Cambridge University Press, Oct 16, 2003 - Computers - 384 pages
Automobiles, space structures, robots, and machines are examples of mechanical and structural systems that consist of interconnected rigid and deformable components. The dynamics of these large-scale, multibody systems are highly nonlinear, presenting complex problems that in most cases can only be solved with computer-based techniques. This book provides an introduction to the subject of multibody dynamics, with an emphasis on flexible body dynamics. The first chapter covers the basic ideas of kinematics and dynamics of rigid and deformable bodies. The book then moves on to advanced topics, including finite element formulations, and concludes with a clear, careful explanation of newer computational techniques. With its wealth of examples and practical applications, this book will be useful to graduate students, researchers, and practising engineers working with a wide variety of flexible multibody systems.
Contents
INTRODUCTION | 1 |
12 Reference Frames | 3 |
13 Particle Mechanics | 6 |
14 Rigid Body Mechanics | 11 |
15 Deformable Bodies | 15 |
16 Constrained Motion | 19 |
17 Computer Formulation and Coordinate Selection | 22 |
18 Objectives and Scope of This Book | 25 |
53 Generalized Forces | 216 |
54 Kinematic Constraints | 222 |
55 Equations of Motion | 226 |
56 Coupling between Reference and Elastic Displacements | 231 |
57 Application to a Multibody System | 234 |
58 Use of Independent Coordinates | 244 |
59 Dynamic Equations with Multipliers | 247 |
510 Generalized Coordinate Partitioning | 251 |
REFERENCE KINEMATICS | 28 |
21 Rotation Matrix | 29 |
22 Properties of the Rotation Matrix | 37 |
23 Successive Rotation | 42 |
24 Angular Velocity Vector | 50 |
25 Acceleration Equations | 60 |
26 Rodriguez Parameters | 63 |
27 Euler Angles | 67 |
28 Direction Cosines | 72 |
29 The 4 x 4 Transformation Matrix | 76 |
210 Relationship between Different Orientation Coordinates | 84 |
Problems | 86 |
ANALYTICAL TECHNIQUES | 89 |
31 Generalized Coordinates and Kinematic Constraints | 90 |
32 Degrees of Freedom and Generalized Coordinate Partitioning | 99 |
33 Virtual Work and Generalized Forces | 108 |
34 Lagrangian Dynamics | 120 |
35 Calculus of Variations | 134 |
36 Eulers Equation in the Case of Several Variables | 140 |
37 Equations of Motion of Rigid Body Systems | 148 |
38 NewtonEuler Equations | 156 |
39 Concluding Remarks | 159 |
Problems | 162 |
MECHANICS OF DEFORMABLE BODIES | 165 |
41 Kinematics of Deformable Bodies | 166 |
42 Strain Components | 169 |
43 Physical Interpretation of Strains | 172 |
44 Rigid Body Motion | 174 |
45 Stress Components | 177 |
46 Equations of Equilibrium | 180 |
47 Constitutive Equations | 182 |
48 Virtual Work of the Elastic Forces | 188 |
Problems | 189 |
FLOATING FRAME OF REFERENCE FORMULATION | 191 |
51 Kinematic Description | 192 |
52 Inertia of Deformable Bodies | 203 |
511 Organization of Multibody Computer Programs | 254 |
512 Numerical Algorithms | 257 |
Problems | 266 |
FINITEELEMENT FORMULATION | 270 |
61 Element Shape Function | 271 |
62 Reference Conditions | 278 |
63 Kinetic Energy | 281 |
64 Generalized Elastic Forces | 289 |
65 Characterization of Planar Elastic Systems | 291 |
66 Characterization of Spatial Elastic Systems | 297 |
67 Coordinate Reduction | 302 |
68 The Floating Frame of Reference and Large Deformation Problem | 306 |
Problems | 309 |
THE LARGE DEFORMATION PROBLEM | 311 |
71 Background | 312 |
72 Absolute Nodal Coordinate Formulation | 316 |
73 Formulation of the Stiffness Matrix | 320 |
74 Equations of Motion | 324 |
75 Relationship to the Floating Frame of Reference Formulation | 325 |
76 Coordinate Transformation | 327 |
77 Consistent Mass Formulation | 330 |
78 The Velocity Transformation Matrix | 333 |
79 Lumped Mass Formulation | 334 |
710 Extension of the Method | 337 |
711 Comparison with Large Rotation Vector Formulation | 341 |
Problems | 344 |
LINEAR ALGEBRA | 347 |
A2 Eigenvalue Analysis | 351 |
A3 Vector Spaces | 352 |
A4 Chain Rule of Differentiation | 355 |
A5 Principle of Mathematical Induction | 356 |
Problems | 357 |
| 359 | |
| 367 | |
Bibliographic information
| Title | Dynamics of Multibody Systems |
| Author | Ahmed A. Shabana |
| Edition | illustrated, revised |
| Publisher | Cambridge University Press, 2003 |
| ISBN | 0521544114, 9780521544115 |
| Length | 384 pages |
| Subjects | › › Computers / Computer Science |
| Export Citation | BiBTeX EndNote RefMan |