• Earthquakes and Structures
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• v.14 no.2
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• pp.103-115
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• 2018

In this work, a simple but accurate hyperbolic plate theory for the free vibration analysis of functionally graded material (FGM) sandwich plates is developed. The significant feature of this formulation is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the classical plate theory (CPT), instead of 5 as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM face sheet and the homogeneous core and the sandwich with the homogeneous face sheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. Numerical results of the present theory are compared with the CPT, FSDT, order shear deformation theories (HSDTs), and 3D solutions. Verification studies show that the proposed theory is not only accurate and simple in solving the free vibration behaviour of FGM sandwich plates, but also comparable with the higher-order shear deformation theories which contain more number of unknowns.

• Steel and Composite Structures
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• v.18 no.2
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• pp.409-423
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• 2015

In the present work, a simple and refined trigonometric higher-order beam theory is developed for bending and vibration of functionally graded beams. The beauty of this theory is that, in addition to modeling the displacement field with only 3 unknowns as in Timoshenko beam theory, the thickness stretching effect (${\varepsilon}_Z{\neq}0$) is also included in the present theory. Thus, the present refined beam theory has fewer number of unknowns and equations of motion than the other shear and normal deformations theories, and it considers also the transverse shear deformation effects without requiring shear correction factors. The neutral surface position for such beams in which the material properties vary in the thickness direction is determined. Based on the present refined trigonometric higher-order beam theory and the neutral surface concept, the equations of motion are derived from Hamilton's principle. Numerical results of the present theory are compared with other theories to show the effect of the inclusion of transverse normal strain on the deflections and stresses.

• 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.22 no.6
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• pp.1281-1299
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• 2016

This paper deals with the analysis of vibration of antisymmetric angle-ply plates using spline method for higher order shear theory. Free vibration of laminated plates is addressed to show the capability of the present method in the vicinity of higher order shear deformation theory and simply supported edges of plates. The coupled differential equations are obtained in terms displacement and rotational functions. These displacement and rotational functions are approximated using cubic and quantic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The antisymmetric angle-ply fiber orientation are taken as design variables. Numerical results enable us to examine the frequencies for various geometric and material parameters and accuracy and effectiveness of the proposed method is also verified by comparative study.

• Journal of Korean Association for Spatial Structures
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• v.5 no.3 s.17
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• pp.65-74
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• 2005

An analytical model was developed to investigate the flexural behavior of a pultruded fiber-reinforced plastic deck of rectangular unit module. The model is based on first-order shea. deformable plate theory (FSDT), and capable of predicting deflection of the deck of arbitrary laminate stacking sequences. To formulate tile problem, two-dimensional plate finite element method is employed. Numerical results are obtained for FRP decks under uniformly-distributed loading, addressing the effects of fiber angle and span-to-height ratio. It is found that the present analytical model is accurate and efficient for solving flexural behavior of FRP decks. Also, as the height of FRP deck plate is higher, the necessity of higher order Shear deformable plate theory(HSDT) is announced, not the FSDT in the plate analysis theory.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.621-631
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• 2018

In this paper, an exact analytical solution is developed for the analysis of the post-buckling non-linear response of simply supported deformable symmetric composite beams. For this, a new theory of higher order shear deformation is used for the analysis of composite beams in post-buckling. Unlike any other shear deformation beam theories, the number of functions unknown in the present theory is only two as the Euler-Bernoulli beam theory, while three unknowns are needed in the case of the other beam theories. The theory presents a parabolic distribution of transverse shear stresses, which satisfies the nullity conditions on both sides of the beam without a shear correction factor. The shear effect has a significant contribution to buckling and post-buckling behaviour. The results of this analysis show that classical and first-order theories underestimate the amplitude of the buckling whereas all the theories considered in this study give results very close to the static response of post-buckling. The numerical results obtained with the novel theory are not only much more accurate than those obtained using the Euler-Bernoulli theory but are almost comparable to those obtained using higher order theories, Accuracy and effectiveness of the current theory.

• Structural Engineering and Mechanics
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• v.64 no.2
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• pp.145-153
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• 2017

In this article, a novel simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) beams is proposed. The beauty of this theory relies on its 2-unknowns displacement field as the Euler-Bernoulli beam theory, which is even less than the Timoshenko beam theory. A shear correction factor is, therefore, not needed. Equations of motion are obtained via Hamilton's principle. Analytical solutions for the bending and free vibration analysis are given for simply supported beams. Efficacy of the proposed model is shown through illustrative examples for bending and dynamic of FG beams. The numerical results obtained are compared with those of other higher-order shear deformation beam theory results. The results obtained are found to be accurate.

• Steel and Composite Structures
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• v.17 no.3
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• pp.321-338
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• 2014

In the present study, a new simple first-order shear deformation theory is presented for laminated composite plates. Moreover, the number of unknowns of this theory is the least one comparing with the traditional first-order and the other higher-order shear deformation theories. Equations of motion and boundary conditions are derived from Hamilton's principle. Analytical solutions of simply supported antisymmetric cross-ply and angle-ply laminates are obtained and the results are compared with the exact three-dimensional (3D) solutions and those predicted by existing theories. It can be concluded that the proposed theory is accurate and simple in solving the static bending and free vibration behaviors of laminated composite plates.

• Advances in materials Research
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• v.8 no.4
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• pp.313-335
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• 2019

The objective of the present paper is to investigate the bending and free vibration behavior of functionally graded material (FGM) sandwich rectangular plates using an efficient and simple higher order shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The most interesting feature of this theory is that it does not require the shear correction factor. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Steel and Composite Structures
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• v.53 no.1
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• pp.77-90
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• 2024

This paper focuses on trigonometric porosity distribution to analyze its effect on the free vibration frequencies of porous orthotropic multi-layered composite plates. Three types of porosity distributions are considered. The governing equations of the free vibration response of porous orthotropic multi-layered composite plates are derived from the Hamilton's principle using higher-order shear deformation theory. The free vibration frequency relation of the problem is obtained by performing Galerkin's method. After the validation process of the relation under the available literature, a few parametric analyses are performed to observe the influence of shear deformation, porosity distribution, orthotropy, layer sequence, and different geometric properties on the frequencies.