On buckling of a thin plate on an elastomeric foundation

Mukherjee, Bikramjit; Dillard, David A.

doi:10.1016/j.ijmecsci.2017.10.015

Cited by 11 publications

(17 citation statements)

References 17 publications

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“…The buckling force N, may result from the thermal expansion of a constrained beam, or directly come from an applied mechanical loading. As commonly assumed, [9,36,[42][43][44] the axial displacement u x of the beam is neglected.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…From the balance of the force and the moment, the differential relation between the upward vertical deflection of the beam u y , the buckling force N, and the lateral normal stress provided by the elastic layer y can be written as [36] = − d 4…”

Section: The Governing Differential Equation For the Beammentioning

confidence: 99%

“…Assuming the beam is perfectly bonded on the top of the elastic layer and its axial displacement u x is negligible, [9,36,[42][43][44] on the upper-surface of the elastic layer one gets a Kerr-type differential relation (see appendix for the derivation details)…”

Section: The Kerr-type Differential Relation For the Elastic Layermentioning

confidence: 99%

“…where n is an integer and n > 3, A l and B l are dimensionless non-negative real constants dependent on the Poisson's ratio of the elastic layer. If the layer's lower-surface is bonded on a rigid substrate as considered in [36],…”

Section: The Kerr-type Differential Relation For the Elastic Layermentioning

confidence: 99%

“…[4,6,7,11,17,[23][24][25][26][27][28][29][30][31][32][33][34] Dillard proposed an incompressible elastomeric foundation model, [35] which was recently employed in the analysis of the buckling of a laterally supported beam. [36] To obtain a precise critical buckling force theoretically, it is essential to find a suitable elastic foundation model which is able to accurately describe the mechanical response of the elastic layer. Therefore, the Kerr-type model, [22] which has been employed to study the indentation [37][38][39][40] and the wrinkling [41] of an elastic film, is developed in this work.…”

Section: Introductionmentioning

confidence: 99%

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A Kerr‐type elastic foundation model for the buckling analysis of a beam bonded on an elastic layer

Zhang

2019

Z Angew Math Mech

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A Kerr-type elastic foundation model is proposed to study the buckling of a beam bonded on the top of a linear elastic layer. The layer's lower-surface is either bonded or sliding on a rigid substrate. The present Kerr-type model provides a linear differential relation between the pressure and the normal deflection of the layer's upper-surface, and reduces to the existing foundation models when high-order differential relations are neglected. The critical buckling force is then obtained for both an infinitely long beam and a simply-supported beam of finite length, based on a simple formula which is valid for both a compressible and an incompressible layer. Reasonable agreement with the existing numerical results and our finite element results shows that the present model has the capability to capture the support effect of the elastic layer, and can be used to study the buckling or the bending of a beam bonded on an elastic layer. K E Y W O R D Sbeam buckling, critical buckling force, elastic foundation, elastic layer, Kerr-type model

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: The Governing Differential Equation For the Beammentioning

confidence: 99%

Section: The Kerr-type Differential Relation For the Elastic Layermentioning

confidence: 99%

Section: The Kerr-type Differential Relation For the Elastic Layermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Kerr‐type elastic foundation model for the buckling analysis of a beam bonded on an elastic layer

Zhang

2019

Z Angew Math Mech

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Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Zhang

Ullah

et al. 2020

Z Angew Math Mech

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This paper investigates the classical buckling problem of rectangular thin plates with two opposite edges free and others rotationally restrained by the finite Fourier integral transform method. The rotationally restrained edges are typically practical boundary conditions in many engineering structures, such as bridge decks. However, these non‐classic edges bring mathematical difficulties in solving boundary value problems of governing partial differential equations of plate. Based on the integral transform theory, the title problem is transformed into solving regular linear algebraic simultaneous equations, which provides a more rational and theoretical solution process than traditional inverse/semi‐inverse approaches. The acquired comprehensive results of critical buckling load factors and mode shapes are in excellent agreement with the ones obtained by finite element method, which verifies the validity and accuracy of the present approach. In addition, classical boundary conditions, such as simply supported and clamped edges, can be investigated by choosing different rotational fixity factors. Furthermore, the features of the employed method that no preselection of trial function and the generality for various boundary conditions enable one to analytically solve static problems for moderately thick plates and thick plates.

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Reprogrammable flexible mechanical metamaterials

Zheng

Uto

et al. 2022

Applied Materials Today

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On buckling of a thin plate on an elastomeric foundation

Cited by 11 publications

References 17 publications

A Kerr‐type elastic foundation model for the buckling analysis of a beam bonded on an elastic layer

A Kerr‐type elastic foundation model for the buckling analysis of a beam bonded on an elastic layer

Buckling analysis of rectangular thin plates with two opposite edges free and others rotationally restrained by finite Fourier integral transform method

Reprogrammable flexible mechanical metamaterials

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