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Solid Mechanics and Its Applications

By: J-C. Samin, P. Fisette

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Hardcover | 30 November 2003

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Hardcover
492 Pages

Dimensions(cm)
24.13 x 15.88 x 2.54

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$249.00

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Modeling and analysing multibody systems require a comprehensive understanding of the kinematics and dynamics of rigid bodies. In this volume, the relevant fundamental principles are first reviewed in detail and illustrated in conformity with the multibody formalisms that follow. Whatever the kind of system (tree-like structures, closed-loop mechanisms, systems containing flexible beams or involving tire/ground contact, wheel/rail contact, etc), these multibody formalisms have a common feature in the proposed approach, viz, the symbolic generation of most of the ingredients needed to set up the model.
The symbolic approach chosen, specially dedicated to multibody systems, affords various advantages: it leads to a simplification of the theoretical formulation of models, a considerable reduction in the size of generated equations and hence in resulting computing time, and also enhanced portability of the multibody models towards other specific environments. Moreover, the generation of multibody models as symbolic toolboxes proves to be an excellent pedagogical medium in teaching mechanics.

Industry Reviews

From the reviews:

"This is a monograph on multibody system modelling and on the associated dynamics of the resulting models. ... The volume is intended for researchers and practitioners concerned with the dynamics of large complex mechanical systems. The book is also represented to be a teaching aid for students. ... The book summarizes many research results developed by the authors and their colleagues at their research institute. ... The book is reasonably well written, and the analyses appear to be sound." (Ronald L. Huston, Zentralblatt MATH, Vol. 1044 (19), 2004)

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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Dynamics & Statics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Solids Dynamics & Vibration Mechanical Engineering Technology in General

Engineering in General Science in General Technical Design

Theory	p. 1
Fundamental Mechanics	p. 3
Mathcmatical background and notations	p. 3
Vectors	p. 3
Tensors	p. 8
Array of vectors	p. 9
Vector pre-product tensor	p. 11
An example: the rotation tensor	p. 12
Transformation matrices	p. 14
Euler's theorem on finite rotations	p. 15
Rotation coordinates	p. 17
Time derivatives of vectors and tensors	p. 21
Angular velocity vector	p. 24
Rigid body representation	p. 26
Rigid body definition	p. 26
Rigid body kinematics	p. 27
Body center of mass	p. 28
Body linear momentum	p. 29
Body angular momentum	p. 30
Inertia tensor	p. 31
Forces and torques acting on a rigid body	p. 34
Power considerations	p. 37
Newton-Euler equations	p. 38
Dynamics of rigid bodies	p. 43
Introduction	p. 43
Generalized coordinates	p. 43
Generalized coordinates and holonomic constraints	p. 43
Generalized velocities and non-holonomic constraints	p. 49
Degrees of freedom	p. 52
Newton-Euler procedure	p. 54
The procedure	p. 54
An example	p. 58
Variational Approach	p. 65
Virtual power principle	p. 65
Generalized forces and Lagrange multipliers	p. 75
Physical interpretation of the Lagrange multipliers	p. 79
An example: a pendulum supported by rollers	p. 81
Application of the Lagrange multiplier technique	p. 84
Appendix	p. 86
Tree-like multibody structures	p. 89
Definitions, conventions and hypotheses	p. 89
Fundamental concepts	p. 89
Topology	p. 92
Kinematics: main definitions	p. 93
Dynamics: main definitions	p. 98
Barycentric quantities	p. 99
Virtual power principle	p. 101
Introduction	p. 101
Kinematics and virtual velocity changes	p. 102
Translational vector equation	p. 103
Rotational vector equation	p. 105
Equations of motion	p. 108
Matrix form of the joint equations	p. 112
Newton-Euler scheme	p. 114
Introduction	p. 114
Forward kinematics	p. 115
Backward dynamics	p. 118
Newton-Euler scheme with barycentric parameters	p. 121
Introduction	p. 121
Inverse Dynamics	p. 122
Recursive direct dynamics	p. 125
Complex multibody structures	p. 129
Closed-loop structures	p. 130
Cut of a body	p. 132
Cut in a ball joint	p. 135
Cut of a connecting rod	p. 136
User joints/constraints	p. 138
Helicoidal joint	p. 138
Kinematically driven joint	p. 140
Transmission by pulley	p. 141
Gear transmission	p. 142
Point-to-point links	p. 143
Sub-system segmentation	p. 146
Equations of motion (without constraints between sub-systems)	p. 148
Equations of motion (with constraints between sub-systems)	p. 150
Complementary multibody kinematics	p. 154
Loop closure kinematics	p. 154
User joint/constraints and point-to-point links	p. 158
Numerical aspects	p. 158
Coordinate partitioning	p. 158
Pseudo rotation constraints	p. 162
Symbolic generation	p. 169
Introduction	p. 169
Symbolic mathematical expressions	p. 172
Tree representation	p. 172
Expression organization	p. 174
Computer memory: allocation and freeing	p. 179
Trigonometric expressions	p. 182
Introduction	p. 182
Symbolic process	p. 13
Illustrative examples	p. 187
Recursive scheme condensation	p. 187
Introduction	p. 187
Recursive symbolic computation	p. 188
Elimination process	p. 190
Scheme vectorization	p. 192
Recursive symbolic differentiation	p. 194
Introduction	p. 194
Recursive scheme differentiation	p. 196
Performance evaluation	p. 198
Introduction	p. 198
Performance comparison	p. 198
Discussion	p. 200
Computer implementation	p. 203
Joint modeling hypothesis	p. 203
Program overview	p. 205
Description of the symbolic models	p. 207
A short example: the four-bar mechanism	p. 209
Symbolic input files	p. 210
Symbolic output files	p. 211
Special topics	p. 217
Road vehicles: wheel/ground model	p. 219
Introduction	p. 219
Definitions and hypotheses	p. 220
Wheel/ground geometrical contact	p. 223
Point and vector definitions	p. 223
Contact point: geometrical solution	p. 225
Wheel/ground forces and torques	p. 228
Wheel/ground contact kinematics	p. 228
Contact force model	p. 230
Numerical examples	p. 238
Introduction	p. 238
The ILTIS vehicle benchmark	p. 239
An off-road vehicle	p. 244
A complete modern car	p. 245
Railway vehicles: wheel/rail model	p. 249
Introduction	p. 249
Wheel/rail kinematic model	p. 251
Contact model of a wheel on a straight track	p. 251
Contact of a wheel on a curved track (with constant radius)	p. 260
Wheel/rail contact forces and torques	p. 261
Wheel/rail contact kinematics	p. 261
Wheel/rail contact forces	p. 262
Applications in railway dynamics	p. 263
Geometrical contact between a S1002 wheelset and UIC60 rails	p. 263
Limit cycle of a rigid wheelset at constant speed	p. 265
BAS 2000 bogie	p. 265
Tramway 2000	p. 269
Mechanisms: cam/follower model	p. 273
Introduction	p. 273
Description of cam/follower systems	p. 274
Hypotheses and general notations	p. 274
Cam and follower profiles	p. 276
Kinematic constraints	p. 278
Preliminary computations	p. 278
Contact constraints	p. 280
Constraint derivatives	p. 283
Contact forces	p. 287
Permanent contact	p. 287
Intermittent contact	p. 291
Numerical examples	p. 293
Introduction	p. 293
Cam/follower model: numerical validation	p. 294
Cam/follower model: experimental validation	p. 294
Modeling of universal wheels	p. 296
Multibody systems with flexible beams	p. 301
Introduction	p. 301
The finite segment approach	p. 304
The assumed mode approach	p. 305
Description of the flexible beam	p. 305
Kinematics	p. 309
Joint equations	p. 315
Deformation equations	p. 321
Symbolic computation of the equations of motion	p. 333
Numerical examples	p. 336
Time integration of flexible MBS	p. 345
Introduction	p. 345
Implicit integration method	p. 347
Residual formulation of the MBS equations in a Newmark scheme	p. 347
Iterative solution of the reduced form	p. 349
Local truncation error estimation	p. 352
Contribution of symbolic generation	p. 352
General algorithm - optimization strategy	p. 354
General algorithm	p. 354
Numerical optimization	p. 354
Numerical Example	p. 357
Validation	p. 358
Evaluation of the proposed method	p. 359
Tutorial	p. 363
Introduction	p. 365
Methodology	p. 366
Analysis	p. 367
Program run	p. 369
Problem statements	p. 372
Problem 1: a double spring-mass system	p. 372
Problem 2: a merry-go-round	p. 372
Problem 3: a small cart	p. 372
Problem 4: a slider-crank mechanism	p. 372
Problem 5: small cart 2	p. 372
Problem 6: a five-point suspension	p. 372
Problem 7: a jeep suspension	p. 373
Problem 8: a jeep	p. 373
Problem 9: a flexible slider-crank	p. 373
Problem 10: a radiation counter	p. 373
Problem 11: a "cam/follower" device	p. 373
Problems	p. 375
A double spring-mass system	p. 375
Analysis	p. 375
Multibody model	p. 376
Computer pre-process	p. 377
Computer process	p. 378
Computer post-process	p. 379
A merry-go-round	p. 380
Analysis	p. 380
Multibody model	p. 382
Computer pre-process	p. 383
Computer process	p. 385
Computer post-process	p. 387
A small cart	p. 388
Analysis	p. 388
Multibody model	p. 389
Computer pre-process	p. 391
Computer process	p. 393
Computer post-process	p. 394
A slider-crank mechanism	p. 395
Analysis	p. 396
Multibody model	p. 397
Computer pre-process	p. 398
Computer process	p. 399
Computer post-process	p. 400
Small cart 2	p. 401
Analysis	p. 401
Multibody model	p. 401
Computer pre-process	p. 402
Computer process	p. 403
Computer post-process	p. 403
A five-point suspension	p. 405
Analysis	p. 405
Multibody model	p. 407
Computer pre-process	p. 408
Computer process	p. 411
Computer post-process	p. 412
A jeep suspension	p. 415
Analysis	p. 416
Multibody model	p. 418
Computer pre-process	p. 420
Computer process	p. 421
Computer post-process	p. 422
A jeep	p. 423
Analysis	p. 423
Multibody model	p. 425
Computer pre-process	p. 426
Computer process	p. 429
Computer post-process	p. 431
A flexible slider-crank	p. 434
Analysis	p. 434
Multibody model	p. 436
Computer pre-process	p. 437
Computer process	p. 437
Computer post-process	p. 439
A radiation counter	p. 440
Analysis	p. 440
Multibody model	p. 441
Computer pre-process	p. 442
Computer process	p. 444
Computer post-process	p. 446
A "cam/follower" device	p. 447
Analysis	p. 447
Multibody model	p. 448
Computer pre-process	p. 449
Computer process	p. 450
Computer post-process	p. 452
Table of Contents provided by Ingram. All Rights Reserved.

Solid Mechanics and Its Applications

At a Glance

Hardcover

Industry Reviews

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