Elastic contact of a stiff thin layer and a half-space

Kaplunov, Julius; Приказчиков, Д. А.; Sultanova, L. B.

doi:10.1007/s00033-018-1068-9

Cited by 12 publications

(5 citation statements)

References 21 publications

(36 reference statements)

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“…Moreover, bending deformation may occur only for a relatively soft foundation. Otherwise, the beam itself behaves as an elastic foundation according to the Winkler assumption, see, e.g., the results of the multiparametric analysis in [27].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

Erbaş

Kaplunov

Elishakoff

2021

Mathematics and Mechanics of Solids

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A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

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Section: Introductionmentioning

confidence: 99%

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

Erbaş

Kaplunov

Elishakoff

2021

Mathematics and Mechanics of Solids

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show abstract

“…It is then tempting to model the response of the layer using the Timoshenko beam theory but still model the response of the half-space using the Winkler assumption. This possibility has indeed been analysed by Erbas et al (2022) for the dynamic case without prestress; see also Kaplunov et al (2019). Adapting equation ( 17) in Goldenveizer et al (1993) to our static case, we obtain…”

Section: Introductionmentioning

confidence: 59%

A refined model for the buckling of film/substrate bilayers

Wang¹,

Liu²,

Fu³

2022

Preprint

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The classical reduced model for a film/substrate bilayer is one in which the film is governed by the Euler-Bernoulli beam equation and the substrate is replaced by an array of springs (the so-called Winkler foundation assumption). We derive a refined model in which the normal and shear tractions at the bottom of the film are expressed in terms of the corresponding horizontal and vertical displacements, and the response of the half-space is described by the exact theory. The self-consistency of the refined model is confirmed by showing that it yields a four-term (in the incompressible case) or six-term (in the compressible case) expansion for the critical strain that agrees with the expansion given by the exact theory.

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“…It is then tempting to model the response of the layer using the Timoshenko beam theory but still model the response of the half-space using the Winkler assumption. This possibility has indeed been analysed by Erbas et al [38] for the dynamic case without prestress (see also [39]). Adapting equation (17) in Goldenveizer et al [40] to our static case, we obtain…”

Section: Introductionmentioning

confidence: 74%

A refined model for the buckling of film/substrate bilayers

Wang¹,

Liu²,

Fu³

2022

Mathematics and Mechanics of Solids

View full text Add to dashboard Cite

The classical reduced model for film/substrate bilayers is the one in which the film is governed by the Euler–Bernoulli beam equation, and the substrate is replaced by an array of springs (the so-called Winkler foundation assumption). We derive a refined model in which the normal and shear tractions at the bottom of the film are expressed in terms of the corresponding horizontal and vertical displacements, and the response of the half-space is described by the exact theory. The self-consistency of the refined model is confirmed by showing that it yields a four-term (in the incompressible case) or six-term (in the compressible case) expansion for the critical strain that agrees with the expansion given by the exact theory.

show abstract

Elastic contact of a stiff thin layer and a half-space

Cited by 12 publications

References 21 publications

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

A refined model for the buckling of film/substrate bilayers

A refined model for the buckling of film/substrate bilayers

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