One-dimensional equations of deformation of thin slightly curved rods. Asymptotical analysis and justification

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One-dimensional equations of deformation of thin slightly curved rods. Asymptotical analysis and justification. / Nazarov, S. A.; Slutskii, A. S.

в: Izvestiya Mathematics, Том 64, № 3, 01.12.2000, стр. 531-562.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{98108139aba04a199f891c4ddcc2aa3d,

title = "One-dimensional equations of deformation of thin slightly curved rods. Asymptotical analysis and justification",

abstract = "We obtain asymptotics for the solution of the spatial problem of elasticity theory in a thin body (a rod) with a smoothly varying cross-section. Any anisotropy and any non-homogeneity of material is admitted. The ends of the a rod, which is under the action of volume forces, are rigidly fixed (clamped), and the lateral surface is under the action of forces. The small parameter h is the ratio of the maximal diameter of the rod to its length. We suggest conditions on the differential properties and the structure of external load under which the solution of the one-dimensional equations yielded by asymptotical analysis provides an acceptable approximation to the three-dimensional displacement and stress fields. The error estimate is based on a special version of Korn's inequality, which is asymptotically sharp if suitable weight factors and powers of h are introduced into the La-norms of displacements and their derivatives.",

author = "Nazarov, {S. A.} and Slutskii, {A. S.}",

year = "2000",

month = dec,

day = "1",

doi = "10.1070/IM2000v064n03ABEH000290",

language = "English",

volume = "64",

pages = "531--562",

journal = "Izvestiya Mathematics",

issn = "1064-5632",

publisher = "IOP Publishing Ltd.",

number = "3",

}

RIS

TY - JOUR

T1 - One-dimensional equations of deformation of thin slightly curved rods. Asymptotical analysis and justification

AU - Nazarov, S. A.

AU - Slutskii, A. S.

PY - 2000/12/1

Y1 - 2000/12/1

N2 - We obtain asymptotics for the solution of the spatial problem of elasticity theory in a thin body (a rod) with a smoothly varying cross-section. Any anisotropy and any non-homogeneity of material is admitted. The ends of the a rod, which is under the action of volume forces, are rigidly fixed (clamped), and the lateral surface is under the action of forces. The small parameter h is the ratio of the maximal diameter of the rod to its length. We suggest conditions on the differential properties and the structure of external load under which the solution of the one-dimensional equations yielded by asymptotical analysis provides an acceptable approximation to the three-dimensional displacement and stress fields. The error estimate is based on a special version of Korn's inequality, which is asymptotically sharp if suitable weight factors and powers of h are introduced into the La-norms of displacements and their derivatives.

AB - We obtain asymptotics for the solution of the spatial problem of elasticity theory in a thin body (a rod) with a smoothly varying cross-section. Any anisotropy and any non-homogeneity of material is admitted. The ends of the a rod, which is under the action of volume forces, are rigidly fixed (clamped), and the lateral surface is under the action of forces. The small parameter h is the ratio of the maximal diameter of the rod to its length. We suggest conditions on the differential properties and the structure of external load under which the solution of the one-dimensional equations yielded by asymptotical analysis provides an acceptable approximation to the three-dimensional displacement and stress fields. The error estimate is based on a special version of Korn's inequality, which is asymptotically sharp if suitable weight factors and powers of h are introduced into the La-norms of displacements and their derivatives.

UR - http://www.scopus.com/inward/record.url?scp=33747029838&partnerID=8YFLogxK

U2 - 10.1070/IM2000v064n03ABEH000290

DO - 10.1070/IM2000v064n03ABEH000290

M3 - Article

AN - SCOPUS:33747029838

VL - 64

SP - 531

EP - 562

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 3

ER -

ID: 40991926