Cover -- Title page -- Contents -- Preface -- Introduction -- List of Main Symbols -- Chapter 1. A One-Dimensional Beam Metamodel -- 1.1. Models and metamodel -- 1.2. Internally unconstrained beams -- 1.2.1. Kinematics -- 1.2.2. Dynamics -- 1.2.3. The hyperelastic law -- 1.2.4. The Fundamental Problem -- 1.3. Internally constrained beams -- 1.3.1. The mixed formulation for the internally constrained beam kinematics and constraints -- 1.3.2. The displacement method for the internally constrained beam -- 1.4. Internally unconstrained prestressed beams -- 1.4.1. The nonlinear theory -- 1.4.2. The linearized theory -- 1.5. Internally constrained prestressed beams -- 1.5.1. The nonlinear mixed formulation -- 1.5.2. The linearized mixed formulation -- 1.5.3. The nonlinear displacement formulation -- 1.5.4. The linearized displacement formulation -- 1.6. The variational formulation -- 1.6.1. The total potential energy principle -- 1.6.2. Unconstrained beams -- 1.6.3. Constrained beams -- 1.6.4. Unconstrained prestressed beams -- 1.6.5. Constrained prestressed beams -- 1.7. Example: the linear Timoshenko beam -- 1.8. Summary -- Chapter 2. Straight Beams -- 2.1. Kinematics -- 2.1.1. The displacement and rotation fields -- 2.1.2. Tackling the rotation tensor -- 2.1.3. The geometric boundary conditions -- 2.1.4. The strain vector -- 2.1.5. The curvature vector -- 2.1.6. The strain-displacement relationships -- 2.1.7. The velocity and spin fields -- 2.1.8. The velocity gradients and strain-rates -- 2.2. Dynamics -- 2.2.1. The balance of virtual powers -- 2.2.2. The inertial contributions -- 2.2.3. The balance of momentum -- 2.2.4. The scalar forms of the balance equations and boundary conditions -- 2.2.5. The Lagrangian balance equations -- 2.3. Constitutive law -- 2.3.1. The hyperelastic law -- 2.3.2. Identification of the elastic law from a 3D-model.

2.3.3. Homogenization of beam-like structures -- 2.3.4. Linear viscoelastic laws -- 2.4. The Fundamental Problem -- 2.4.1. Exact equations -- 2.4.2. The linearized theory for elastic prestressed beams -- 2.5. The planar beam -- 2.5.1. Kinematics -- 2.5.2. Dynamics -- 2.5.3. The Virtual Power Principle -- 2.5.4. Constitutive laws -- 2.5.5. The Fundamental Problem -- 2.6. Summary -- Chapter 3. Curved Beams -- 3.1. The reference configuration and the initial curvature -- 3.2. The beam model in the 3D-space -- 3.2.1. Kinematics -- 3.2.2. Dynamics -- 3.2.3. The elastic law -- 3.2.4. The Fundamental Problem -- 3.3. The planar curved beam -- 3.3.1. Kinematics -- 3.3.2. Dynamics -- 3.3.3. The Virtual Power Principle -- 3.3.4. Constitutive law -- 3.3.5. Fundamental Problem -- 3.4. Summary -- Chapter 4. Internally Constrained Beams -- 4.1. Stiff beams and internal constraints -- 4.2. The general approach -- 4.3. The unshearable straight beam in 3D -- 4.3.1. The mixed formulation -- 4.3.2. The displacement formulation -- 4.4. The unshearable straight planar beam -- 4.5. The inextensible and unshearable straight beam in 3D -- 4.5.1. Hybrid formulation: Version I -- 4.5.2. Hybrid formulation: Version II -- 4.6. The inextensible and unshearable straight planar beam -- 4.6.1. Hybrid formulation: Version I -- 4.6.2. Hybrid formulation: Version II -- 4.6.3. The mixed formulation -- 4.6.4. The direct condensation of the elastica equilibrium equations -- 4.7. The inextensible, unshearable and untwistable straight beam -- 4.8. The foil-beam -- 4.9. The shear-shear-torsional beam -- 4.10. The planar unshearable and inextensible curved beam -- 4.10.1. The hybrid formulation -- 4.10.2. The mixed formulation -- 4.11. Summary -- Chapter 5. Flexible Cables -- 5.1. Flexible cables as a limit of slender beams -- 5.2. Unprestressed cables -- 5.2.1. Kinematics -- 5.2.2. Dynamics.

5.2.3. Constitutive law -- 5.2.4. The Fundamental Problem -- 5.3. Prestressed cables -- 5.3.1. Quasi-exact models -- 5.3.2. The linearized theory -- 5.3.3. Taut strings -- 5.4. Shallow cables -- 5.4.1. An approximated nonlinear model -- 5.4.2. An approximated linearized model -- 5.5. Inextensible cables -- 5.5.1. Inextensible unprestressed cables -- 5.5.2. Inextensible prestressed cables . -- 5.6. Summary -- Chapter 6. Stiff Cables -- 6.1. Motivations -- 6.2. Unprestressed stiff cables -- 6.2.1. Kinematics -- 6.2.2. Dynamics -- 6.2.3. The elastic law -- 6.2.4. The Fundamental Problem -- 6.3. Prestressed stiff cables -- 6.3.1. Nonlinear model -- 6.3.2. The linearized model -- 6.3.3. Taut strings -- 6.4. Reduced models -- 6.4.1. Sagged cables -- 6.4.2. Shallow cables -- 6.5. Inextensible stiff cables -- 6.5.1. Unprestressed cables -- 6.5.2. Prestressed cables -- 6.5.3. Reduced model -- 6.6. Summary -- Chapter 7. Locally-Deformable Thin-Walled Beams -- 7.1. Motivations -- 7.2. A one-dimensional direct model for double-symmetric TWB -- 7.3. A one-dimensional direct model for non-symmetric TWB -- 7.4. Identification strategy from 3D-models of TWB -- 7.5. A fiber-model of TWB -- 7.6. Warpable, cross-undeformable TWB -- 7.6.1. Kinematics -- 7.6.2. Identification procedure -- 7.6.3. The Fundamental Problem -- 7.7. Unwarpable, cross-deformable, planar TWB -- 7.7.1. Kinematics -- 7.7.2. Identification procedure -- 7.7.3. The Fundamental Problem -- 7.8. Summary -- Chapter 8. Distortion-Constrained Thin-Walled Beams -- 8.1. Introduction -- 8.2. Internal constraints -- 8.2.1. The Vlasov constraint for open TWB -- 8.2.2. The Bredt constraint for tubular TWB -- 8.2.3. The Brazier constraint for planar TWB -- 8.3. The non-uniform torsion problem for bi-symmetric cross-sections -- 8.3.1. The unconstrained model.

8.3.2. The mixed formulation for the constrained model -- 8.3.3. The displacement formulation for the constrained model -- 8.4. The general problem for warpable TWB -- 8.5. Cross-deformable planar TWB -- 8.6. Summary -- Bibliography -- Index.