Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates

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Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates. / Nazarov, S. A.; Chechkin, G. A.

In: Journal of Mathematical Sciences (United States), Vol. 210, No. 4, 2015, p. 399-428.

Research output: Contribution to journal › Article › peer-review

Author

Nazarov, S. A. ; Chechkin, G. A. / Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates. In: Journal of Mathematical Sciences (United States). 2015 ; Vol. 210, No. 4. pp. 399-428.

BibTeX

@article{2011c07aca97417a92ca3becb5042bd5,

title = "Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates",

abstract = "In a thin isotropic homogeneous three-dimensional plate of thickness h, we consider the limit passage of elastic fields as h → +0. It is assumed that the connected component ΓNof the boundary of the median cross section ω is a broken line with links of length ah, where a > 0 is a fixed parameter. We consider the Lam{\'e} equations with the Neumann condition (a free surface) on the plate bases, the Dirichlet condition (a rigidly clamped surface) on a smooth part, and some linear contact conditions on a ribbed part of the lateral surface. For the solution to the boundary value problem we obtain an asymptotic expansion with different boundary layers. In the two-dimensional model, new boundary conditions, different from the contact ones, arise on the limit smooth contour Γ0, thereby for the spatial elasticity problem, we confirm the Babu{\v s}ka paradox caused by linear boundary conditions on the plate edge, but not unilateral constraints of Signorini type. Bibliography: 42 titles. Illustrations: 5 figures.",

keywords = "Dirichlet condition, Unilateral Constraint, Rigid Displacement, Asymptotic Term, Limit Passage",

author = "Nazarov, {S. A.} and Chechkin, {G. A.}",

note = "Nazarov, S.A., Chechkin, G.A. Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates. J Math Sci 210, 399–428 (2015). https://doi.org/10.1007/s10958-015-2573-4",

year = "2015",

doi = "10.1007/s10958-015-2573-4",

language = "English",

volume = "210",

pages = "399--428",

journal = "Journal of Mathematical Sciences",

issn = "1072-3374",

publisher = "Springer Nature",

number = "4",

}

RIS

TY - JOUR

T1 - Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates

AU - Nazarov, S. A.

AU - Chechkin, G. A.

N1 - Nazarov, S.A., Chechkin, G.A. Approximation of Thin Three-Dimensional Plates with Smooth Lateral Surface by Polygonal Plates. J Math Sci 210, 399–428 (2015). https://doi.org/10.1007/s10958-015-2573-4

PY - 2015

Y1 - 2015

N2 - In a thin isotropic homogeneous three-dimensional plate of thickness h, we consider the limit passage of elastic fields as h → +0. It is assumed that the connected component ΓNof the boundary of the median cross section ω is a broken line with links of length ah, where a > 0 is a fixed parameter. We consider the Lamé equations with the Neumann condition (a free surface) on the plate bases, the Dirichlet condition (a rigidly clamped surface) on a smooth part, and some linear contact conditions on a ribbed part of the lateral surface. For the solution to the boundary value problem we obtain an asymptotic expansion with different boundary layers. In the two-dimensional model, new boundary conditions, different from the contact ones, arise on the limit smooth contour Γ0, thereby for the spatial elasticity problem, we confirm the Babuška paradox caused by linear boundary conditions on the plate edge, but not unilateral constraints of Signorini type. Bibliography: 42 titles. Illustrations: 5 figures.

AB - In a thin isotropic homogeneous three-dimensional plate of thickness h, we consider the limit passage of elastic fields as h → +0. It is assumed that the connected component ΓNof the boundary of the median cross section ω is a broken line with links of length ah, where a > 0 is a fixed parameter. We consider the Lamé equations with the Neumann condition (a free surface) on the plate bases, the Dirichlet condition (a rigidly clamped surface) on a smooth part, and some linear contact conditions on a ribbed part of the lateral surface. For the solution to the boundary value problem we obtain an asymptotic expansion with different boundary layers. In the two-dimensional model, new boundary conditions, different from the contact ones, arise on the limit smooth contour Γ0, thereby for the spatial elasticity problem, we confirm the Babuška paradox caused by linear boundary conditions on the plate edge, but not unilateral constraints of Signorini type. Bibliography: 42 titles. Illustrations: 5 figures.

KW - Dirichlet condition

KW - Unilateral Constraint

KW - Rigid Displacement

KW - Asymptotic Term

KW - Limit Passage

UR - http://www.scopus.com/inward/record.url?scp=84944698977&partnerID=8YFLogxK

U2 - 10.1007/s10958-015-2573-4

DO - 10.1007/s10958-015-2573-4

M3 - Article

AN - SCOPUS:84944698977

VL - 210

SP - 399

EP - 428

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -

ID: 41040409