Mechanics of Continuous Media and Analysis of Structures

1st Edition

Authors: R. Valid
Hardcover ISBN: 9780444861504
eBook ISBN: 9780080984612
Imprint: North Holland
Published Date: 1st January 1981
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Mechanics of Continuous Media and Analysis of Structures is a six-chapter book that begins by elucidating the mechanics of solid continuous media. The text then describes the finite elements method, which undoubtedly dominates the methods used for structural analysis. Subsequent chapters explain the variational principles in linear elasticity, vibration of linear structure, non-linear deformations, and the shell theory. This book will be valuable to all those who need certain theoretical developments in mechanics, including mechanical engineers, economists, and mathematicians.

Table of Contents

Introduction Preface Foreword Chapter I: Mechanics of Solid Continuous Media

1. General Hypotheses - Hyperelastic Media - Extension to Arbitrary Media 2. Stresses 3. Deformation 4. Equilibrium Equations 5. Homogeneous and Isotropic Linear Elasticity 5.1. Isotropy 5.2. Stress 5.3. Small Deformation-Linearization 5.4. Equilibrium Equations 5.5. Stability of Material 6. Variational Principle for a Linear Elastic Medium 7. Theorem of Reciprocity for a Linearized Hyperelastic Medium 8. Stress Functions 9. Polarized Media

Chapter II: The Finite Element Method

1. The Displacement Method in Static Problems 1.1. General 1.2. Remarks and Complements 2. Other Types of Elements and Static Problems 2.1. Axisymmetrical Three-dimensional Bodies with Axisymmetrical Loading 2.2. Improved Elements in the Bidimensional Case 2.3. Three-dimensional Elements and Problems 2.4. Plate Bending 2.5. Straight Beams in Bending 2.6. Shells as Assembly of Flat Elements 2.7. Axisymmetrical Shells 2.8. Structures under Elastoplastic Behaviour 2.9. Improvement of Elements 3. Other Types of Problems

Chapter III: Variational Principles in Linear Elasticity

1. Principle of Potential Energy 2. Hu-Washizu Principle, or Three Field Principle 3. Hellinger-Reissner Principle, or Two Field Principle 4. A Fraeijs de Veubeke Two Field Principle 5. Principle of Complementary Energy 6. Two Field Hybrid Principle of Pian 7. Principle of Virtual Displacements and Principle of Virtual Stresses 8. Application of Variational Principles 8.1. Stress Functions 8.2. Linearized Compatibility Condition 8.3. Application of the Finite Element Method 8.4. Upper Bound for the Error o


© North Holland 1981
North Holland
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About the Author

R. Valid