Author | Veubeke, B. M. Fraeijs de. author |
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Title | A Course in Elasticity [electronic resource] / by B. M. Fraeijs de Veubeke |
Imprint | New York, NY : Springer New York, 1979 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6226-8 |
Descript | XII, 330 p. online resource |
1. Kinematics of Continuous Media -- 1.1. Material and Spatial Coordinates -- 1.2. Neighborhood Transformations -- 1.3 Composition of Changes of Configuration -- 1.4 Measure of the State of Local Deformation. Greenโs and Jaumannโs Strain -- 1.5 Rigid-Body Rotations of a Neighborhood -- 1.6 The Kinematical Decomposition of the Jacobian Matrix -- 1.7 Geometric Interpretation of Infinitesimal Strains -- 1.8 The Eulerian Viewpoint in Kinematics. Almansiโs Strain -- 1.9 Eulerian Measures of Rates of Deformation and Rotation -- 1.10 Temporal, Variation of the Polar Decomposition of the Jacobian Matrix -- 2. Statics and Virtual Work -- 2.1. The Concept of Stress. True Stress -- 2.2. The Piola Stresses -- 2.3. Translational Equilibrium Equations -- 2.4. Rotational Equilibrium Equations -- 2.5. Statics and Virtual Work -- 2.6. Commutativity of the Operators ? and Di -- 2.7 Virtual Work in a Continuous Medium -- 2.8. Statics and Virtual Power for True Stresses -- 2.9. Statics and Virtual Work in Infinitesimal Changes of Configuration -- 3. Conservation of Energy -- 3.1. Constitutive Equations for Piolaโs Stresses -- 3.2. The Kirchhoff-Trefftz Stresses -- 3.3 The Constitutive Equations of Geometrically Linear Elasticity -- 4. Cartesian Tensors -- 4.1. Bases and Change of Basis -- 4.2 Tensors -- 4.3 Some Special Tensors -- 4.4 The Vector Product -- 4.5. Structure of Symmetric Cartesian Tensors of Order Two. Principal Axes -- 4.6. Fundamental Invariants and the Deviator -- 4.7. Structure of Skew-Symmetric Cartesian Tensors of the Second Order -- 4.8. Matrix Representation of Tensor Operations -- 5. The Equations of Linear Elasticity -- 5.1. Compatibility of Strains in a Simply Connected Region -- 5.2. Compatibility of Strains in a Multiply Connected Region -- 5.3. Principal Elongations and Fundamental Invariants of Strain -- 5.4. Principal Stresses and Fundamental Invariants of the Stress State -- 5.5. Octahedral Stresses and Strains -- 5.6. Mohrโs Circles -- 5.7. Statics and Virtual Work -- 5.8. Taylorโs Development of the Strain Energy -- 5.9. Infinitesimal Stability -- 5.10. Hadamardโs Condition for Infinitesimal Stability -- 5.11. Isotropy and Anisotropy -- 5.12. Criteria for Elastic Limits -- 5.13. Navierโs Equations -- 5.14. The Beltrami-Michell Equations -- 6. Extension, Bending, and Torsion of Prismatic Beams -- 6.1. Greenโs and Stokesโ Formulas -- 6.2. The Centroid -- 6.3. Moments of Inertia -- 6.4. The Semi-Inverse Method of Saint-Venant -- 6.5. Resultants of Stresses on a Cross Section -- 6.6. Calculation of the Transverse Displacements -- 6.7. Equations Governing the Shear Stresses -- 6.8. Calculation of the Longitudinal Displacement -- 6.9. Separation of Solutions -- 6.10. Pure Torsion -- 6.11. The Center of Torsion for a Fully Constrained Section -- 6.12. Bending without Torsion -- 6.13. The Stiffness Relation for the Twist -- 6.14. Total Energy as a Function of the Deformations of the Fibers -- 6.15. Total Energy as a Function of Generalized Forces -- 6.16. The Generalized Constitutive Equations for Bending and Torsion of Beams -- 6.17. One-Dimensional Formulation of Bending and Torsion of Beams -- 6.18. Applications -- 7. Plane Stress and Plane Strain -- 7.1. Lemmas for the Integration of Partial Differential Equations in Complex Form -- 7.2. The Structure of a Biharmonic Function -- 7.3. Structure of the Solution of the Problems of Plane Strain -- 7.4.Structure of the Solution of the Problem of Plane Stress -- 7.5. Generalized Plane Stress -- 7.6. Airyโs Stress Function -- 7.7. Complex Representation of Airyโs Function -- 7.8. Polar Coordinates -- 7.9. Applications in Cartesian Coordinates -- 7.10. Applications in Polar Coordinates -- 8. Bending of Plates -- 8.1. Basic Hypotheses -- 8.2. Application of the Canonical Variational Principle -- 8.3. The Two-Dimensional Canonical Principle -- 8.4. Further Connections Between the Two- and Three-Dimensional Theories -- 8.5. Other Types of Approximations -- 8.6. Kirchhoffโs Hypothesis -- 8.7. Boundary Conditions in Kirchhoffโs Theory -- 8.8. Kirchhoffโs Variational Principle -- 8.9. Structure of the Solution of the Equations of Plates of Moderate Thickness -- 8.10. The Edge Effect -- 8.11. Torsion of a Plate -- 8.12. Saint-Venantโs Bending of a Plate -- 8.13. Particular Solutions for Transverse Load -- 8.14. Solutions in Polar Coordinates -- 8.15. Axisymmetric Bending