• 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.

• Advances in nano research
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• v.5 no.2
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• pp.113-126
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• 2017

This paper proposes a new nonlocal higher-order hyperbolic shear deformation beam theory (HSBT) for the static bending and vibration of nanoscale-beams. Eringen's nonlocal elasticity theory is incorporated, in order to capture small size effects. In the present model, the transverse shear stresses account for a hyperbolic distribution and satisfy the free-traction boundary conditions on the upper and bottom surfaces of the nanobeams without using shear correction factor. Employing Hamilton's principle, the nonlocal equations of motion are derived. The governing equations are solved analytically for the edges of the beam are simply supported, and the obtained results are compared, as possible, with the available solutions found in the literature. Furthermore, the influences of nonlocal coefficient, slenderness ratio on the static bending and dynamic responses of the nanobeam are examined.

• Steel and Composite Structures
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• v.25 no.4
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• pp.389-401
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• 2017

In this work, a new higher shear deformation theory (HSDT) is developed for the free vibration and buckling of functionally graded (FG) sandwich plates. The proposed theory presents a new displacement field by using undetermined integral terms. Only four unknowns are employed in this theory, which is less than the classical first shear deformation theory (FSDT) and others HSDTs. Equations of motion are obtained via Hamilton's principle. The analytical solutions of FG sandwich plates are determined by employing the Navier method. A good agreement between the computed results and the available solutions of existing HSDTs is found to prove the accuracy of the developed theory.

• Structural Engineering and Mechanics
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• v.57 no.1
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• pp.127-140
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• 2016

In this paper, a new first shear deformation plate theory based on neutral surface position is developed for the static and the free vibration analysis of functionally graded plates (FGPs). 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. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Based on the present shear deformation plate theory and the neutral surface concept, the governing equations are derived from the principle of Hamilton. There is no stretching-bending coupling effect in the neutral surface based formulation. Numerical illustrations concern flexural and dynamic behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, length to thickness ratios. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Geomechanics and Engineering
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• v.22 no.2
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• pp.119-132
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• 2020

In this study a new innovative three unknowns trigonometric shear deformation theory is proposed for the buckling and vibration responses of exponentially graded sandwich plates resting on elastic mediums under various boundary conditions. The key feature of this theoretical formulation is that, in addition to considering shear deformation effect, it has only three unknowns in the displacement field as in the case of the classical plate theory (CPT), contrary to five as in the first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). Material characteristics of the sandwich plate faces are considered to vary within the thickness direction via an exponential law distribution as a function of the volume fractions of the constituents. Equations of motion are obtained by employing Hamilton's principle. Numerical results for buckling and free vibration analysis of exponentially graded sandwich plates under various boundary conditions are obtained and discussed. Verification studies confirmed that the present three -unknown shear deformation theory is comparable with higher-order shear deformation theories which contain a greater number of unknowns.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.04a
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• pp.42-48
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• 1997

The dynamic response of symmetric cross-ply and angle-ply composite laminated plates under impact loads is investigated using a higher order shear deformation theory. A modified Hertz law is used to predict the impact loads and a four node finite element is used to model the plate. By using a higher order shear deformation theory, the out-of-plane shear stresses, which can be a crucial factor in the failure of composite plates, are determined with significant accuracy. The results compared with previous investigations showed good agreement. The effect of ply sequence and ply angle on the contact force is also studied.

• 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.

• Structural Engineering and Mechanics
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• v.55 no.5
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• pp.1001-1014
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• 2015

Bending analysis of functionally graded (FG) nano-plates is investigated in the present work based on a new sinusoidal shear deformation theory. The theory accounts for sinusoidal distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The material properties of nano-plate are assumed to vary according to power law distribution of the volume fraction of the constituents. The size effects are considered based on Eringen's nonlocal theory. Governing equations are derived using energy method and Hamilton's principle. The closed-form solutions of simply supported nano-plates are obtained and the results are compared with those of first-order shear deformation theory and higher-order shear deformation theory. The effects of different parameters such as nano-plate length and thickness, elastic foundation, orientation of foundation orthtotropy direction and nonlocal parameters are shown in dimensionless displacement of system. It can be found that with increasing nonlocal parameter, the dimensionless displacement of nano-plate increases.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.489-505
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• 2016

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

• Advances in materials Research
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• v.6 no.1
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• pp.13-26
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• 2017

In this work we introduce a higher-order hyperbolic shear deformation model for bending and frees vibration analysis of functionally graded beams. In this theory and by making a further supposition, the axial displacement accounts for a refined hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the beam boundary surfaces, so no need of any shear correction factors (SCFs). The material properties are continuously varied through the beam thickness by the power-law distribution of the volume fraction of the constituents. Based on the present refined hyperbolic shear deformation beam model, the governing equations of motion are obtained from the Hamilton's principle. Analytical solutions for simply-supported beams are developed to solve the problem. To verify the precision and validity of the present theory some numerical results are compared with the existing ones in the literature and a good agreement is showed.