Modeling and Control in Solid Mechanics

  • A. M. Khludnev
  • J. Sokolowski

Part of the International Series of Numerical Mathematics book series (ISNM, volume 122)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. A. M. Khludnev, J. Sokolowski
    Pages 1-25
  3. A. M. Khludnev, J. Sokolowski
    Pages 27-98
  4. A. M. Khludnev, J. Sokolowski
    Pages 99-175
  5. A. M. Khludnev, J. Sokolowski
    Pages 177-268
  6. A. M. Khludnev, J. Sokolowski
    Pages 269-351
  7. Back Matter
    Pages 353-366

About this book


New trends in free boundary problems and new mathematical tools together with broadening areas of applications have led to attempts at presenting the state of art of the field in a unified way. In this monograph we focus on formal models representing contact problems for elastic and elastoplastic plates and shells. New approaches open up new fields for research. For example, in crack theory a systematic treatment of mathematical modelling and optimization of problems with cracks is required. Similarly, sensitivity analysis of solutions to problems subjected to perturbations, which forms an important part of the problem solving process, is the source of many open questions. Two aspects of sensitivity analysis, namely the behaviour of solutions under deformations of the domain of integration and perturbations of surfaces seem to be particularly demanding in this context. On writing this book we aimed at providing the reader with a self-contained study of the mathematical modelling in mechanics. Much attention is given to modelling of typical constructions applied in many different areas. Plates and shallow shells which are widely used in the aerospace industry provide good exam­ ples. Allied optimization problems consist in finding the constructions which are of maximal strength (endurance) and satisfy some other requirements, ego weight limitations. Mathematical modelling of plates and shells always requires a reasonable compromise between two principal needs. One of them is the accuracy of the de­ scription of a physical phenomenon (as required by the principles of mechanics).


Boundary value problem Finite Rigid body Variable calculus equation function theorem wave equation

Authors and affiliations

  • A. M. Khludnev
    • 1
  • J. Sokolowski
    • 2
  1. 1.Lavrentyev Institute of Hydrodynamics of the Russian Academy of SciencesNovosibirskRussia
  2. 2.Institut Elie Cartan Laboratoire de MathématiquesUniversité Henri Poincaré Nancy IVandoeuvre-Les-NancyFrance

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