# Singular Problems in Shell Theory Computing and Asymptotics

## Evariste Sanchez-Palencia, Olivier Millet, Fabien Bechet

Part of the Lecture Notes in Applied and Computational Mechanics Series

## Synopsis

Singular Problems in Shell Theory Computing and Asymptotics by Evariste Sanchez-Palencia, Olivier Millet, Fabien Bechet

Thin shells are three-dimensional structures with a dimension (the thickness) small with respect to the two others.Such thin structures are widely used in automobileandaviation industries,or in civil engineering, because they provide animportantsti?ness, due to theircurvature,with a small weight. Fig. 0.1. Airbus A380 Fig. 0.2. Hemispherical roof (Marseille, France) One ofthechallenges is often to reduce the weight (andconsequently the thickness)oftheshells, preservingtheirsti?ness.So that it is essential to have 1 accuratemodelsforthinandevenverythinshells ,andtobeabletocomputethe displacements resultingfromagivenloading.In particular, singularities leading to fractures in some cases must be absolutely predicted a priori and ofcourse avoided (see Fig.0.3 forexample). Since the pioneeringmodels of Novozhilov-Donnell [81] and Koiter [65][66], numerous works havebeen devoted to establish linear and non linear elastic shell model usingdirect orsurfacic approaches [18][25][100]. More recently, the asymptoticmethods [87] havebeen used, to try tojustify rigorously, fromthe three-dimensional equations, the shell models obtained by direct approaches - lying onapriori assumption, andto construct new models [54][55]. This way, 1 Very thin shells are present in certain domains of industry, as plastic ?lms for pa- aging or for electronics, streched sails, or even very thin metal sheets obtained by drawing. E. Sanchez-Palencia et al.: Singular Problems in Shell Theory, LNACM 54, pp. 1-11.

## Reviews

From the reviews:

The book under review is devoted to a mathematically rigorous study of singularities in linear elastic shell theory which appear for very small thickness. ... This well-written book is a reader-friendly and good organized research work in the field of mathematical theory of shells. It can be recommended to highly-qualified experts in this field. (Igor Andrianov, Zentralblatt MATH, Vol. 1208, 2011)

## Book Info

#### Publication date

13th October 2012

#### Author

Evariste Sanchez-Palencia, Olivier Millet, Fabien Bechet

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#### Publisher

Springer-Verlag Berlin and Heidelberg GmbH & Co. K an imprint of Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Paperback
266 pages

#### Categories

Mechanical engineering
Classical mechanics
Mechanical engineering & materials
Civil engineering, surveying & building

#### ISBN

9783642264337

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