Screen LibraryMathematical theory of elastic and elasto-plastic bodies : an introduction /
The book acquaints the reader with the basic concepts and relations of elasticity and plasticity, and also with the contemporary state of the theory, covering such aspects as the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variati...
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| Main Authors: | |
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| Corporate Authors: | |
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| Published: |
Elsevier Pub. Co. ; Distributors for the U.S. and Canada, Elsevier/North Holland,
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| Publisher Address: | Amsterdam ; New York : New York : |
| Publication Dates: | 1981. |
| Literature type: | eBook |
| Language: |
English Czech |
| Series: |
Studies in applied mechanics ;
3 |
| Subjects: | |
| Online Access: |
http://www.sciencedirect.com/science/bookseries/09225382/3 |
| Summary: |
The book acquaints the reader with the basic concepts and relations of elasticity and plasticity, and also with the contemporary state of the theory, covering such aspects as the nonlinear models of elasto-plastic bodies and of large deflections of plates, unilateral boundary value problems, variational principles, the finite element method, and so on. |
| Carrier Form: | 1 online resource (342 pages) : illustrations. |
| Bibliography: | Includes bibliographical references (pages 335-339) and index. |
| ISBN: |
9781483291918 148329191X |
| Index Number: | QA931 |
| CLC: | O343 |
| Contents: |
Front Cover; Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction; Copyright Page; Table of Contents; Preface; SUMMARY OF NOTATION; CHAPTER 1. STRESS TENSOR; 1.1. Tensors. Green's Theorem; 1.2. Stress Vector; 1.3. Components of the Stress Tensor; 1.4. Equations of Equilibrium; 1.5. Tensor Character of Stress; 1.6. Principal Stresses and the Quadric of Stress; CHAPTER 2. STRAIN TENSOR; 2.1. Finite Strain Tensor; 2.2. Small Strain Tensor; 2.3. Equations of the Compatibility of Strain; CHAPTER 3. GENERALIZED HOOKE'S L AW; 3.1. Tension Test; 3.2. Generalized Hooke's Law. 3.3. Elasto-Plastic Materials. Deformation Theory. (A Special Case of the Nonlinear Hooke's Law)3.4. Elasto-Inelastic Bodies. A Model with Internal State Variables; 3.5. Hooke's Law with a Perfectly Plastic Domain; 3.6. Flow Theory of Plasticity; CHAPTER 4. FORMULATION OF BOUNDARY VALUE PROBLEMS OF THE THEORY OF ELASTICITY; 4.1. Lame Equations. Beltrami-Michell Equations; 4.2. The Classical Formulation of Basic Boundary Value Problems of Elasticity; CHAPTER 5. VARIATIONAL PRINCIPLES IN SMALL DISPLACEMENT THEORY; 5.1. Principles of Virtual Work, Virtual Displacements and Virtual Stresses. 5.2. Principle of Minimum Potential Energy in the Theory of Elasticity5.3. Principle of Minimum Complementary Energy in the Theory of Elasticity; 5.4. Hybrid Principles in the Theory of Elasticity. The Hellinger-Reissner Principle; CHAPTER 6. FUNCTIONS WITH FINITE ENERGY; 6.1. The Space of Functions with Finite Energy; 6.2. The Trace Theorem. Equivalent Norms, Rellich's Theorem; 6.3. Coerciveness of Strains. Korn's Inequality; CHAPTER 7. VARIATIONAL FORMULATION AND SOLUTION OF BASIC BOUNDARY VALUE PROBLEMS OF ELASTICITY; 7.1. Weak (Generalized) Solution. 7.2. Solution of Basic Boundary Value Problems by the Variational Method7.3. Solution of the First Basic Boundary Value Problem of Elasticity; 7.4. Contact and Other Boundary Value Problems; 7.5. Variational Formulation in Terms of Stresses. Method of Orthogonal Projections and Castigliano's Principle; 7.6. Basic Boundary Value Problems of Elasticity in Orthogonal Curvilinear Coordinates; CHAPTER 8. SOLUTION OF BOUNDARY VALUE PROBLEMS FOR THE ELASTO-PLASTIC BODY. DEFORMATION THEORY; 8.1. Formulation of the Weak Solution. 8.2. Application of the Variational Method to the Solution of Basic Boundary Value ProblemsCHAPTER 9. SOLUTION OF BOUNDARY VALUE PROBLEMS FOR THE ELASTO-INELASTIC BODY; 9.1. Elasto-Inelastic Material; 9.2. Solution of the First Boundary Value Problem for the Elasto-Inelastic Body; 9.3. Solution of the Second Boundary Value Problem; CHAPTER 10. TWO- AND ONE-DIMENSIONAL PROBLEMS; 10.1. Saint-Venant's Principle; 10.2. Plane Elasticity; 10.3. Axisymmetric Boundary Value Problems; 10.4. Reduction of Dimension in the Theory of Elasticity; 10.5. Torsion of a Bar. |