Uni-directional buckling of a pinned elastica with external pressure

Plaut, Raymond H.; Mróz, Z.

doi:10.1016/0020-7683(92)90196-z

Cited by 13 publications

(4 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One common simplification when addressing these types of problems is the assumption that the medium, being a beam or a plate, is infinite. The buckling of a unilaterally constrained infinite beam (thin strip) was addressed by many investigators (Allan, 1968 ;Anderson, 1972 ;Yun and Kyriakides, 1983 ;Wang, 1984a,b ;Hobbs, 1985 ;Roorda, 1988 ; Plaut and Mroz, 1992), and it was shown that such a system is completely imperfectionsensitive, with theoretically infinite buckling load in the absence of imperfections or weightlessness. An analysis to extend the classic variational theory for eigenvalue problems so as to define the Euler critical load of a unilaterally constrained beam is presented in Villaggio (1979).…”

Section: Introductionmentioning

confidence: 99%

A mechanical model for the buckling of unilaterally constrained rectangular plates

Waas

1994

International Journal of Solids and Structures

View full text Add to dashboard Cite

A mechanical model is described for the problem of buckling of unilaterally constrained, finite, rectangular plates. Due to the nature of the imposed constraint on the plate's lateral deflection, w, solving for the buckling load required the solution of a nonlinear partial differential equation in w. While the plates were modeled along the lines of classical plate theory, the nonlinearity arose from the fact that the plates were attached to nonlinear elastic foundations exhibiting a deformation sign dependent force-displacement relationship. This feature was introduced to model the unilateral constraint. The influence of different boundary conditions, material orthotropy and transverse load distributions was investigated. For each case, the weak form of the governing differential equation was solved via the Galerkin's method. Investigations of the buckling loads of rectangular plates attached to such foundations and subjected to a uniform inplane stress field showed the validity of this approach for the cases investigated and compared to some previous exact results reported in the literature. NOMENCLATURE generalized displacement (Galerkin's) coefficients (also denoted A) generalized displacement coefficients at I = 0 and Q(x, y) # 0 @ate-bending stiffnesses D,lD, I foundation force pre-buckling inplane loads q(-%9))b4/6,h strain energy density of the elastic foundation plate's dimension in the &direction plate's dimension in the jjdirection displacement function that characterizes the foundation model plate's thickness stiffness parameter transverse load length coordinate E [0, a]

show abstract

Section: Introductionmentioning

confidence: 99%

A mechanical model for the buckling of unilaterally constrained rectangular plates

Waas

1994

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…Other related problems include blow-up of concrete pavements [3], buckling of rock strata [4], growth oflarninations in composite materials [5], and bulging of sheets of paper, textiles, plastics, or metals. Reference [6] treats the same problem as considered here except that the mechanism is replaced by a continuous elastic beam. …”

Section: Introductionmentioning

confidence: 98%

Upheaval Buckling of a Mechanism under External Pressure and Compressive Loading

Plaut

Mróz

1994

International Journal of Mechanical Engineering Education

Self Cite

View full text Add to dashboard Cite

A mechanical or structural element often buckles when it is compressed beyond a certain amount. Constraints may raise the value of the critical compressive load. In some cases a constraint may completely prevent the occurrence of buckling. This situation is demonstrated here by a simple twobar model that rests on a rigid foundation and is subjected to pressure and compressive loading. If the system is 'perfect', buckling is not possible. However, if the foundation is not flat, or if the load is applied eccentrically, a sudden jump in deflection may occur as the load is increased.

show abstract

“…Wang [8,9,10] investigated extensively the behavior of a heavy elastica, finite or infinitely long, on a rigid foundation. Plaut and Mró z [2] studied the effects of initial curvature and load eccentricity on the deformation of a pinned heavy elastica on a rigid surface. Kublanov and Bottega [3] calculated the deformation of a thin buckled film on a flat substrate under a point force at the tip.…”

Section: Introductionmentioning

confidence: 99%

Deformation and stability of an elastica under a point force and constrained by a flat surface

Chen

2011

International Journal of Mechanical Sciences

View full text Add to dashboard Cite

Uni-directional buckling of a pinned elastica with external pressure

Cited by 13 publications

References 21 publications

A mechanical model for the buckling of unilaterally constrained rectangular plates

A mechanical model for the buckling of unilaterally constrained rectangular plates

Upheaval Buckling of a Mechanism under External Pressure and Compressive Loading

Deformation and stability of an elastica under a point force and constrained by a flat surface

Contact Info

Product

Resources

About