Nonlinear Elasticity

Nonlinear Elasticity

Proceedings of a Symposium Conducted by the Mathematics Research Center, the University of Wisconsin—Madison April 16—18, 1973

1st Edition - January 28, 1973

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  • Editor: R. W. Dickey
  • eBook ISBN: 9781483264790

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Nonlinear Elasticity presents a description of research and result on various nonlinear problems arising in elasticity. This book covers a variety of topics, including shallow elastic membranes, nonlinear elasticity, finite deformations of elastic solids, and nonlinear thermoelasticity. Organized into 11 chapters, this book begins with an overview of the nonlinear theory of buckling of elastic shells. This text then examines the ways in which the energy criterion supplies a necessary condition for asymptotic stability. Other chapters consider some of the phenomena, both physical and mathematical, that typify the large deformation of a nonlinearly elastic body. This book discusses as well the concepts leading to a criterion for instabilities and discusses how the criterion applies to some well-known ideal materials. The final chapter deals with the structure of strong shocks and studies the evolution of such a shock produced by a suddenly-applied strain. This book is a valuable resource for mathematicians.

Table of Contents

  • Preface

    On the Collapse of Shallow Elastic Membranes

    On the Energy Criterion for Stability

    Monotonicity and Invertibility Conditions in One-Dimensional Nonlinear Elasticity

    Saddle Point Analysis for an Ordinary Differential Equation in a Banach Space, and an Application to Dynamic Buckling of a Beam

    Loading Devices and Stability of Equilibrium

    Approximations and Numerical Analysis of Finite Deformations of Elastic Solids

    Buckling of Complete Spherical Shells Under Slightly Nonuniform Loads

    On the Interrelation Between Stability and Computations

    On Nonlinear Thermoelasticity and Nonequilibrium Thermodynamics

    Nonlinear Elastic Properties of Molten Plastics

    Nonlinear Wave Propagation in Viscoelastic Materials


Product details

  • No. of pages: 414
  • Language: English
  • Copyright: © Academic Press 1973
  • Published: January 28, 1973
  • Imprint: Academic Press
  • eBook ISBN: 9781483264790

About the Editor

R. W. Dickey

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