Buckling of wide struts/plates resting on isotropic foundations

Sironic, L; Murray, N.W.; Grzebieta, Raphael

doi:10.1016/s0263-8231(99)00029-4

Cited by 8 publications

(7 citation statements)

References 6 publications

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“…Analogous to (2) the buckling coefficient k for a simply supported plate on a Pasternak foundation can be expressed as [10,11] where the foundation parameter f P and the foundation shear stiffness are defined as [11,18] By minimising k for m as before the critical wavelength and buckling coefficient become…”

Section: Two-parameter or Pasternak Foundation Approachmentioning

confidence: 99%

Buckling of laser-welded sandwich panels. Part 1: Elastic buckling parallel to the webs

Kolsters

Zenkert

2006

Proceedings of the Institution of Mechanical Engineers, Part M:

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This is the first of three companion papers which examine the elastic buckling and collapse of laser-welded sandwich panels with an adhesively bonded core and uni-directional vertical webs. In compression parallel to the webs the face sheet in between two webs can be treated as a long rectangular plate supported at the sides and resting on a continuous elastic foundation. Using a generalised form of the Kirchoff equation the plate buckling load is evaluated for a Winkler and Pasternak foundation, and for a foundation model where the core is characterised by an elastic halfspace. Although the elastic half-space model is most sophisticated in the way that the decay of transverse stress through the core is described, it requires that the buckling load is calculated iteratively and is therefore not suitable for engineering applications. In contrast, the Pasternak foundation model is able to demonstrate the effect of different boundary conditions at the laser weld and different core properties by the variation of a simple clamping factor and two foundation moduli. By changing the clamping factor the model can be used to describe plate buckling as well as wrinkling, and by varying the foundation moduli it is possible to distinguish between symmetrical and anti-symmetrical buckling modes. Evaluation of the buckling solution shows that for low modulus core materials the plate buckling strength is determined only by the boundary conditions at the laser weld, while for high modulus materials anti-symmetrical wrinkling dominates. To improve the accuracy of the solution for non-standard configurations the foundation moduli are calibrated using the elastic half-space model and finite element results as a reference. It is found that by using a smaller Winkler foundation modulus the accuracy and consistency of the Pasternak model are improved considerably. However, the results also show that for current sandwich configurations the proportional limit of the face plate material is usually reached well before elastic buckling occurs. All experimental work is therefore delegated to the third paper, which deals with extension of the Pasternak foundation model into the elasto-plastic regime and non-linear finite element modeling.

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Section: Two-parameter or Pasternak Foundation Approachmentioning

confidence: 99%

Buckling of laser-welded sandwich panels. Part 1: Elastic buckling parallel to the webs

Kolsters

Zenkert

2006

Proceedings of the Institution of Mechanical Engineers, Part M:

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“…This model is suitable for foundation materials with relatively great shear sti®ness, including relatively deep foundations. 4,13 For a plate with out-of-plane de°ection w, the Pasternak foundation o®ers a restoring forceq, given by 14…”

Section: Buckling Modelmentioning

confidence: 99%

Buckling of a Plate on a Pasternak Foundation Under Uniform in-Plane Bending Loads

Briscoe

Mantell

Davidson

2013

Int. J. Str. Stab. Dyn.

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In-plane bending loads occur in many thin-walled structures, including web core sandwich panels (foam-¯lled panels with interior webs) under transverse loading. The design of such structures is limited in part by local buckling of the thin webs and the subsequent impact on sti®ness and strength. However, the core material can have a signi¯cant impact on web buckling strength and thus must be considered in design. This paper presents solutions for the buckling strength of simply supported plates under in-plane bending loads. The location of the neutral bending axis is allowed to vary and is characterized by a load parameter. A Pasternak model is used to account for the resistance of the foundation to compression and shear. Using the principle of minimum potential energy, buckling solutions are developed for in¯nitely long plates and representative foundation materials. The solutions match known results for two special cases: Uniform loading with variable foundation, and bending loads with no foundation. An order of magnitude increase in buckling strength is possible, depending on loading and foundation sti®ness. The results suggest an important avenue for future development of lightweight structures, including sandwich panels and structures such as plate girders that are not typically associated with the use of foam¯lling.

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“…This deformation pattern is transferred to the top surface of the foundation. If the bottom surface of the foundation is fixed at z=H, the displacement in the foundation decays with distance from the beam according to a function of the form [17] w ¼ ½A coshðpz=LÞþB sinhðpz=LÞW;…”

Section: Foundation Stiffness Modelmentioning

confidence: 99%

“…Foundation constants can be deduced from the results by solving for the governing equations at the plate surface. More recently, Sironic et al [17] used the Airy's stress functions to solve for the displacement field within the foundation layer. They found that the model in Refs.…”

Section: Introductionmentioning

confidence: 99%

Shear buckling in foam-filled web core sandwich panels using a Pasternak foundation model

Briscoe

Mantell

Davidson

2010

Thin-Walled Structures

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Buckling of wide struts/plates resting on isotropic foundations

Cited by 8 publications

References 6 publications

Buckling of laser-welded sandwich panels. Part 1: Elastic buckling parallel to the webs

Buckling of laser-welded sandwich panels. Part 1: Elastic buckling parallel to the webs

Buckling of a Plate on a Pasternak Foundation Under Uniform in-Plane Bending Loads

Shear buckling in foam-filled web core sandwich panels using a Pasternak foundation model

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