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Boundary Value Problems of Finite Elasticity

Local Theorems on Existence, Uniqueness, and Analytic Dependence on Data

  • Tullio Valent

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 31)

About this book

Introduction

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 Part of the matter presented is unpublished; other arguments have been only partially published and in lesser generality.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.

Keywords

Implicit function banach spaces deformation development elasticity elastostatics material measure statics

Authors and affiliations

  • Tullio Valent
    • 1
  1. 1.Dipartimento di Matematica Pura ed ApplicataUniversità di PadovaPadovaItaly

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-3736-5
  • Copyright Information Springer-Verlag New York 1988
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8326-3
  • Online ISBN 978-1-4612-3736-5
  • Series Print ISSN 0081-3877
  • Buy this book on publisher's site