• Structural Engineering and Mechanics
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• v.57 no.3
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• pp.457-471
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• 2016

To analyze laminated composite and sandwich beams under temperature loads, a $C^0$-type Reddy's beam theory considering transverse normal strain is proposed in this paper. Although transverse normal strain is taken into account, the number of unknowns is not increased. Moreover, the first derivatives of transverse displacement have been taken out from the in-plane displacement fields, so that the $C^0$ interpolation functions are only required for the finite element implementation. Based on the proposed model, a three-node beam element is presented for analysis of thermal responses. Numerical results show that the proposed model can accurately and efficiently analyze the thermoelastic problems of laminated composites.

• Steel and Composite Structures
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• v.23 no.6
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• pp.623-631
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• 2017

Present paper deals with the temperature-dependent buckling analysis of sandwich nanocomposite plates resting on elastic medium subjected to magnetic field. The lamina layers are reinforced with carbon nanotubes (CNTs) as uniform and functionally graded (FG). The elastic medium is considered as orthotropic Pasternak foundation with considering the effects of thermal loading on the spring and shear constants of medium. Mixture rule is utilized for obtaining the effective material properties of each layer. Adopting the Reddy shear deformation plate theory, the governing equations are derived based on energy method and Hamilton's principle. The buckling load of the structure is calculated with the Navier's method for the simply supported sandwich nanocomposite plates. Parametric study is conducted on the combined effects of the volume percent and distribution types of the CNTs, temperature change, elastic medium, magnetic field and geometrical parameters of the plates on the buckling load of the sandwich structure. The results show that FGX distribution of the CNTs leads to higher stiffness and consequently higher buckling load. In addition, considering the magnetic field increases the buckling load of the sandwich nanocomposite plate.

• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.847-868
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• 2016

In this study, the free vibration analysis of axially moving beams is investigated according to Reddy-Bickford beam theory (RBT) by using dynamic stiffness method (DSM) and differential transform method (DTM). First of all, the governing differential equations of motion in free vibration are derived by using Hamilton's principle. The nondimensionalised multiplication factors for axial speed and axial tensile force are used to investigate their effects on natural frequencies. The natural frequencies are calculated by solving differential equations using analytical method (ANM). After the ANM solution, the governing equations of motion of axially moving Reddy-Bickford beams are solved by using DTM which is based on Finite Taylor Series. Besides DTM, DSM is used to obtain natural frequencies of moving Reddy-Bickford beams. DSM solution is performed via Wittrick-Williams algorithm. For different boundary conditions, the first three natural frequencies that calculated by using DTM and DSM are tabulated in tables and are compared with the results of ANM where a very good proximity is observed. The first three mode shapes and normalised bending moment diagrams are presented in figures.

• Smart Structures and Systems
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• v.5 no.5
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• pp.531-546
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• 2009

In the present analysis, the spline finite strip with higher-order shear deformation is formulated for the static analysis of piezoelectric composite plates. The proposed method incorporates Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model, Cho's higher-order zigzag laminate theory, as well as the classic plate theory and the first-order plate theory. Thus, the analysis can be conducted based on any of the above-mentioned theories. The selection of a specific method is done by simply changing a few terms in a 2 by 2 square matrix and the results, obtained according to different plate theories, can be compared to each other. Numerical examples are presented for piezoelectric composite plates subjected to mechanical loading. The results based on different shear deformation theories are compared with the three-dimensional solutions. The behaviours of piezoelectric composite plates with different length-to-thickness ratios, fibre orientations, and boundary conditions are also investigated in these examples.

• Advances in nano research
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• v.6 no.2
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• pp.113-133
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• 2018

In this work, free vibration characteristics of functionally graded piezoelectric (FGP) nanobeams based on third order parabolic shear deformation beam theory are studied by presenting a Navier type solution as the first attempt. Electro-mechanical properties of FGP nanobeam are supposed to change continuously throughout the thickness based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for third order shear deformable piezoelectric FG nanobeams are obtained and they are solved applying analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of the FGP nanobeams. The influences of several parameters including, external electric voltage, power-law exponent, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams is discussed in detail.

• Structural Engineering and Mechanics
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• v.27 no.1
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• pp.1-16
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• 2007

In the present study, a spline finite strip with higher-order shear deformation is formulated for the stability and free vibration analysis of composite plates. The analysis is conducted based on Reddy's third-order shear deformation theory, Touratier's "Sine" model, Afaq's exponential model and Cho's higher-order zigzag laminate theory. Consequently, the shear correction coefficients are not required in the analysis, and an improved accuracy for thick laminates is achieved. The numerical results, based on different shear deformation theories, are presented in comparison with the three-dimensional elasticity solutions. The effects of length-to-thickness ratio, fibre orientation, and boundary conditions on the critical buckling loads and natural frequencies are investigated through numerical examples.

• Steel and Composite Structures
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• v.21 no.4
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• pp.883-919
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• 2016

In this research, buckling analysis of an embedded laminated composite plate is investigated. The elastic medium is simulated with spring constant of Winkler medium and shear layer. With considering higher order shear deformation theory (Reddy), the total potential energy of structure is calculated. Using Principle of Virtual Work, the constitutive equations are obtained. The analytical solution is performed in order to obtain the buckling loads. A detailed parametric study is conducted to elucidate the influences of the layer numbers, orientation angle of layers, geometrical parameters, elastic medium and type of load on the buckling load of the system. Results depict that the highest buckling load is related to the structure with angle-ply orientation type and with increasing the angle up to 45 degrees, the buckling load increases.

• Advances in nano research
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• v.14 no.6
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• pp.495-506
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• 2023

We study the bending wave, shear wave and longitudinal wave characteristics in the double nanobeams in this paper for the first time, in the process of research, based on the Reddy's higher-order shear deformation theory and considering shear layer stiffness, linear stiffness, inter-laminar stiffness, the pore volume fraction, temperature variation, functionally graded index influence on wave propagation, based on the nonlocal strain gradient theory and Hamilton variational principle, the wave equation of the double-nanometer beams are derived. Since there are three different motion states for the double nanobeams, which includes the cases of "in phase", "out of phase" and "one nanobeam fixed", the propagation characteristics of shear-, bending-, and longitudinal- waves in these three cases are discussed respectively, and some valuable conclusions are obtained.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.623-637
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• 1999

This paper presents a four-noded quadrilateral $C^0$ strain plate element for the analysis of thick laminated composite plates. The element formulation is based on: 1) the third-order shear deformation theory; 2) assumed strain element formulation; and 3) interrelated edge displacements and rotations along element boundaries. Unlike the existing displacement-type composite plate elements based on the third-order theory, which rely on the $C^1$-continuity formulation, the present plate element is of $C^0$-continuity, and its element stiffness matrix is evaluated explicitly. Because of the third-order expansion of the in-plane displacements through the thickness, the resulting theory and hence elements do not need shear correction factors. The explicit element stiffness matrix makes the present element more computationally efficient than the composite plate elements using numerical integration for the analysis of thick layered composite plates.

• Smart Structures and Systems
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• v.19 no.3
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• pp.309-322
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• 2017

In this paper, the buckling, and free vibration analysis of tapered functionally graded carbon nanotube reinforced composite (FG-CNTRC) micro Reddy beam under longitudinal magnetic field using finite element method (FEM) is investigated. It is noted that the material properties of matrix is considered as Poly methyl methacrylate (PMMA). Using Hamilton's principle, the governing equations of motion are derived by applying a modified strain gradient theory and the rule of mixture approach for micro-composite beam. Micro-composite beam are subjected to longitudinal magnetic field. Then, using the FEM, the critical buckling load, and natural frequency of micro-composite Reddy beam is solved. Also, the influences of various parameters including ${\alpha}$ and ${\beta}$ (the constant coefficients to control the thickness), three material length scale parameters, aspect ratio, different boundary conditions, and various distributions of CNT such as uniform distribution (UD), unsymmetrical functionally graded distribution of CNT (USFG) and symmetrically linear distribution of CNT (SFG) on the critical buckling load and non-dimensional natural frequency are obtained. It can be seen that the non-dimensional natural frequency and critical buckling load decreases with increasing of ${\beta}$ for UD, USFG and SFG micro-composite beam and vice versa for ${\alpha}$. Also, it is shown that at the specified value of ${\alpha}$ and ${\beta}$, the dimensionless natural frequency and critical buckling load for SGT beam is more than for the other state. Moreover, it can be observed from the results that employing magnetic field in longitudinal direction of the micro-composite beam increases the natural frequency and critical buckling load. On the other hands, by increasing the imposed magnetic field significantly increases the stability of the system that can behave as an actuator.