Advertisement

Uniqueness Theorems in Linear Elasticity

  • Robin John Knops
  • Lawrence Edward Payne

Part of the Springer Tracts in Natural Philosophy book series (STPHI, volume 19)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Robin John Knops, Lawrence Edward Payne
    Pages 1-8
  3. Robin John Knops, Lawrence Edward Payne
    Pages 9-22
  4. Robin John Knops, Lawrence Edward Payne
    Pages 23-31
  5. Robin John Knops, Lawrence Edward Payne
    Pages 32-60
  6. Robin John Knops, Lawrence Edward Payne
    Pages 61-69
  7. Robin John Knops, Lawrence Edward Payne
    Pages 70-87
  8. Robin John Knops, Lawrence Edward Payne
    Pages 88-97
  9. Back Matter
    Pages 118-130

About this book

Introduction

The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniqueness in elasticity theory in the hope that such an exposition will provide a convenient access to the literature while at the same time indicating what progress has been made and what problems still await solution. Naturally, the continuing announcement of new results thwarts any attempt to provide a complete assessment. Apart from linear elasticity theory itself, there are several other areas where elastic uniqueness is significant.

Keywords

Elastizität dynamics elasticity elastostatics stability statics time

Authors and affiliations

  • Robin John Knops
    • 1
  • Lawrence Edward Payne
    • 2
  1. 1.The UniversityNewcastle upon TyneAustralia
  2. 2.Cornell UniversityIthacaUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65101-4
  • Copyright Information Springer-Verlag Berlin Heidelberg 1971
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-65103-8
  • Online ISBN 978-3-642-65101-4
  • Series Print ISSN 0081-3877
  • Buy this book on publisher's site