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Mathematical Models of Beams and Cables [Hardback]

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  • Formāts: Hardback, 410 pages, height x width x depth: 241x163x28 mm, weight: 708 g
  • Izdošanas datums: 25-Oct-2013
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1848214219
  • ISBN-13: 9781848214217
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Mathematical Models of Beams and CablesPalielināt
  • Formāts: Hardback, 410 pages, height x width x depth: 241x163x28 mm, weight: 708 g
  • Izdošanas datums: 25-Oct-2013
  • Izdevniecība: ISTE Ltd and John Wiley & Sons Inc
  • ISBN-10: 1848214219
  • ISBN-13: 9781848214217
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781848214217.html
Keywords:
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 aeroelasticity. Contents

1. A One-Dimensional Beam Metamodel. 2. Straight Beams. 3. Curved Beams. 4. Internally Constrained Beams. 5. Flexible Cables. 6. Stiff Cables. 7. Locally-Deformable Thin-Walled Beams. 8. Distortion-Constrained Thin-Walled Beams.
Preface xi
Introduction xiii
List of Main Symbols xxiii
Chapter 1 A One-Dimensional Beam Metamodel 1(54)
1.1 Models and metamodel
2(1)
1.2 Internally unconstrained beams
3(9)
1.2.1 Kinematics
3(2)
1.2.2 Dynamics
5(4)
1.2.3 The hyperelastic law
9(2)
1.2.4 The Fundamental Problem
11(1)
1.3 Internally constrained beams
12(12)
1.3.1 The mixed formulation for the internally constrained beam kinematics and constraints
13(5)
1.3.2 The displacement method for the internally constrained beam
18(6)
1.4 Internally unconstrained prestressed beams
24(5)
1.4.1 The nonlinear theory
25(1)
1.4.2 The linearized theory
26(3)
1.5 Internally constrained prestressed beams
29(4)
1.5.1 The nonlinear mixed formulation
29(1)
1.5.2 The linearized mixed formulation
30(1)
1.5.3 The nonlinear displacement formulation
31(1)
1.5.4 The linearized displacement formulation
32(1)
1.6 The variational formulation
33(11)
1.6.1 The total potential energy principle
34(2)
1.6.2 Unconstrained beams
36(1)
1.6.3 Constrained beams
37(2)
1.6.4 Unconstrained prestressed beams
39(2)
1.6.5 Constrained prestressed beams
41(3)
1.7 Example: the linear Timoshenko beam
44(3)
1.8 Summary
47(8)
Chapter 2 Straight Beams 55(78)
2.1 Kinematics
55(27)
2.1.1 The displacement and rotation fields
55(5)
2.1.2 Tackling the rotation tensor
60(3)
2.1.3 The geometric boundary conditions
63(1)
2.1.4 The strain vector
64(4)
2.1.5 The curvature vector
68(5)
2.1.6 The strain-displacement relationships
73(1)
2.1.7 The velocity and spin fields
74(4)
2.1.8 The velocity gradients and strain-rates
78(4)
2.2 Dynamics
82(20)
2.2.1 The balance of virtual powers
83(5)
2.2.2 The inertial contributions
88(3)
2.2.3 The balance of momentum
91(6)
2.2.4 The scalar forms of the balance equations and boundary conditions
97(2)
2.2.5 The Lagrangian balance equations
99(3)
2.3 Constitutive law
102(12)
2.3.1 The hyperelastic law
102(2)
2.3.2 Identification of the elastic law from a 3D-model
104(6)
2.3.3 Homogenization of beam-like structures
110(2)
2.3.4 Linear viscoelastic laws
112(2)
2.4 The Fundamental Problem
114(8)
2.4.1 Exact equations
115(3)
2.4.2 The linearized theory for elastic prestressed beams
118(4)
2.5 The planar beam
122(7)
2.5.1 Kinematics
122(2)
2.5.2 Dynamics
124(2)
2.5.3 The Virtual Power Principle
126(1)
2.5.4 Constitutive laws
127(1)
2.5.5 The Fundamental Problem
127(2)
2.6 Summary
129(4)
Chapter 3 Curved Beams 133(30)
3.1 The reference configuration and the initial curvature
133(4)
3.2 The beam model in the 3D-space
137(15)
3.2.1 Kinematics
137(5)
3.2.2 Dynamics
142(2)
3.2.3 The elastic law
144(1)
3.2.4 The Fundamental Problem
144(8)
3.3 The planar curved beam
152(8)
3.3.1 Kinematics
153(2)
3.3.2 Dynamics
155(2)
3.3.3 The Virtual Power Principle
157(1)
3.3.4 Constitutive law
157(1)
3.3.5 Fundamental Problem
158(2)
3.4 Summary
160(3)
Chapter 4 Internally Constrained Beams 163(42)
4.1 Stiff beams and internal constraints
163(3)
4.2 The general approach
166(2)
4.3 The unshearable straight beam in 3D
168(9)
4.3.1 The mixed formulation
169(3)
4.3.2 The displacement formulation
172(5)
4.4 The unshearable straight planar beam
177(3)
4.5 The inextensible and unshearable straight beam in 3D
180(3)
4.5.1 Hybrid formulation: Version I
181(1)
4.5.2 Hybrid formulation: Version II
182(1)
4.6 The inextensible and unshearable straight planar beam
183(7)
4.6.1 Hybrid formulation: Version I
183(2)
4.6.2 Hybrid formulation: Version II
185(1)
4.6.3 The mixed formulation
186(2)
4.6.4 The direct condensation of the elastica equilibrium equations
188(2)
4.7 The inextensible, unshearable and untwistable straight beam
190(2)
4.8 The foil-beam
192(1)
4.9 The shear-shear-torsional beam
193(4)
4.10 The planar unshearable and inextensible curved beam
197(4)
4.10.1 The hybrid formulation
197(3)
4.10.2 The mixed formulation
200(1)
4.1 1 Summary
201(4)
Chapter 5 Flexible Cables 205(38)
5.1 Flexible cables as a limit of slender beams
205(2)
5.2 Unprestressed cables
207(13)
5.2.1 Kinematics
207(6)
5.2.2 Dynamics
213(4)
5.2.3 Constitutive law
217(1)
5.2.4 The Fundamental Problem
218(2)
5.3 Prestressed cables
220(10)
5.3.1 Quasi-exact models
220(5)
5.3.2 The linearized theory
225(2)
5.3.3 Taut strings
227(3)
5.4 Shallow cables
230(5)
5.4.1 An approximated nonlinear model
231(3)
5.4.2 An approximated linearized model
234(1)
5.5 Inextensible cables
235(5)
5.5.1 Inextensible unprestressed cables
236(1)
5.5.2 Inextensible prestressed cables
237(3)
5.6 Summary
240(3)
Chapter 6 Stiff Cables 243(28)
6.1 Motivations
243(3)
6.2 Unprestressed stiff cables
246(6)
6.2.1 Kinematics
246(3)
6.2.2 Dynamics
249(2)
6.2.3 The elastic law
251(1)
6.2.4 The Fundamental Problem
251(1)
6.3 Prestressed stiff cables
252(9)
6.3.1 Nonlinear model
253(3)
6.3.2 The linearized model
256(2)
6.3.3 Taut strings
258(3)
6.4 Reduced models
261(3)
6.4.1 Sagged cables
261(2)
6.4.2 Shallow cables
263(1)
6.5 Inextensible stiff cables
264(5)
6.5.1 Unprestressed cables
265(1)
6.5.2 Prestressed cables
266(2)
6.5.3 Reduced model
268(1)
6.6 Summary
269(2)
Chapter 7 Locally-Deformable Thin-Walled Beams 271(40)
7.1 Motivations
271(2)
7.2 A one-dimensional direct model for double-symmetric TWB
273(4)
7.3 A one-dimensional direct model for non-symmetric TWB
277(7)
7.4 Identification strategy from 3D-models of TWB
284(1)
7.5 A fiber-model of TWB
285(4)
7.6 Warpable, cross-undeformableTWB
289(10)
7.6.1 Kinematics
289(4)
7.6.2 Identification procedure
293(6)
7.6.3 The Fundamental Problem
299(1)
7.7 Unwarpahle, cross-deformable, planar TWB
299(9)
7.7.1 Kinematics
300(3)
7.7.2 Identification procedure
303(4)
7.7.3 The Fundamental Problem
307(1)
7.8 Summary
308(3)
Chapter 8 Distortion-Constrained Thin-Walled Beams 311(24)
8.1 Introduction
311(1)
8.2 Internal constraints
312(5)
8.2.1 The Vlasov constraint for open TWB
312(2)
8.2.2 The Bredt constraint for tubular TWB
314(2)
8.2.3 The Brazier constraint for planar TWB
316(1)
8.3 The non-uniform torsion problem for bi-symmetric cross-sections
317(7)
8.3.1 The unconstrained model
317(2)
8.3.2 The mixed formulation for the constrained model
319(4)
8.3.3 The displacement formulation for the constrained model
323(1)
8.4 The general problem for warpable TWB
324(4)
8.5 Cross-deformable planar TWB
328(4)
8.6 Summary
332(3)
Bibliography 335(10)
Index 345
Angelo Luongo is Full Professor at University of L'Aquila, Italy.

Daniele Zulli, Assistant Professor, University of L'Aquila, Italy.