Mathematical Models of Beams and Cables

Angelo Luongo is Full Professor at the University of L'Aquila, Italy. His main research areas are the dynamics and elastic stability of structural systems.Daniele Zulli is Assistant Professor at the University of L'Aquila, Italy.

• Preface xiIntroduction xiiiList of Main Symbols xxiiiChapter 1. A One-Dimensional Beam Metamodel 11.1. Models and metamodel 21.2. Internally unconstrained beams 31.3. Internally constrained beams 121.4. Internally unconstrained prestressed beams 241.5. Internally constrained prestressed beams 291.6. The variational formulation 331.7. Example: the linear Timoshenko beam 441.8. Summary 47Chapter 2. Straight Beams 552.1. Kinematics 552.2. Dynamics 822.3. Constitutive law 1022.4. The Fundamental Problem 1142.5. The planar beam 1222.6. Summary 129Chapter 3. Curved Beams 1333.1. The reference configuration and the initial curvature 1333.2. The beam model in the 3D-space 1373.3. The planar curved beam 1523.4. Summary 160Chapter 4. Internally Constrained Beams 1634.1. Stiff beams and internal constraints 1634.2. The general approach 1664.3. The unshearable straight beam in 3D 1684.4. The unshearable straight planar beam 1774.5. The inextensible and unshearable straight beam in 3D 1804.6. The inextensible and unshearable straight planar beam 1834.7. The inextensible, unshearable and untwistable straight beam 1904.8. The foil-beam 1924.9. The shear–shear–torsional beam 1934.10. The planar unshearable and inextensible curved beam 1974.11. Summary 201Chapter 5. Flexible Cables 2055.1. Flexible cables as a limit of slender beams 2055.2. Unprestressed cables 2075.3. Prestressed cables 2205.4. Shallow cables 2305.5. Inextensible cables 2355.6. Summary 240Chapter 6. Stiff Cables 2436.1. Motivations 2436.2. Unprestressed stiff cables 2466.3. Prestressed stiff cables 2526.4. Reduced models 2616.5. Inextensible stiff cables 2646.6. Summary 269Chapter 7. Locally-Deformable Thin-Walled Beams 2717.1. Motivations 2717.2. A one-dimensional direct model for double-symmetric TWB 2737.3. A one-dimensional direct model for non-symmetric TWB 2777.4. Identification strategy from 3D-models of TWB 2847.5. A fiber-model of TWB 2857.6. Warpable, cross-undeformable TWB 2897.7. Unwarpable, cross-deformable, planar TWB 2997.8. Summary 308Chapter 8. Distortion-Constrained Thin-Walled Beams 3118.1. Introduction 3118.2. Internal constraints 3128.3. The non-uniform torsion problem for bi-symmetric cross-sections 3178.4. The general problem for warpable TWB 3248.5. Cross-deformable planar TWB 3288.6. Summary 332Bibliography 335Index 345