On the existence of equilibrium states of an elastic beam on a nonlinear foundation

Elgindi, M. B. M.; Yen, David H. Y.

doi:10.1155/s0161171293000225

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…Similar techniques are valid for the other boundary conditions. This way, we extend the results established in [14] and [15] to the graphene beam with nonlinear support.…”

Section: Introductionsupporting

confidence: 75%

On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load

Elgindi¹,

Wei²,

Soukiassian³

et al. 2014

WJET

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In this paper, we consider the buckling of an Euler-Bernoulli graphene beam due to an axial compressive load. We formulate the problem as a non-linear (eigenvalue) two-point boundary value problem, prove some properties of the eigenpairs and introduce a suitable numerical shooting method scheme for approximating them. We present the perturbation and the numerical approximations of the first and second buckling loads and the corresponding shapes.

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“…Similar techniques are valid for the other boundary conditions. This way, we extend the results established in [14] and [15] to the graphene beam with nonlinear support.…”

Section: Introductionsupporting

confidence: 75%

On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load

Elgindi¹,

Wei²,

Soukiassian³

et al. 2014

WJET

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“…The reader is referred to [1], [3] and [4] and the references therein for an extensive account on the subject. In all these works the necessary coercivity condition, which ensures the existence of solutions, was derived from the linear parts of the equations.…”

Section: Introductionmentioning

confidence: 99%

On the global solvability of a class of fourth‐order nonlinear boundary value problems

Elgindi

Guan

1997

International Journal of Mathematics and Mathematical Sciences

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ABSTRACT. This paper is concerned with the global solvability of a class of fourth-order nonlinear boundary value problems that govern the deformation of an elastic beam which is acted upon by axial compression, lateral forces and is in contact with a semi-infinite medium acting as a foundation For certain ranges of the acting axial compression force, the solvability of the equations follows from the coerciVity of their linear parts. Beyond these ranges this coercivity is lost It is shown here that the coercivity which ensures the global solvability can be generated by the nonlinear parts ofthe equations for a certain type offoundation.KEY WORDS AND PHRASES: Global solvability, fourth-order nonlinear boundary value problems, homogeneous nonlinearity, Leray-Schauder fixed point theorem, coercivity 1991 AMS SUBJECT CLASSIFICATION CODES: 49G99, 73H05, 73K15.

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On the existence of equilibrium states of an elastic beam on a nonlinear foundation

Cited by 2 publications

References 5 publications

On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load

On the Buckling of Euler Graphene Beams Subject to Axial Compressive Load

On the global solvability of a class of fourth‐order nonlinear boundary value problems

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