Research output: Contribution to journal › Article › peer-review
Models of Riveting : Asymptotic Analyses of Kirchhoff Plates with Sobolev Point Conditions. / Nazarov, S. A.
In: Doklady Physics, Vol. 64, No. 11, 01.11.2019, p. 424-429.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Models of Riveting
T2 - Asymptotic Analyses of Kirchhoff Plates with Sobolev Point Conditions
AU - Nazarov, S. A.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - Abstract: The Sobolev embedding theorem implies correct formulation of the Dirichlet condition at isolated points or transmission conditions that simulate contact welding, bolt or screw fastening, etc. The problems on bending the Kirchhoff plate with periodically distributed point supports and the joint of two plates by rows of rivets are considered. The asymptotic analysis performed provides asymptotic expansions of solutions and error estimates, namely, the one-dimensional model of a narrow plate and the transmission conditions at the common boundary of two plates. The results of homogenization differ seriously in the cases of one or several rows of supports and rivets. In particular, one-row riveting provides only a hinge joint of plates (discontinuities in the rotation angle are allowed), but two-row riveting provides an almost complete clutch at which all elastic fields become, in main, continuous at the common edge.
AB - Abstract: The Sobolev embedding theorem implies correct formulation of the Dirichlet condition at isolated points or transmission conditions that simulate contact welding, bolt or screw fastening, etc. The problems on bending the Kirchhoff plate with periodically distributed point supports and the joint of two plates by rows of rivets are considered. The asymptotic analysis performed provides asymptotic expansions of solutions and error estimates, namely, the one-dimensional model of a narrow plate and the transmission conditions at the common boundary of two plates. The results of homogenization differ seriously in the cases of one or several rows of supports and rivets. In particular, one-row riveting provides only a hinge joint of plates (discontinuities in the rotation angle are allowed), but two-row riveting provides an almost complete clutch at which all elastic fields become, in main, continuous at the common edge.
UR - http://www.scopus.com/inward/record.url?scp=85077027964&partnerID=8YFLogxK
U2 - 10.1134/S1028335819110028
DO - 10.1134/S1028335819110028
M3 - Article
AN - SCOPUS:85077027964
VL - 64
SP - 424
EP - 429
JO - Doklady Physics
JF - Doklady Physics
SN - 1028-3358
IS - 11
ER -
ID: 60873805