Mathematical Methods in Continuum Mechanics of Solids

Authors: Kruzik, Martin, Roubíček, Tomáš

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  • Serves as an advanced textbook for graduate students, as well as a monograph for theoretically oriented researchers
  • Merges rational continuum mechanics with mathematical analysis. Focuses on rigorous mathematical formulation and treatment of static and evolutionary problems arising in mechanics of solids
  • Includes exercises, and also appendices that briefly present the basic mathematical concepts and results needed 
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  • ISBN 978-3-030-02065-1
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  • ISBN 978-3-030-30019-7
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  • ISBN 978-3-030-02064-4
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この教本について

This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited.

This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.

 

著者について

Martin Kružík is a Senior Researcher at the Institute of Information Theory and Automation of the Czech Academy of Sciences and an Associate Professor at Charles University and at the Czech Technical University in Prague, having received his habilitation from the Technical University Munich. His research interests range from calculus of variations and applied mathematical analysis to mathematical problems of continuum physics.
Tomáš Roubíček is a Professor at Charles University in Prague, as well as a Researcher at the Institutes of Thermomechanics and of Information Theory and Automation of the Czech Academy of Sciences. With an engineering background, his professional activity has evolved from computer simulations of systems of nonlinear partial differential equations, numerical mathematics and optimization theory to applied mathematical analysis focused on mathematical modeling in engineering and physics.

Table of contents (9 chapters)

Table of contents (9 chapters)
  • Description of Deformable Stressed Bodies

    Pages 3-23

    Kružík, Martin (et al.)

  • Elastic Materials

    Pages 25-50

    Kružík, Martin (et al.)

  • Polyconvex Materials: Existence of Energy-Minimizing Deformations

    Pages 51-86

    Kružík, Martin (et al.)

  • General Hyperelastic Materials: Existence/Nonexistence Results

    Pages 87-159

    Kružík, Martin (et al.)

  • Linearized Elasticity

    Pages 161-191

    Kružík, Martin (et al.)

書籍の購入

イーブック n/a
  • ISBN 978-3-030-02065-1
  • ウォーターマーク付、 DRMフリー
  • ファイル形式: PDF
  • どの電子書籍リーダーからでもすぐにお読みいただけます。
ハードカバー n/a
  • ISBN 978-3-030-30019-7
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
ソフトカバー n/a
  • ISBN 978-3-030-02064-4
  • 個人のお客様には、世界中どこでも配送料無料でお届けします。
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書誌情報

Bibliographic Information
Book Title
Mathematical Methods in Continuum Mechanics of Solids
Authors
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
イーブック ISBN
978-3-030-02065-1
DOI
10.1007/978-3-030-02065-1
ハードカバー ISBN
978-3-030-30019-7
ソフトカバー ISBN
978-3-030-02064-4
Edition Number
1
Number of Pages
XIII, 617
Topics