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Hemivariational Inequalities

Applications in Mechanics and Engineering

  • Panagiotis D. Panagiotopoulos

Table of contents

  1. Front Matter
    Pages I-XVI
  2. Introductory Topics

    1. Front Matter
      Pages 1-1
    2. Panagiotis D. Panagiotopoulos
      Pages 3-29
  3. Mechanical Theory

    1. Front Matter
      Pages 31-31
    2. Panagiotis D. Panagiotopoulos
      Pages 33-64
    3. Panagiotis D. Panagiotopoulos
      Pages 65-98
    4. Panagiotis D. Panagiotopoulos
      Pages 99-134
    5. Panagiotis D. Panagiotopoulos
      Pages 135-151
  4. Mathematical Theory

    1. Front Matter
      Pages 153-153
    2. Panagiotis D. Panagiotopoulos
      Pages 155-177
    3. Panagiotis D. Panagiotopoulos
      Pages 179-221
    4. Panagiotis D. Panagiotopoulos
      Pages 223-236
  5. Numerical Applications

    1. Front Matter
      Pages 237-237
    2. Panagiotis D. Panagiotopoulos
      Pages 239-279
    3. Panagiotis D. Panagiotopoulos
      Pages 317-344
    4. Panagiotis D. Panagiotopoulos
      Pages 345-359
    5. Panagiotis D. Panagiotopoulos
      Pages 361-376
    6. Panagiotis D. Panagiotopoulos
      Pages 393-415
  6. Back Matter
    Pages 417-451

About this book

Introduction

The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

Keywords

Differential Equations Hemivariationsungleichungen Integral Equations Integralgleichung Ungleichungen Variational Formulations beam differential equation fractal geometry mechanics neural networks numerical methods robotics stress

Authors and affiliations

  • Panagiotis D. Panagiotopoulos
    • 1
    • 2
  1. 1.Department of Civil EngineeringAristotle UniversityThessalonikiGreece
  2. 2.Faculty of Mathematics and PhysicsRWTH AachenAachenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-51677-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-51679-5
  • Online ISBN 978-3-642-51677-1
  • Buy this book on publisher's site