Postbuckling behavior of infinite beams on elastic foundations using Koiter's improved theory

Existence and uniqueness of nonlinear deflections of an infinite beam resting on a non-uniform nonlinear elastic foundation

“…The analysis of the problem is thus of interest to many mechanical, civil engineers and, so on: a number of researchers have made their contributions to the problem. For example, from a very early time, the problem of a linear elastic beam resting on a linear elastic foundation and subjected to lateral forces, was investigated by many techniques [1][2][3][4][5][6][7][8].…”

Analytic postbuckling solution of a pre-stressed infinite beam bonded to a linear elastic foundation

“…This consistent relative error is attributed to nonlinear effects that are included in the numerical simulation but are not considered in (1) (e.g. curvature nonlinearity (Hui, 1988)). When shear effects are considered in the finite element simulation, the minimal relative error is of the order of $0.86%, which may still be considered small.…”

“…In some previous studies the elastic beam was assumed to be inextensible (Hui, 1988;Wadee et al, 1997;Wu and Zhong, 1999). In the case of very long (or infinite) beams, this assumption may result in a mechanical inconsistency in the sense that at the edges (or at infinity), the shear deformation of the elastic foundation is exceedingly large (unbounded).…”

“…In the last two decades many studies of the postbuckling response of a beam that is bonded to an elastic foundation were presented (Kerr, 1980;Tvergaard and Needleman, 1981;Hui, 1988;Hunt et al, 1989;Hunt et al, 1996;Wadee et al, 1997;Hunt and Wadee, 1998;Wu and Zhong, 1999;Everall and Hunt, 2000;Tvergaard and Needleman, 2000;Wadee and Bassom, 2000;Chen and Baker, 2003;Rao and Raju, 2003). In these studies the nonlinear postbuckling response was solved numerically or by approximated analytic methods.…”

An efficient method for the static deflection analysis of an infinite beam on a nonlinear elastic foundation of one-way spring model

“…It is always fascinating to find the closed form solution, some authors constructed closed-form solutions for the static and dynamic response of a uniform beam resting on a linear elastic foundation [1][2][3] and others proposed closed-form solution under the linearity assumption by using Green's function technique [4][5][6][7]. The static, dynamic and elastic stability analysis of a beam resting on a nonlinear elastic foundation was discussed by Beaufait and Hoadley [8], Massalas [9], Lakshmanan [10], and Hui [11], and by the same author and co-authors [12][13][14][15].…”