Homogenization Of Kirchhoff Plates Joined By Rivets Which Are Modeled By The Sobolev Point Conditions

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Homogenization Of Kirchhoff Plates Joined By Rivets Which Are Modeled By The Sobolev Point Conditions. / Nazarov, S. A.

In: St. Petersburg Mathematical Journal, Vol. 32, No. 2, 01.2021, p. 307-348.

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

BibTeX

@article{8d7e5130054244b09c3f388c644db21b,

title = "Homogenization Of Kirchhoff Plates Joined By Rivets Which Are Modeled By The Sobolev Point Conditions",

abstract = "Two Kirchhoff plates, which are described by Neumann problems for biharmonic equations, overlap along a thin strip. In the interior of the strip, the plates are connected by rivets, which are modeled by the Sobolev point transmission conditions. By taking the boundary layer phenomenon into account, homogenization with respect to a small parameter (the relative period of the distribution of rivets) is done, and transmission conditions are obtained on the common edge of two touching plates (in the limiting case, overlapping disappears). Differences are found between a single row and multiple row riveting that appear in different types of limiting transmission conditions, and the reasons are shown for the preference of double row riveting in practical engineering. Several related unsolved problems are formulated.",

keywords = "Biharmonic equation, boundary layer, homogenization, Kirchhoff plate, rivet model, Sobolev point conditions",

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

year = "2021",

month = jan,

doi = "10.1090/spmj/1649",

language = "English",

volume = "32",

pages = "307--348",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "2",

}

RIS

TY - JOUR

T1 - Homogenization Of Kirchhoff Plates Joined By Rivets Which Are Modeled By The Sobolev Point Conditions

AU - Nazarov, S. A.

PY - 2021/1

Y1 - 2021/1

N2 - Two Kirchhoff plates, which are described by Neumann problems for biharmonic equations, overlap along a thin strip. In the interior of the strip, the plates are connected by rivets, which are modeled by the Sobolev point transmission conditions. By taking the boundary layer phenomenon into account, homogenization with respect to a small parameter (the relative period of the distribution of rivets) is done, and transmission conditions are obtained on the common edge of two touching plates (in the limiting case, overlapping disappears). Differences are found between a single row and multiple row riveting that appear in different types of limiting transmission conditions, and the reasons are shown for the preference of double row riveting in practical engineering. Several related unsolved problems are formulated.

AB - Two Kirchhoff plates, which are described by Neumann problems for biharmonic equations, overlap along a thin strip. In the interior of the strip, the plates are connected by rivets, which are modeled by the Sobolev point transmission conditions. By taking the boundary layer phenomenon into account, homogenization with respect to a small parameter (the relative period of the distribution of rivets) is done, and transmission conditions are obtained on the common edge of two touching plates (in the limiting case, overlapping disappears). Differences are found between a single row and multiple row riveting that appear in different types of limiting transmission conditions, and the reasons are shown for the preference of double row riveting in practical engineering. Several related unsolved problems are formulated.

KW - Biharmonic equation

KW - boundary layer

KW - homogenization

KW - Kirchhoff plate

KW - rivet model

KW - Sobolev point conditions

UR - http://www.scopus.com/inward/record.url?scp=85102792788&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/5a099a51-0fd2-34f0-9779-a107b81a2dd1/

U2 - 10.1090/spmj/1649

DO - 10.1090/spmj/1649

M3 - Article

AN - SCOPUS:85102792788

VL - 32

SP - 307

EP - 348

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 2

ER -

ID: 88366063