Non-linear free vibrations and post-buckling analysis of shear flexible functionally graded beams

Anandrao, K. Sanjay; Gupta, Rekha; Ramchandran, P.; Rao, G. Venkateswara

doi:10.12989/sem.2012.44.3.339

Cited by 11 publications

(3 citation statements)

References 27 publications

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“…Gupta et al [8] studied the *For correspondence thermal post-buckling analysis of composite columns to obtain simple and accurate closed form expressions. Anandrao et al [9,10] studied thermal post-buckling of slender as well as shear flexible FGM columns using the classical Rayleigh-Ritz and the finite element method. Raju and Rao [11] studied thermal post-buckling of tapered columns using finite element method.…”

Section: Introductionmentioning

confidence: 99%

Thermal post-buckling of slender composite and FGM columns through a simple and novel FE formulation

Rao¹,

Anandrao

Gupta

2016

Sādhanā

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A simple and novel finite element (FE) formulation is proposed to study the thermal post-buckling of composite and FGM columns with axially immovable ends and operating in severe thermal environment. A linear eigenvalue analysis gives the critical buckling temperature but practically the buckled columns can withstand additional thermal load beyond critical temperature, which can be obtained using von-Karman geometric nonlinearity, applicable for moderately large deflections. In the present study, the solution of the nonlinear post-buckling problem is obtained by treating it as a linear eigenvalue problem using the concept of effective stiffness. Here, the total degrees of freedom (dof) of the discretized column are reduced and the postbuckling load is obtained without the need for iterative analysis. Comparison of the numerical results obtained from this FE formulation is in very good agreement with those obtained from the earlier FE formulations.

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Section: Introductionmentioning

confidence: 99%

Thermal post-buckling of slender composite and FGM columns through a simple and novel FE formulation

Rao¹,

Anandrao

Gupta

2016

Sādhanā

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“…Kocatürk and Akbaş [2012] investigated the post-buckling behavior of FG Timoshenko beams by using Total Langragian finite element approximation. Anandrao et al [2012a] studied Large amplitude free vibration and thermal post-buckling of shear flexible FG Timoshenko beams by using finite element method. Zhao et al [2012] analyzed the post-buckling behavior of right movable simply supported FGM beam subjected to nonconservative forces and in-plane thermal loading Based on the Kirchhoff large deformation theory.…”

Section: Introductionmentioning

confidence: 99%

Post-Buckling Analysis of Axially Functionally Graded Three-Dimensional Beams

Akbaş

2015

Int. J. Appl. Mechanics

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Post-buckling analysis of an axially functionally graded (AFG) cantilever beam subjected to an axial nonfollower compression load is studied in this paper by using the total Lagrangian finite element model of three-dimensional continuum approximations. Material properties of the beam change in the axial direction according to a powerlaw function. In this study, finite element model of the beam is constructed by using total Lagrangian finite element model of three-dimensional continuum for an eight-node quadratic element. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations. The obtained results are compared with the published results. In this study, the effects of the material distribution on the post-buckling response of the AFG beam are investigated in detail. The differences between of material distributions are investigated in the post-buckling analysis. Numerical results show that the above-mentioned effects play a very important role on the post-buckling responses of the beam, and it is believed that new results are presented for post-buckling of AFG beams which are of interest to the scientific and engineering community in the area of FGM structures.

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“…In a recent study by , free and forced vibrations of cracked FG beams subjected to an axial force and a moving load were investigated by using the modal expansion technique. Anandrao et al (2012) studied the free vibration and thermal post-buckling of shear flexible FGM beams using finite element formulation based on first order Timoshenko beam theory by considering classical boundary conditions. Tajalli et al (2013) developed a formulation for Timoshenko beams made of functionally graded materials based on the strain gradient theory, and investigated the static bending and free vibration of a FG simply supported beam.…”

Section: Introductionmentioning

confidence: 99%

Vibration analysis of functionally graded material (FGM) grid systems

Darılmaz¹

2015

Steel Compos. Struct.

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The paper considers the free vibration analysis of FGM grid systems. Up to now, very little work has been done on this type of system and the paper aspires to fill this gap. Based on the hybrid-stress finite element formulation free vibration solutions for FGM grid systems of various aspect ratios, different types of gradations functions, and support conditions are determined. The tabulation of these results, not available thus far, should be useful to designers and researchers who may use them.

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Non-linear free vibrations and post-buckling analysis of shear flexible functionally graded beams

Cited by 11 publications

References 27 publications

Thermal post-buckling of slender composite and FGM columns through a simple and novel FE formulation

Thermal post-buckling of slender composite and FGM columns through a simple and novel FE formulation

Post-Buckling Analysis of Axially Functionally Graded Three-Dimensional Beams

Vibration analysis of functionally graded material (FGM) grid systems

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