Junction of elastic plates and beams

Antonio Gaudiello; Régis Monneau; Jacqueline Mossino; François Murat; Ali Sili

ESAIM: Control, Optimisation and Calculus of Variations (2007)

  • Volume: 13, Issue: 3, page 419-457
  • ISSN: 1292-8119

Abstract

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We consider the linearized elasticity system in a multidomain of 𝐑 3 . This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius r ε . The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and r ε tend to zero simultaneously, with r ε ε 2 , we identify the limit problem. This limit problem involves six junction conditions.

How to cite

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Gaudiello, Antonio, et al. "Junction of elastic plates and beams." ESAIM: Control, Optimisation and Calculus of Variations 13.3 (2007): 419-457. <http://eudml.org/doc/249992>.

@article{Gaudiello2007,
abstract = { We consider the linearized elasticity system in a multidomain of $\{\bf R\}^3$. This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius $r^\{\varepsilon\}$. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and $r^\{\varepsilon\}$ tend to zero simultaneously, with $r^\{\varepsilon\}\gg \varepsilon^2$, we identify the limit problem. This limit problem involves six junction conditions. },
author = {Gaudiello, Antonio, Monneau, Régis, Mossino, Jacqueline, Murat, François, Sili, Ali},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Junctions; thin structures; plates; beams; linear elasticity; asymptotic analysis; multidomain},
language = {eng},
month = {7},
number = {3},
pages = {419-457},
publisher = {EDP Sciences},
title = {Junction of elastic plates and beams},
url = {http://eudml.org/doc/249992},
volume = {13},
year = {2007},
}

TY - JOUR
AU - Gaudiello, Antonio
AU - Monneau, Régis
AU - Mossino, Jacqueline
AU - Murat, François
AU - Sili, Ali
TI - Junction of elastic plates and beams
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2007/7//
PB - EDP Sciences
VL - 13
IS - 3
SP - 419
EP - 457
AB - We consider the linearized elasticity system in a multidomain of ${\bf R}^3$. This multidomain is the union of a horizontal plate with fixed cross section and small thickness ε, and of a vertical beam with fixed height and small cross section of radius $r^{\varepsilon}$. The lateral boundary of the plate and the top of the beam are assumed to be clamped. When ε and $r^{\varepsilon}$ tend to zero simultaneously, with $r^{\varepsilon}\gg \varepsilon^2$, we identify the limit problem. This limit problem involves six junction conditions.
LA - eng
KW - Junctions; thin structures; plates; beams; linear elasticity; asymptotic analysis; multidomain
UR - http://eudml.org/doc/249992
ER -

References

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