Post-buckling analysis of composite beams: Simple and accurate closed-form expressions

Gupta, Rekha; Gunda, Jagadish Babu; Janardhan, G. Ranga; Rao, G. Venkateswara

doi:10.1016/j.compstruct.2009.12.010

Cited by 51 publications

(26 citation statements)

References 16 publications

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“…Solutions of Eqs. (20)(21)(22) provide the critical buckling loads at k th order, 7 5 4 3 5 2 2 2 2 2 2 2 2 6 3 2 7 2 8 9 6 9 3 2 2 2 2 2 2 2 2 2 2 2 11 12 13 2 2 22 10 2 -36 17 -156 -498 +3120 -4284 +1800 ( -1) ln ( 2 3 2 3 2 3 3 1 1 1 1 1 1 1 1 1 1 2 4 3 2 5 4 4 3 1 1 1 1 1 1 1 1 1 1 2 2 2 1 1 1 1 1 10 +39 -30 +3 -9 +18 -10 ln(1-) -8 11 -141 +294 -162 ( -1) ln (1-)…”

Section:  mentioning

confidence: 99%

“…determination of critical load for a known material property and geometry, is still a challenging one. Yet, there are valuable contributions in the modern literature, such as the ones by Ruta et al [17,18], based on a onedimensional model for thin-walled beams [19], which provides exact solution to critical loads in closed-form, by Gupta et al [20] for post-buckling behavior of laminated beams, Mercan and Civalek [21] for critical load of nanobeams, and Abbondanza et al [22] for vibration frequencies and buckling loads of nanobeams. In addition, there are numerous studies which focus on numerical solutions of such problems, which ensures required accuracy for engineering applications when tackled the numerical problems, such as locking, but lack generality as they require the numerical values of the parameters of the problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Eroğlu

Tüfekçi

2018

International Journal of Engineering and Applied Sciences

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This study aims to derive approximate closed-form solutions for critical loads of straight beams with variable cross-section. The governing equations are derived for purely flexible beam for small displacements and rotation and turned into non-dimensional form. Approximate solutions to the set of equations for stability problems are searched by Variational Iteration Method with Generalized Lagrange Multipliers. It turns out that highly accurate approximate buckling loads for cantilever beams with constant or variable section can be obtained in closed-form. Many novel closed-form solutions for critical load of such structures, which may serve as benchmark solutions, are presented.

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Section:  mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Eroğlu

Tüfekçi

2018

International Journal of Engineering and Applied Sciences

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“…He solved the problem using the Ritz method with the polynomial series and showed that some cross-ply beams buckle upon cooling rather than heating and some of them do not buckle regardless of whether they are heated or cooled. Gupta et al [5] applied the Rayleigh-Ritz technique to obtain closed-form expressions for the postbuckling of composite beams subject to different boundary conditions with axially immovable ends. Baghani et al [6] used the variational iteration method to investigate the postbuckling of unsymmetrically laminated composite beams on a nonlinear elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Free vibration and postbuckling of laminated composite Timoshenko beams

Ansari

Shojaei

Mohammadi

et al. 2014

Science and Engineering of Composite Materials

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A numerical solution method was developed to investigate the postbuckling behavior and vibrations around the buckled configurations of symmetrically and unsymmetrically laminated composite Timoshenko beams subject to different boundary conditions. The Hamilton principle was employed to derive the governing equations and corresponding boundary conditions which are then discretized by introducing a set of matrix differential operators. The pseudo-arc-length continuation method was used to solve the postbuckling problem.To study the free vibration that takes place around the buckled configurations, the corresponding eigenvalue problem was solved by means of the postbuckling configuration modes obtained in the previous step. The static bifurcation diagrams for composite beams with different lay-up laminates are given, and it is shown that the lay-up configuration considerably affects the magnitude of critical buckling load and postbuckling behavior. The study of the vibrations of composite beams with different laminations around the buckled configurations indicates that the natural frequency in the prebuckling domain increases as the stiffness of a beam increases, while there is no specific relation between the lay-up lamination and natural frequency in the postbuckling domain which necessitates conducting an accurate analysis in this area.

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“…Gupta et al [7] carried out a comparative study of thermal post-buckling analysis of columns using an equilibrium path method and an iterative equivalent eigenvalue problem. 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.…”

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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Post-buckling analysis of composite beams: Simple and accurate closed-form expressions

Cited by 51 publications

References 16 publications

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Some closed-form solutions for buckling of straight beams with varying cross-section by Variational Iteration Method with Generalized Lagrange Multipliers

Free vibration and postbuckling of laminated composite Timoshenko beams

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

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