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Theory of Elasticity

  • Book
  • © 2005

Overview

Authors:
  1. A. I. Lurie
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    You can also search for this author in PubMed   Google Scholar

  2. Alexander Belyaev

    1. Dept. Mechanical and Control Processes, St. Petersburg Technical University, St. Petersburg Russian Federation

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Translation of a famous book that belongs to the cultural heritage of Russian mechanics
  • Reference for classical and analytical approaches to continuum mechanics

Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)

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Table of contents (9 chapters)

  1. Front Matter

    Pages 1-25
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  2. Basic concepts of continuum mechanics

    1. Front Matter

      Pages 27-27
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    2. Stress tensor

      • A. I. Lurie, Alexander Belyaev
      Pages 29-76

    3. Deformation of a continuum

      • A. I. Lurie, Alexander Belyaev
      Pages 77-123

  3. Governing equations of the linear theory of elasticity

    1. Front Matter

      Pages 125-125
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    2. The constitutive law in the linear theory of elasticity

      • A. I. Lurie, Alexander Belyaev
      Pages 127-150

    3. Governing relationships in the linear theory of elasticity

      • A. I. Lurie, Alexander Belyaev
      Pages 151-239

  4. Special problems of the linear theory of elasticity

    1. Front Matter

      Pages 241-241
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    2. Three-dimensional problems in the theory of elasticity

      • A. I. Lurie, Alexander Belyaev
      Pages 243-407

    3. Saint-Venant’s problem

      • A. I. Lurie, Alexander Belyaev
      Pages 409-511

    4. The plane problem of the theory of elasticity

      • A. I. Lurie, Alexander Belyaev
      Pages 513-689

  5. Basic relationships in the nonlinear theory of elasticity

    1. Front Matter

      Pages 691-691
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    2. Constitutive laws for nonlinear elastic bodies

      • A. I. Lurie, Alexander Belyaev
      Pages 693-753

    3. Problems and methods of the nonlinear theory of elasticity

      • A. I. Lurie, Alexander Belyaev
      Pages 755-878

  6. Back Matter

    Pages 879-1050
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Keywords

About this book

The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods forstating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelas­ ticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics. The first two chapters form Part I of this book and are devoted to the basic definitions ofcontinuum mechanics; namely stress tensors (Chapter 1) and strain tensors (Chapter 2). The necessity to distinguish between initial and actual states in the nonlinear theory does not allow one to be content with considering a single strain measure. For this reason, it is expedient to introduce more rigorous tensors to describe the stress-strain state. These are considered in Section 1.3 for which the study of Sections 2.3-2.5 should precede. The mastering of the content of these sections can be postponed until the nonlinear theory is studied in Chapters 8 and 9.

Reviews

From the reviews:

"Prof. Lurie presented … his famous course "Theory of Elasticity" which was the basis of the reviewed monograph … . It can be recommended as a textbook for graduated students or PhD students … . In addition, who has no experiences in the tensor calculus based on the absolute notation can get a brief introduction in this topic … . who want to learn the basics of continuum mechanics can use this monograph too." (Holm Altenbach, ZAMM, Vol. 85(2), 2005)

Authors and Affiliations

  • Dept. Mechanical and Control Processes, St. Petersburg Technical University, St. Petersburg Russian Federation

    Alexander Belyaev

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