• Journal of the Earthquake Engineering Society of Korea
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• v.7 no.4
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• pp.1-13
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• 2003

For spatial free vibration of non-symmetric thin-walled curved beams with shear deformation, an improved formulation is proposed in the present study. The elastic strain and the kinetic energies are first derived by considering constant curvature and shear deformation effects due to shear forces and restrained warping torsion. Next equilibrium equations and force-deformation relations are obtained using a stationary condition of total potential energy. And the finite element procedures are developed by using isoparametric curved beam element with arbitray thin-walled sections. Particularly not only shear deformation and thickness-curvature effects on vibration behaviors of curved beams but also mode transition and crossover phenomena with change in curvatures of beams are parametrically investigated. In order to illustrate the accuracy and the reliability of this study, various numerical solutions for spatial free vibration are compared with results by available references and ABAQUS's shell element.

• Smart Structures and Systems
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• v.22 no.1
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• pp.121-132
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• 2018

This research investigates the free vibration analysis of advanced composite plates such as functionally graded plates (FGPs) resting on a two-parameter elastic foundations using a hybrid quasi-3D (trigonometric as well as polynomial) higher-order shear deformation theory (HSDT). This present theory, which does not require shear correction factor, accounts for shear deformation and thickness stretching effects by a sinusoidal and parabolic variation of all displacements across the thickness. Governing equations of motion for FGM plates are derived from Hamilton's principle. The closed form solutions are obtained by using Navier technique, and natural frequencies are found, for simply supported plates, by solving the results of eigenvalue problems. The accuracy of the present method is verified by comparing the obtained results with First-order shear deformation theory, and other predicted by quasi-3D higher-order shear deformation theories. It can be concluded that the proposed theory is efficient and simple in predicting the natural frequencies of functionally graded plates on elastic foundations.

• Steel and Composite Structures
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• v.25 no.6
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• pp.717-726
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• 2017

In this paper, a new simple shear deformation theory for bending analysis of functionally graded plates is developed. The present theory involves only three unknown and three governing equation as in the classical plate theory, but it is capable of accurately capturing shear deformation effects, instead of five as in the well-known first shear deformation theory and higher-order shear deformation theory. A shear correction factor is, therefore, not required. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. Equations of motion are obtained by utilizing the principle of virtual displacements and solved via Navier's procedure. The elastic foundation is modeled as two parameter elastic foundation. The results are verified with the known results in the literature. The influences played by transversal shear deformation, plate aspect ratio, side-to-thickness ratio, elastic foundation, and volume fraction distributions are studied. Verification studies show that the proposed theory is not only accurate and simple in solving the bending behaviour of functionally graded plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.43-50
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• 2000

In the first-order shear deformation laminated beam theory (FSDT), the Kirchhoff hypothesis is relaxed such that the transverse normals do not remain perpendicular to the midsurface after deformation. Bending behavior of laminated composite thin-walled beams with singly- and doubly-symmetric open sections under uniformly distributed and concentrated loads is analyzed by the Timoshenko-type thin-walled beam theory. A closed-form expression for the shear correction factor of I-shaped composite laminated section is obtained. Numerical examples are presented to compare present analytical solutions by FSDT with the finite element solutions obtained by using three dimensional model. The effects of lamination of scheme and length-to-height ratio on the shear deformation of laminated composite beams with various boundary conditions are studied.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.977-981
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• 2002

The ordinary differential equations governing free vibrations of elastic horizontally curved beams are derived, in which the effect of shear deformation as well as the effects of vertical, rotatory and torsional inertias are included. Frequencies and mode shapes are computed numerically for parabolic curved beams with the hinged-hinged, hinged-clamped and clamped-clamped ends. Comparisons of natural frequencies between this study and ADINA are made to validate the theories and numerical methods developed herein. The lowest three natural frequency parameters are reported, with and without the effect of shear deformation, as functions of the three non-dimensional system parameters: the horizontal rise to span length ratio, the slenderness ratio and the stiffness parameter.

• Smart Structures and Systems
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• v.21 no.1
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• pp.113-122
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• 2018

In this article, an exact analytical solution for mechanical buckling analysis of magnetoelectroelastic plate resting on pasternak foundation is investigated based on the third-order shear deformation plate theory. The in-plane electric and magnetic fields can be ignored for plates. According to Maxwell equation and magnetoelectric boundary condition, the variation of electric and magnetic potentials along the thickness direction of the plate is determined. The von Karman model is exploited to capture the effect of nonlinearity. Navier's approach has been used to solve the governing equations for all edges simply supported boundary conditions. Numerical results reveal the effects of (i) lateral load, (ii) electric load, (iii) magnetic load and (iv) higher order shear deformation theory on the critical buckling load have been investigated. These results must be the analysis of intelligent structures constructed from magnetoelectroelastic materials.

• Steel and Composite Structures
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• v.15 no.5
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• pp.467-479
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• 2013

In this paper, a new first-order shear deformation beam theory based on neutral surface position is developed for bending and free vibration analysis of functionally graded beams. The proposed theory is based on assumption that the in-plane and 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 neutral surface position for a functionally graded beam which its material properties vary in the thickness direction is determined. Based on the present new first-order shear deformation beam theory and the neutral surface concept together with Hamilton's principle, the motion equations are derived. To examine accuracy of the present formulation, several comparison studies are investigated. Furthermore, the effects of different parameters of the beam on the bending and free vibration responses of functionally graded beam are discussed.

• Advances in aircraft and spacecraft science
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• v.10 no.3
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• pp.281-302
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• 2023

In this paper, bending analysis of exponentially varying functionally graded (FG) plate is presented using trigonometric shear deformation theory (TSDT) considering both transverse shear and normal deformation effects. The in-plane displacement field consists of sinusoidal functions in thickness direction to include transverse shear strains and transverse displacement include the effect of transverse normal strain using the cosine function in thickness coordinate. The governing equations and boundary conditions of the theory are derived using the virtual work principle. System of governing equations, for simply supported conditions, Navier's solution technique is used to obtain results. Plate material properties vary across thickness direction according to exponential distribution law. In the current theory, transverse shear stresses are distributed accurately through the plate thickness, hence obviates the need for a shear correction factor. TSDT results are compared with those from other theories to ensure the accuracy and effectiveness of the present theory. The current theory is in excellent agreement with the semi-analytical theory.

• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.942-947
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• 2004

The differential equations governing free, in-plane vibrations of stepped non-circuiar arches are derived as nondimensional forms including the effects of rotatory inertia, shear deformation and axial deformation. The governing equations are solved numerically to obtain frequencies and mode shapes. The lowest four natural frequencies and mode shapes are calculated for the stepped parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of arch rise to span length ratios, slenderness ratios, section ratios, and discontinuous sector ratios are considered. The effect of rotatory inertia and shear deformation on natural frequencies is reported. Typical mode shapes of vibrating arches are also presented.