Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data: 31 (Springer Tracts in Natural Philosophy) - Softcover

Valent, Tullio

 
9781461283263: Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data: 31 (Springer Tracts in Natural Philosophy)
Softcover
ISBN 10: 1461283264 ISBN 13: 9781461283263
Verlag: Springer, 2011

Inhaltsangabe

In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be­ sides being quite spontaneous, allows us to consider a great many inter­ esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis­ tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub­ sequent developments.

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Reseña del editor

In this book I present, in a systematic form, some local theorems on existence, uniqueness, and analytic dependence on the load, which I have recently obtained for some types of boundary value problems of finite elasticity. Actually, these results concern an n-dimensional (n ~ 1) formal generalization of three-dimensional elasticity. Such a generalization, be­ sides being quite spontaneous, allows us to consider a great many inter­ esting mathematical situations, and sometimes allows us to clarify certain aspects of the three-dimensional case. Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality. Note that I concentrate on simultaneous local existence and uniqueness; thus, I do not deal with the more general theory of exis­ tence. Moreover, I restrict my discussion to compressible elastic bodies and I do not treat unilateral problems. The clever use of the inverse function theorem in finite elasticity made by STOPPELLI [1954, 1957a, 1957b], in order to obtain local existence and uniqueness for the traction problem in hyperelasticity under dead loads, inspired many of the ideas which led to this monograph. Chapter I aims to give a very brief introduction to some general concepts in the mathematical theory of elasticity, in order to show how the boundary value problems studied in the sequel arise. Chapter II is very technical; it supplies the framework for all sub­ sequent developments.

Reseña del editor

The object of this book is the systematic exposition of recent work of the author's on boundary value problems of finite elasticity. These results concern an n-dimensional generalization of the three-dimensional elasticity which, aside from leading to a great many interesting mathematical situations, often shed light on certain aspects of the three-dimensional case. The book begins with a brief introduction to some general concepts, in order to show how the boundary value problems studied in the text arise. This is followed by the development of some technical material needed in the rest of the book. Subsequent chapters are devoted to obtaining theorems of existence, uniqueness and analytic dependence on the load, near special deformations for boundary value problems of place, and traction in finite elastostatics.

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Verlag
Springer
Erscheinungsdatum
2011
Sprache
Englisch
ISBN 10 
1461283264
ISBN 13 
9781461283263
Einband
Tapa blanda
Anzahl der Seiten
208
Kontakt zum Hersteller
Nicht verfügbar
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Weitere beliebte Ausgaben desselben Titels

9780387965505: Boundary Value Problems of Finite Elasticity: Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data: 31 (Springer Tracts in Natural Philosophy)

Vorgestellte Ausgabe

ISBN 10:  0387965505 ISBN 13:  9780387965505
Verlag: Springer-Verlag New York Inc., 1987
Hardcover