Exact Solutions for Buckling of Structural Members

Wang, Chen; Wang, C. Y.; Reddy, J. N.

doi:10.1201/9780203483534

Cited by 226 publications

(199 citation statements)

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“…The solutions may be specialized for CNT by assuming that it is a hollow cylinder, i.e., the CNT is viewed as a thin-walled circular tube. 10 Consider the mass and stiffness properties of SWCNT that is viewed as a thin-walled circular tube,…”

Section: Introductionmentioning

confidence: 99%

“…For such small beamlike structures, many researchers have applied the nonlocal elasticity concept for the bending, buckling and vibration analyses. 2,6,[8][9][10][11][12][13] Recently, Wang et al 7 derived the closed form solutions for the free vibration problem of nanobeams using the nonlocal Timoshenko beam theory. The solutions may be specialized for CNT by assuming that it is a hollow cylinder, i.e., the CNT is viewed as a thin-walled circular tube.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics

Duan¹,

Wang²,

Zhang³

2007

Journal of Applied Physics

339

146

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In this paper, the small scaling parameter e0 of the nonlocal Timoshenko beam theory is calibrated for the free vibration problem of single-walled carbon nanotubes (SWCNTs). The calibration exercise is performed by using vibration frequencies generated from molecular dynamics simulations at room temperature. It was found that the calibrated values of e0 are rather different from published values of e0. Instead of a constant value, the calibrated e0 values vary with respect to length-to-diameter ratios, mode shapes, and boundary conditions of the SWCNTs. In addition, the physical meaning of the scaling parameter is explored. The results show that scaling parameter assists in converting the kinetic energy to the strain energy, thus enabling the kinetic energy to be equal to the strain energy. The calibrated e0 presented herein should be useful for researchers who are using the nonlocal beam theories for analysis of micro and nano beams/rods/tubes.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics

Duan¹,

Wang²,

Zhang³

2007

Journal of Applied Physics

339

146

View full text Add to dashboard Cite

show abstract

“…Derivation of governing equations related to stability analysis is given in detail in Timoshenko and Gere [5], Simitses and Hodges [6], and Wang et al [8]. The reader can also refer to any textbook related to the subject.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Iyengar [7] made some analysis on buckling of uniform with several elastic supports. Wang et al [8] have given exact mathematical solutions for buckling of structural members for various cases of columns, beams, arches, rings, plates and shells. Ermopoulos [9] found the solution for buckling of tapered bars axially compressed by concentrated loads applied at various locations along their axes.…”

Section: Introductionmentioning

confidence: 99%

Elastic Stability Analysis of Euler Columns Using Analytical Approximate Techniques

Coşkun¹,

Öztürk²

2012

Advances in Computational Stability Analysis

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“…They considered a rotational spring in lieu of the built-in end so that the solution may be tuned from the simply supported-clamped to the simply supported. A treatment of the buckling problem on the elastica of the column can also be found in [8][9][10][11].…”

Section: Introductionmentioning

confidence: 99%

Buckling and post‐buckling of a nonlinearly elastic column

Brojan¹,

Puksic²,

Kosel³

2007

Z Angew Math Mech

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The classical problem of buckling of an inextensible elastic column, under the action of a compressive force is examined. The column is made of nonlinearly elastic material for which the stress-strain relation is represented by the Ludwick constitutive law. An approximative formula for determination of the force at immediate post-buckling is given. Further post-buckling solutions are obtained for different values of the nonlinearity parameter by numerical integration using the Runge-Kutta-Fehlberg algorithm, and are presented in non-dimensional diagrams. It is shown that no bifurcation point is found in the case of nonlinearly elastic column. Key words stability, post-buckling, material nonlinearity, large deflections, critical force, Ludwick formula, bifurcation, limit load, finite disturbance buckling The classical problem of buckling of an inextensible elastic column, under the action of a compressive force is examined. The column is made of nonlinearly elastic material for which the stress-strain relation is represented by the Ludwick constitutive law. An approximative formula for determination of the force at immediate post-buckling is given. Further post-buckling solutions are obtained for different values of the nonlinearity parameter by numerical integration using the Runge-Kutta-Fehlberg algorithm, and are presented in non-dimensional diagrams. It is shown that no bifurcation point is found in the case of nonlinearly elastic column.

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Exact Solutions for Buckling of Structural Members

Cited by 226 publications

References 0 publications

Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics

Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics

Elastic Stability Analysis of Euler Columns Using Analytical Approximate Techniques

Buckling and post‐buckling of a nonlinearly elastic column

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