deformation theory (RHSDT) with four independent unknown variables. The kinematics of the proposed theoretical model is defined by an undetermined integral component and uses the hyperbolic shape function to include the effects of the transverse shear stresses through the plate/shell thickness; hence a shear correction factor is not required. The governing differential equations and associated boundary conditions are derived by employing the principle of virtual work and solved via Navier-type analytical procedure. To verify the validity and applicability of the present refined theory, some numerical results related to displacements, stresses and fundamental frequencies of simply supported laminated composite/sandwich plates and shells are presented and compared with those obtained by other shear deformation models considered in this paper. From the analysis, it can be concluded that the kinematics based on the undetermined integral component is very efficient, and its use leads to reach higher accuracy than conventional models in the study of laminated plates and shells.

• Structural Engineering and Mechanics
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• v.72 no.1
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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.

• Steel and Composite Structures
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• v.26 no.3
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• pp.273-287
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• 2018

Buckling and free vibration analysis of sandwich micro plate (SMP) integrated with piezoelectric layers embedded in orthotropic Pasternak are investigated in this paper. The refined Zigzag theory (RZT) is taken into consideration to model the SMP. Four different types of functionally graded (FG) distribution through the thickness of the SMP core layer which is reinforced with single-wall carbon nanotubes (SWCNTs) are considered. The modified couple stress theory (MCST) is employed to capture the effects of small scale effects. The sandwich structure is exposed to a two dimensional magnetic field and also, piezoelectric layers are subjected to external applied voltages. In order to obtain governing equation, energy method as well as Hamilton's principle is applied. Based on an analytical solution the critical buckling loads and natural frequency are obtained. The effects of volume fraction of carbon nanotubes (CNTs), different distributions of CNTs, foundation stiffness parameters, magnetic and electric fields, small scale parameter and the thickness of piezoelectric layers on the both critical buckling loads and natural frequency of the SMP are examined. The obtained results demonstrate that the effects of volume fraction of CNTs play an important role in analyzing buckling and free vibration behavior of the SMP. Furthermore, the effects of magnetic and electric fields are remarkable on the mechanical responses of the system and cannot be neglected.

• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.205-219
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• 2019

This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

• Steel and Composite Structures
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• v.39 no.2
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• pp.149-158
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• 2021

In this research paper, the free vibrational response of laminated composite plates is investigated using a non-polynomial refined shear deformation theory (NP-RSDT). The most interesting feature of this theory is the parabolic distribution of transverse shear deformations while ensuring the conditions of nullity of shear stresses at the free surfaces of the plate without requiring the Shear correction factor "Ks". A fourth-nodded isoparametric element with four degrees of freedom per node is employed for laminated composite plates. The numerical analysis of simply supported square anti-symmetric cross-ply and angle-ply laminated plate is carried out using a special discretization based on four-node finite element method which four degrees of freedom per node. Several numerical results are presented to show the effect of the coupling parameters of the plate such as the modulus ratios, the thickness ratio and the plate layers number on adimensional eigen frequencies. All numerical results presented using the current finite element method (FEM) is presented in 3D curve form.

• Steel and Composite Structures
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• v.24 no.5
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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.

• Coupled systems mechanics
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• v.13 no.4
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• pp.359-373
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• 2024

The present study aims to investigate the free vibration of bi-directional functionally graded (BDFG) beams using a refined shear deformation (RSD) theory. Power law variation of material composition was considered along thickness and longitudinal directions. The beams are considered simply supported. The methodology adopted is the Hamilton principle and the governing equation was solved using Navier's method for simply supported boundary conditions. A metal-ceramic combination of materials was used to provide gradation as per power law variation. The equivalent elasticity modulus and density of BDFG were computed using the rule of mixture. The results of the study were related to published works and found to be a good match. The effect of grading parameters in the thickness and longitudinal direction was studied to investigate its impact on the natural frequency.

• 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.

• Advances in aircraft and spacecraft science
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• v.6 no.3
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• pp.189-206
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• 2019

In this work, a novel first-order shear deformation beam theory is applied to explore the vibration and buckling characteristics of thick functionally graded beams. The material properties are assumed to vary across the thickness direction in a graded form and are estimated by a power-law model. A Fourier series-based solution procedure is implemented to solve the governing equation derived from Hamilton's principle. The obtained results of natural frequencies and buckling loads of functionally graded beam are checked with those supplied in the literature and demonstrate good achievement. Influences of several parameters such as power law index, beam geometrical parameters, modulus ratio and axial load on dynamic and buckling behaviors of FGP beams are all discussed.

• Steel and Composite Structures
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• v.18 no.6
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• pp.1493-1515
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• 2015

A new refined hyperbolic shear deformation theory (RHSDT), which involves only four unknown functions as against five in case of other shear deformation theories, is presented for the thermoelastic bending analysis of functionally graded sandwich plates. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. 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. The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson's ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic ceramic material. Several kinds of sandwich plates are used taking into account the symmetry of the plate and the thickness of each layer. The influences played by the transverse shear deformation, thermal load, plate aspect ratio and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded metal-ceramic plates are investigated. It can be concluded that the proposed theory is accurate and simple in solving the thermoelastic bending behavior of functionally graded plates.