Tensor Analysis and Continuum Mechanics

Preface. 1: Tensors. 1. First steps with tensors. 2. Operations of tensors. 3. Euclidean vector space. 4. Exterior algebra. 5. Point spaces. Exercises. 2 : Lagrangian and Eulerian Descriptions. 1. Lagrangian description. 2. Eulerian description. Exercises. 3 : Deformations. 1. Homogeneous transformation. 2. Tangential homogeneous transformation. 3. Infinitesimal transformation. Exercises. 4: Kinematics of Continua. 1. Lagrangian kinematics. 2. Eulerian kinematics. 3. Material derivatives of circulation, flux, and volume. Exercises. 5: Fundamental Laws: Principle of Virtual Work. 1. Conservation of mass and continuity equation. 2. Fundamental laws of dynamics. 3. Theorem of kinetic energy. 4. Study of stresses. 5. Principle of virtual work. 6. Thermomechanics and balance equations. Exercises. 6: Linear Elasticity. 1. Elasticity and tests. 2. Generalized Hooke's law in linear elasticity. 3. Equations and principles in elastostatics. 4. Classical problems. Exercises. Summary of Formulae. Bibliography. Glossary of Symbols. Index.