Mechanics of Continuous Media and Analysis of Structures

IntroductionPrefaceForewordChapter 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 MediaChapter 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 ProblemsChapter 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 of an Approximate Solution 8.5. Non-conforming Elements - Patch Test 8.6. Hellinger-Reissner Principle and Saddle-Point 8.7. Legendre TransformationChapter IV: Vibration 1. Introduction 2. Discretized Structures 3. Riesz' Theorem 4. Variational Principles 5. Methods of Dynamic Reduction 6. Responses to Forced External ExcitationsChapter V: Non-Linear Deformations - Buckling 1. Formulation from the Natural State for a Hyperelastic Medium 2. Formulation from a Prestressed State for an Arbitrary Medium 3. Discretization 4. Methods of Solution 5. Static Buckling 5.1. General 5.2. The Criterion of Static Stability 5.3. Application of the Energy Criterion 5.4. Limit Point and Bifurcation PointChapter VI: Shell Theory 1. General 1.1. Introduction 1.2. Definitions 1.3. General Hypotheses 2. Equilibrium Equations 2.1. Equilibrium Equations in the Case of Hypothesis (w) 2.2. Equilibrium Equations in the Case of Hypothesis (wo) 2.3. Relation of Symmetry of Generalized Surface Stresses 3. Deformations 3.1. Deformation in the Case of Hypothesis (w), Linearized Case 3.2. Deformation in the Case of Hypothesis (wo), Linearized Case 3.3. Transverse Shear Deformation and Normal Deformation 3.4. Linearized Conditions of Compatibility 3.5. Non-linear Deformations 4. Stresses 4.1. Indeterminate Stresses in the Case of Hypothesis (wo) 4.2. Symmetrical Stresses in the Case of Hypothesis (wo) 4.3. Stress Functions in the Case of Hypothesis (wo) 4.4. Stress Functions in the Case of Hypothesis (w) 5. Variational Principles 6. Linear Constitutive Laws 7. Shells of Revolution 8. DiscretizationAppendix : Notations and FormulaeReferences Chapter I Chapter II Chapter III Chapter IV Chapter V Chapter VI AppendixIndex