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Justification of the two‐dimensional equations of a linearly elastic shallow shell
Author(s) -
Ciarlet P. G.,
Miara B.
Publication year - 1992
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160450305
Subject(s) - shell (structure) , mathematics , elasticity (physics) , mathematical analysis , surface (topology) , zero (linguistics) , linear elasticity , geometry , finite element method , physics , materials science , composite material , linguistics , philosophy , thermodynamics
We consider a problem in three‐dimensional linearized elasticity, posed over a shell with a specific geometry, subjected to general loadings, and clamped on a portion of its lateral surface. We show that, as the thickness of the shell goes to zero, the solution of the three‐dimensional problem converges to the solution of two‐dimensional shallow shell equations. This approach, which provides in particular a mathematical definition of “shallowness”, clearly delineates conditions under which a three‐dimensional problem may be deemed asymptotically equivalent to a two‐dimensional shallow shell problem.