• Steel and Composite Structures
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• 제39권1호
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• pp.51-64
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• 2021

This paper presents a high-order shear and normal deformation theory for the bending of FGM plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. Based on the novel shear and normal deformation theory, the position of neutral surface is determined and the governing equilibrium equations based on neutral surface are derived. There is no stretching-bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. Navier-type analytical solution is obtained for functionally graded plate subjected to transverse load for simply supported boundary conditions. The accuracy of the present theory is verified by comparing the obtained results with other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending responses of the FGM plates are studied.

• Earthquakes and Structures
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• 제17권5호
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• pp.447-462
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• 2019

This present paper concerned with the analytic modelling for vibration of the functionally graded (FG) plates resting on non-variable and variable two parameter elastic foundation, based on two-dimensional elasticity using higher shear deformation theory. Our present theory has four unknown, which mean that have less than other higher order and lower theory, and we denote do not require the factor of correction like the first shear deformation theory. The indeterminate integral are introduced in the fields of displacement, it is allowed to reduce the number from five unknown to only four variables. The elastic foundations are assumed a classical model of Winkler-Pasternak with uniform distribution stiffness of the Winkler coefficient (kw), or it is with variables distribution coefficient (kw). The variable's stiffness of elastic foundation is supposed linear, parabolic and trigonometry along the length of functionally plate. The properties of the FG plates vary according to the thickness, following a simple distribution of the power law in terms of volume fractions of the constituents of the material. The equations of motions for natural frequency of the functionally graded plates resting on variables elastic foundation are derived using Hamilton principal. The government equations are resolved, with respect boundary condition for simply supported FG plate, employing Navier series solution. The extensive validation with other works found in the literature and our results are present in this work to demonstrate the efficient and accuracy of this analytic model to predict free vibration of FG plates, with and without the effect of variables elastic foundations.

• Advances in materials Research
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• 제13권5호
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• pp.335-353
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• 2024

In the present paper, a simple quasi-3D integral higher-order beam theory (HBT) is presented, in which both shear deformation and thickness stretching effects are included for mechanical analysis of advanced composite beams with simply supported boundary conditions, handling mainly bending, buckling, and free vibration problems. The kinematics is based on a novel displacement field which includes the undetermined integral terms and the parabolic function is used in terms of thickness coordinate to represent the effect of transverse shear deformation. The governing equilibrium equations are drawn from the dynamic version of the principle of virtual work; whereas the solution of the problem is obtained by assuming a Navier technique for simply supported advanced composite beams subjected to sinusoidally and uniformly distributed loads. The correctness of the present computational method is checked by comparing the obtained numerical results with quasi-3D solutions found in the literature and with those provided by other shear deformation beam theories. It can be confirmed that the proposed model, which does not involve any shear correction factor, is not only accurate but also simple and useful in solving the static and dynamic response of advanced composite beams.

• Structural Engineering and Mechanics
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• 제62권2호
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• pp.143-149
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• 2017

In this work, various higher-order shear deformation beam theories for wave propagation in functionally graded beams are developed. The material properties of FG beam are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, the governing equations of the wave propagation in the FG beam are derived by using the Hamilton's principle. The analytic dispersion relations of the FG beam are obtained by solving an eigenvalue problem. The effects of the volume fraction distributions on wave propagation of functionally graded beam are discussed in detail. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

• Earthquakes and Structures
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• 제13권3호
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• pp.255-265
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• 2017

In this paper, an efficient shear deformation theory is developed for wave propagation analysis in a functionally graded beam. More particularly, porosities that may occur in Functionally Graded Materials (FGMs) during their manufacture are considered. The proposed shear deformation theory is efficient method because it permits us to show the effect of both bending and shear components and this is carried out by dividing the transverse displacement into the bending and shear parts. Material properties are assumed graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents; but the rule of mixture is modified to describe and approximate material properties of the functionally graded beams with porosity phases. The governing equations of the wave propagation in the functionally graded beam are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded beam is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions, the depth of beam, the number of wave and the porosity on wave propagation in functionally graded beam are discussed in details. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded beam.

• Structural Engineering and Mechanics
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• 제74권3호
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• pp.365-380
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• 2020

The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.

• Structural Engineering and Mechanics
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• 제54권4호
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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.

• Earthquakes and Structures
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• 제22권5호
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• pp.447-460
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• 2022

In this article, wave propagation in functional gradation plates (FG) resting on an elastic foundation with two parameters is studied using a new quasi-three-dimensional (3D) higher shear deformation theory (HSDT). The new qausi-3D HSOT has only five variables in fields displacement, which means has few numbers of unknowns compared with others quasi-3D. This higher shear deformation theory (HSDT) includes shear deformation and effect stretching with satisfying the boundary conditions of zero traction on the surfaces of the FG plate without the need for shear correction factors. The FG plates are considered to rest on the Winkler layer, which is interconnected with a Pasternak shear layer. The properties of the material graded for the plates are supposed to vary smoothly, with the power and the exponential law, in the z-direction. By based on Hamilton's principle, we derive the governing equations of FG plates resting on an elastic foundation, which are then solved analytically to obtain the dispersion relations. Numerical results are presented in the form of graphs and tables to demonstrate the effectiveness of the current quasi-3D theory and to analyze the effect of the elastic foundation on wave propagation in FG plates.

• Steel and Composite Structures
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• 제29권3호
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• pp.349-362
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• 2018

Thermal buckling behavior of porous functionally graded nanobeam integrated with piezoelectric sensor and actuator based on the nonlocal higher-order shear deformation beam theory is investigated for the first time. Its material properties are assumed to be temperature-dependent and varying along the thickness direction according to the modified power-law rule. Note that the porosity with even type is considered herein. The equations of motion are obtained through Hamilton's principle. The influences of several parameters (such as type of temperature distribution, external electric voltage, material composition, porosity, small-scale effect, Ker foundation parameters, and beam thickness) on the thermal buckling of FG nanobeam are investigated in detail.

• 대한기계학회논문집
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• 제15권3호
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• pp.735-750
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• 1991

본 연구에서는 적층 복합판의 충격 해석을 위하여 Reddy의 고차 전단 변형 이 론에 기초를 두고, 정적 압입 실험에 의한 접촉 법칙을 고려한 동적 유한 요소 해석 (dynamic finite element analysis)을 행하여 충격 실험에 의한 결과와 1차 전단변형 이론에 의한 해와 비교 검토하므로서, 그 유용성과 우수성을 입증하고, 적층 복합재의 충격 응력 및 응력파 전파 특성에 대하여 연구하고자 한다.