05617nam 2200721 450 991014018770332120200520144314.01-118-57755-81-118-57763-91-118-57764-7(CKB)2670000000494155(EBL)1575622(SSID)ssj0001100646(PQKBManifestationID)11642265(PQKBTitleCode)TC0001100646(PQKBWorkID)11063909(PQKB)11175133(MiAaPQ)EBC4036443(MiAaPQ)EBC1575622(Au-PeEL)EBL1575622(CaPaEBR)ebr10814441(CaONFJC)MIL550403(OCoLC)865333128(EXLCZ)99267000000049415520131211d2013 uy 0engur|n|---|||||txtccrMathematical models of beams and cables /Angelo Luongo, Daniele Zulli ; series editor, Noël ChallamelLondon, England ;Hoboken, New Jersey :Wiley,2013.©20131 online resource (379 p.)Mechanical engineering and solid mechanics seriesDescription based upon print version of record.1-84821-421-9 Includes bibliographical references and index.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 theory1.5. 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 fields2.1.2. 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 law2.3.2. 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 law3.2.4. 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 II4.6. The inextensible and unshearable straight planar beamNonlinear 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 aeroelasticitISTEStructural analysis (Engineering)Mathematical modelsGirdersCablesStructural analysis (Engineering)Mathematical models.Girders.Cables.624.1772Luongo Angela974469Challamel Noël974470John Wiley & Sons,MiAaPQMiAaPQMiAaPQBOOK9910140187703321Mathematical models of beams and cables2218597UNINA