Mathematical models of beams and cables / / Angelo Luongo, Daniele Zulli ; series editor, Noël Challamel

• Autore: Luongo Angela
• Pubblicazione: London, England ; ; Hoboken, New Jersey : , : Wiley, , 2013; ©2013
• Descrizione fisica: 1 online resource (379 p.)
• Disciplina: 624.1772
• Soggetto topico: Structural analysis (Engineering) - Mathematical models; Girders; Cables
• Altri autori: ChallamelNoël
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 beams1.5.1. 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 tensor2.1.3. 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-model2.3.3. 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 Problem3.3. 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
• Sommario/riassunto: Nonlinear models of elastic and visco-elastic onedimensional continuous structures (beams and cables) are formulated by the authors of this title. Several models of increasing complexity are presented: straight/curved, planar/non-planar, extensible/inextensible, shearable/unshearable, warpingunsensitive/ sensitive, prestressed/unprestressed beams, both in statics and dynamics. Typical engineering problems are solved via perturbation and/or numerical approaches, such as bifurcation and stability under potential and/or tangential loads, parametric excitation, nonlinear dynamics and aeroelasticit
• Titolo autorizzato: Mathematical models of beams and cables
• ISBN: 1-118-57755-8; 1-118-57763-9; 1-118-57764-7
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910807702703321
• Lo trovi qui: Univ. Federico II
• Serie: ISTE