Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening

Ke, Liao-Liang; Yang, Jie; Kitipornchai, S.

doi:10.1016/j.compstruct.2009.03.003

Cited by 97 publications

(28 citation statements)

References 29 publications

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“…Also, besides the Euler-Bernoulli beams which neglect shear deformation during bending, an efficient model for analyzing FGBs with various end conditions and arbitrary loadings and shear deformation during bending is still lacking. Recently, buckling, flexural vibration and postbuckling of cracked functionally graded Timoshenko beams have been studied in [16,17]. This paper develops the higher-order shear deformation theory to suit FGBs subjected to various end conditions including free, hinged, clamped and elastically restrained beams.…”

Section: Introductionmentioning

confidence: 98%

A higher-order theory for static and dynamic analyses of functionally graded beams

2010

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The higher-order theory is extended to functionally graded beams (FGBs) with continuously varying material properties. For FGBs with shear deformation taken into account, a single governing equation for an auxiliary function F is derived from the basic equations of elasticity. It can be used to deal with forced and free vibrations as well as static behaviors of FGBs. A general solution is constructed, and all physical quantities including transverse deflection, longitudinal warping, bending moment, shear force, and internal stresses can be represented in terms of the derivatives of F. The static solution can be determined for different end conditions. Explicit expressions for cantilever, simply supported, and clamped-clamped FGBs for typical loading cases are given. A comparison of the present static solution with existing elasticity solutions indicates that the method is simple and efficient. Moreover, the gradient variation of Young's modulus and Poisson's ratio may be arbitrary functions of the thickness direction. Functionally graded Rayleigh and Euler-Bernoulli beams are two special cases when the shear modulus is sufficiently high. Moreover, the classical Levinson beam theory is recovered from the present theory when the material constants are unchanged. Numerical computations are performed for a functionally graded cantilever beam with a gradient index obeying power law and the results are displayed graphically to show the effects of the gradient index on the deflection and stress distribution, indicating that both stresses and deflection are sensitive to the gradient variation of material properties.

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Section: Introductionmentioning

confidence: 98%

A higher-order theory for static and dynamic analyses of functionally graded beams

2010

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“…A semi inverse method to study the instability and vibration of axially FGM beams is carried out by Aydogdu [10]. Ke et al [11] presented the postbuckling of a cracked beam for hinged-hinged and clamped-hinged edge conditions based on the Timoshenko beam theory. Also, Ke et al [12] presented the free vibration and mechanical buckling of cracked beams using the first order shear deformation beam theory for three types of boundary conditions.…”

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confidence: 99%

Thermomechanical buckling oftemperature-dependent FGM beams

Kiani

Eslami

2013

Lat. Am. j. solids struct.

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“…[20][21][22][23][24]). Hosseini Hashemi and Nazemnezhad [25] presented an analytical study on the nonlinear free vibration of functionally graded nano-beams with considering the surface effects.…”

Section: Introductionmentioning

confidence: 98%

Nonlinear forced vibration response of smart two-phase nano-composite beams to external harmonic excitations

Mareishi

Kalhori

Rafiee

et al. 2015

Curved and Layered Structures

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This paper presents an analytical solution for nonlinear free and forced vibration response of smart laminated nano-composite beams resting on nonlinear elastic foundation and under external harmonic excitation. The structure is under a temperature change and an electric excitation through the piezoelectric layers. Different distribution patterns of the single walled aligned and straight carbon nanotubes (SWCNTs) through the thickness of the beam are considered. The beam complies with Euler-Bernoulli beam theory and von Kármán geometric nonlinearity. The nonlinearity is due to the mid-plane stretching of the beam and the nonlinear stiffness of the elastic foundation. The Multiple Time Scales perturbation scheme is used to perform the nonlinear dynamical analysis of functionally graded carbon nanotube-reinforced beams. Analytical expressions of the nonlinear natural frequencies, nonlinear dynamic response and frequency response of the system in the case of primary resonance have been presented. The effects of different parameters including applied voltage, temperature change, beam geometry, the volume fraction and distribution pattern of the carbon nanotubes on the nonlinear natural frequencies and frequency-response curves are presented. It is found that the volume fractions of SWCNTs as well as their distribution pattern significantly change the behavior of the system.

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Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening

Cited by 97 publications

References 29 publications

A higher-order theory for static and dynamic analyses of functionally graded beams

A higher-order theory for static and dynamic analyses of functionally graded beams

Thermomechanical buckling oftemperature-dependent FGM beams

Nonlinear forced vibration response of smart two-phase nano-composite beams to external harmonic excitations

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