Edge effect in the bending of a thin three-dimensional plate

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Edge effect in the bending of a thin three-dimensional plate. / Zorin, I. S.; Nazarov, S. A.

In: Journal of Applied Mathematics and Mechanics, Vol. 53, No. 4, 01.01.1989, p. 500-507.

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

Author

Zorin, I. S. ; Nazarov, S. A. / Edge effect in the bending of a thin three-dimensional plate. In: Journal of Applied Mathematics and Mechanics. 1989 ; Vol. 53, No. 4. pp. 500-507.

BibTeX

@article{21550ae3eb664d6283f0ed0fd48de489,

title = "Edge effect in the bending of a thin three-dimensional plate",

abstract = "The boundary layer near the rigidly clamped edge of a thin three-dimensional plate subjected to bending loads is investigated. It is shown that taking account of the next term in the deflection asymptotic form results in the appearance of inhomogeneities in the boundary conditions on the plate edge. It is proved that far from the edge the difference in the solution of the problem in an invariant formulation and the three-dimensional solution is inversely proportional to the plate thickness (the error for the Kirchhoff solution is inversely proportional to the square of the thickness; near the edge the accuracies of both solutions is identical). A correction term is found in a representation of the eigenfrequencies of the bending vibrations and a comparison is made with the Reissner theory. {\textcopyright} 1990.",

author = "Zorin, {I. S.} and Nazarov, {S. A.}",

year = "1989",

month = jan,

day = "1",

doi = "10.1016/0021-8928(89)90059-2",

language = "English",

volume = "53",

pages = "500--507",

journal = "Journal of Applied Mathematics and Mechanics",

issn = "0021-8928",

publisher = "Elsevier",

number = "4",

}

RIS

TY - JOUR

T1 - Edge effect in the bending of a thin three-dimensional plate

AU - Zorin, I. S.

AU - Nazarov, S. A.

PY - 1989/1/1

Y1 - 1989/1/1

N2 - The boundary layer near the rigidly clamped edge of a thin three-dimensional plate subjected to bending loads is investigated. It is shown that taking account of the next term in the deflection asymptotic form results in the appearance of inhomogeneities in the boundary conditions on the plate edge. It is proved that far from the edge the difference in the solution of the problem in an invariant formulation and the three-dimensional solution is inversely proportional to the plate thickness (the error for the Kirchhoff solution is inversely proportional to the square of the thickness; near the edge the accuracies of both solutions is identical). A correction term is found in a representation of the eigenfrequencies of the bending vibrations and a comparison is made with the Reissner theory. © 1990.

AB - The boundary layer near the rigidly clamped edge of a thin three-dimensional plate subjected to bending loads is investigated. It is shown that taking account of the next term in the deflection asymptotic form results in the appearance of inhomogeneities in the boundary conditions on the plate edge. It is proved that far from the edge the difference in the solution of the problem in an invariant formulation and the three-dimensional solution is inversely proportional to the plate thickness (the error for the Kirchhoff solution is inversely proportional to the square of the thickness; near the edge the accuracies of both solutions is identical). A correction term is found in a representation of the eigenfrequencies of the bending vibrations and a comparison is made with the Reissner theory. © 1990.

UR - http://www.scopus.com/inward/record.url?scp=0009129712&partnerID=8YFLogxK

U2 - 10.1016/0021-8928(89)90059-2

DO - 10.1016/0021-8928(89)90059-2

M3 - Article

AN - SCOPUS:0009129712

VL - 53

SP - 500

EP - 507

JO - Journal of Applied Mathematics and Mechanics

JF - Journal of Applied Mathematics and Mechanics

SN - 0021-8928

IS - 4

ER -

ID: 102552419