Ambrosio / Eberhard Advanced Design of Mechanical Systems: From Analysis to Optimization

1. Auflage 2009
ISBN: 978-3-211-99461-0
Verlag: Springer Vienna
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 511, 426 Seiten

Reihe: CISM International Centre for Mechanical Sciences

Multibody systems are used extensively in the investigation of mechanical systems including structural and non-structural applications. It can be argued that among all the areas in solid mechanics the methodologies and applications associated to multibody dynamics are those that provide an ideal framework to aggregate d- ferent disciplines. This idea is clearly reflected, e. g. , in the multidisciplinary applications in biomechanics that use multibody dynamics to describe the motion of the biological entities, in finite elements where multibody dynamics provides - werful tools to describe large motion and kinematic restrictions between system components, in system control where the methodologies used in multibody dynamics are the prime form of describing the systems under analysis, or even in many - plications that involve fluid-structure interaction or aero elasticity. The development of industrial products or the development of analysis tools, using multibody dynamics methodologies, requires that the final result of the devel- ments are the best possible within some limitations, i. e. , they must be optimal. Furthermore, the performance of the developed systems must either be relatively insensitive to some of their design parameters or be sensitive in a controlled manner to other variables. Therefore, the sensitivity analysis of such systems is fundamental to support the decision making process. This book presents a broad range of tools for designing mechanical systems ranging from the kinematic and dynamic analysis of rigid and flexible multibody systems to their advanced optimization.

Autoren/Hrsg.

Ambrosio, Jorge A. C.

Eberhard, Peter

Inhaltsverzeichnis

1;PREFACE;6
2;TABLE OF CONTENTS;8
3;1 Planar Multibody Systems;12
3.1;1.1 Introduction;12
3.2;1.2 Cartesian Coordinates;12
3.3;1.3 Kinematic Constraints;15
3.4;1.4 Drivers;19
3.5;1.5 Solution of the Kinematic Problem;21
3.6;1.6 Velocities and Accelerations;24
3.7;1.7 Newton's Equation;26
3.8;1.8 Forces;28
3.9;1.9 Numerical Integration;31
3.10;References;32
4;2 Spatial Multibody Systems;33
4.1;2.1 Introduction to Spatial Kinematic Constraints;33
4.2;2.2 Rotational Coordinates;33
4.3;2.3 Kinematic Constraints;37
4.4;2.4 Kinematic Joints;40
4.5;2.5 Newton-Euler Equations;43
4.6;2.6 Forces;46
4.7;2.7 Solution of the Equations of Motion;47
4.8;References;48
5;3 Synthesis of Mechanisms;49
5.1;3.1 Introduction;49
5.2;3.2 The Joint Coordinate Method;52
5.3;3.3 Optimization;57
5.4;3.4 Optimization;62
5.5;3.5 Synthesis Allowing for Non-Assembly;64
5.6;References;76
6;4 Differential-Geometric Aspects of Constrained System Dynamics;77
6.1;4.1. Introduction;77
6.2;4.2. Unconstrained System Dynamics 4.2.1. Equations of Motion;77
7;5 Dependent Variable Formulations;92
7.1;5.1. Introduction;92
7.2;5.2. Governing Equations in DAE Forms;92
7.3;5.2.1. Index-One Governing DAEs;93
7.4;5.2.2. Direct Numerical Solution of the Governing DAEs;96
7.5;5.3. ODE Forms of the Equations of Motion 5.3.1. Implicit Elimination of Lagrange Multipliers;98
7.6;5.3.2. Explicit Elimination of Lagrange Multipliers;99
7.7;5.3.3. Projective Elimination of Lagrange Multipliers;99
7.8;H H;100
7.9;5.4. Constraint Violation Problem;100
7.10;5.4.1. Baumgarte’s Constraint Violation Stabilization Method Method Method Method;101
7.11;5.4.2. Projective Elimination of Constraint Violations;102
7.12;5.4.3. Case Study;104
7.13;5.5. Aspects of Accuracy of Constraint-Consistent Solutions;106
8;6 Independent Variable Formulations;115
8.1;6.1. Introduction;115
8.2;6.2. Joint Coordinate Formulation for Open-Loop Systems 6.2.1. Joint Coordinates;115
8.3;6.2.2. The Joint Coordinate Formulation Scheme;117
8.4;6.3. Velocity Partitioning Formulation;120
8.5;6.4. General Projective Scheme for Independent Variable Formulations 6.4.1. The Projective Scheme;125
8.6;D;126
8.7;6.4.2. Relevance to Other Methods;126
8.8;6.5. Treatment of Closed-Loop Multibody Systems;128
8.9;6.5.1. Joint Coordinate Formulation for the Equivalent Open- Loop System;130
8.10;6.5.2. The Minimal-Form Formulation;131
9;7 Other Useful Modeling and Simulation Techniques;138
9.1;7.1. Introduction;138
9.2;7.2. Augmented Lagrangian Formulation;138
9.3;7.2.1. Penalty Formulation;139
9.4;7.2.2. Physical Interpretation and Computational Code of the Augmented Lagrangian Formulation;140
9.5;7.2.3. Application Range and Computational Issues;145
9.6;7.2.4. Case Study;147
9.7;7.3. Augmented Joint Coordinate Method 7.3.1. Formulation for Open- Loop Systems;149
9.8;, ,;153
9.9;7.3.2. Extension to Closed-Loop Systems;156
9.10;· · · · · · · · · · · ·;280
9.11;Manipulator;283
9.12;14.4 Topology Optimization of Mechanisms;298
9.13;I;301
9.14;{;301
9.15;••;301
9.16;14.5 Concluding Remarks;301
10;8 Sensitivity Analysis: Linear Static Spring Systems;158
10.1;8.1 Introduction;158
10.2;8.2 Notation;159
10.3;8.3 Static Analysis;161
10.4;8.4 Solution Strategy;165
10.5;8.5 Finite Element Program;168
10.6;8.6 Sensitivity Analysis;179
10.7;8.7 Sensitivity Computer Program;189
10.8;8.8 Optimization Problems;197
10.9;References;199
11;9 Sensitivity Analysis: Nonlinear Static Spring Systems;201
11.1;9.1 Nonlinear Linear Static Spring Systems;201
11.2;9.2 Newton Raphson Method;203
11.3;9.3 Sensitivity Analysis: Nonlinear Elastic Static Spring Sys-tems;212
11.4;9.4 Transient Problems;222
11.5;References;223
12;10 Sensitivity Analysis: Generalized Coordinate Kinematic Systems;224
12.1;10.1 Position Analysis;224
12.2;10.2 Velocity and Acceleration Analysis;230
12.3;10.3 Inverse Dynamic Analysis;231
12.4;10.4 Sensitivity Analysis;236
12.5;10.5 Conclusion;240
12.6;References;240
13;11 Optimization of Mechanical Systems;241
13.1;11.1 Introduction;241
13.2;11.2 Optimization Algorithms;244
13.3;11.3 An Example from Multibody Dynamics;249
13.4;11.4 Concluding Remarks;254
13.5;References;255
14;12 Using Augmented Lagrangian Particle Swarm Optimization for Constrained Problems in Engineering;257
14.1;12.1 The Basic PSO Algorithm;260
14.2;12.2 Augmented Lagrange Multiplier Method;261
14.3;12.3 Augmented Lagrange Particle Swarm Optimization;264
14.4;12.4 Web-Based Optimization with ALPSO;268
14.5;12.5 Engineering Example: Hexapod Robot;269
14.6;12.6 Concluding remarks;273
14.7;References;274
15;13 Optimization of Mechatronic Systems using the Software Package NEWOPT/AIMS*;276
15.1;13.1 Optimization of Mechatronic Systems;277
15.2;13.2 Software Package NEWOPT/AIMS;279
15.3;13.3 Example: Hexapod;283
15.4;13.4 Concluding Remarks;287
15.5;References;287
16;14 Topology Optimized Synthesis of Planar Kinematic Rigid Body Mechanisms;289
16.1;14.1 Topology Representation of Mechanisms;291
16.2;14.2 Genetic Algorithms;293
16.3;14.3 Kinematic Analysis and Dimensional Synthesis;294
16.4;References;302
17;15 Grid-Based Topology Optimization of Rigid Body Mechanisms;305
17.1;15.1 Grid Structures for Topology Optimization;306
17.2;15.2 Kinematic Analysis;307
17.3;15.3 Mechanism Design Using Grid Structures;309
17.4;15.4 Amplifier Mechanism Example;315
17.5;15.5 Concluding Remarks;315
17.6;References;316
18;16 Lumped Deformations: a Plastic Hinge Approach;318
18.1;16.1 Introduction;318
18.2;16.2 Flexible Multibody Dynamics by Lumped Deformations;320
18.3;16.2.1 Finite Segment Approach to Elastic Flexible Multibody Systems;320
18.4;16.2.2 Plastic Hinges in Multibody Nonlinear Deformations;321
18.5;16.3 Plastic Hinges Constitutive Relations Implementation;323
18.6;16.4 Continuous Contact Force Model;325
18.7;16.4.1 A Penalty Contact Formulation;325
18.8;16.4.2 Numerical Issues Using a Penalty Contact Formulation;326
18.9;16.5 Road Vehicle Multibody Model for Crash Analysis;327
18.10;16.5.1 Road Vehicle Model Construction;329
18.11;16.5.2 Improvement of the Multibody Model: Trial and Error;333
18.12;16.5.3 Vehicle Model Upgrading as an Optimal Problem;334
18.13;16.6 Application to the Design of Railway Dynamics Crash Tests;337
18.14;16.6.1 Railway Vehicles and Crash Scenario;338
18.15;16.6.2 Optimal Design of a Railway Crash Test;341
18.16;16.6.3 Experimental Validation of the Design;345
18.17;References;348
19;17 Distributed Deformation: a Finite Element Method;351
19.1;17.1 Introduction;351
19.2;17.2 Brief Literature Overview;351
19.3;17.3 General Deformation of a Flexible Body;354
19.4;17.4 Reference Conditions in a Flexible Body: Linear Elastic Deformations;356
19.5;17.4.1 Body Fixed Frames Frames Frames;356
19.6;17.4.2 Mean Axis Conditions;357
19.7;17.4.3 Principal Axis Conditions Conditions Conditions Conditions Conditions Conditions Conditions;357
19.8;17.5 Generalized Elastic Coordinates for Linear Flexible Bodies;358
19.9;17.5.1 Modes of Vibration;358
19.10;17.5.2 Static Correction Modes;359
19.11;17.6 Generalized Coordinates for Nonlinear Flexible Bodies;361
19.12;17.7 Kinematic Joints Involving Flexible Bodies;362
19.13;17.7.1 Rigid Joint in Flexible and Virtual Body: Local Nodal Coordinates;363
19.14;17.7.2 Rigid Joint in Flexible and Virtual Body: Modal Coordi-nates;365
19.15;17.7.3 Rigid Joint in Flexible and Virtual Bodies: Global Nodal Coordinates;366
19.16;17.8 Demonstration Examples;368
19.17;17.8.1 Slider-Crank with an Elastic Connecting Rod;368
19.18;17.8.2 Spin-Up Maneuver of a Rotating Beam;371
19.19;References;373
20;18 Optimization of Flexible Multibody Systems;375
20.1;18.1 Introduction;375
20.2;18.2 Road Vehicle Multibody Model;376
20.3;18.2.1 Finite Element Model of the Vehicle Chassis;377
20.4;18.2.2 Vehicle Models;380
20.5;18.3 Road Vehicle Simulations for Comfort and Handling;383
20.6;18.3.1 Vehicle Comfort Evaluation;384
20.7;18.3.2 Study of the Road Vehicle for Comfort Evaluation;387
20.8;18.3.3 Vehicle Handling Evaluation;389
20.9;18.3.4 Study of the Road Vehicle for Handling Evaluation;391
20.10;18.4 Vehicle Dynamics Optimization for Comfort and Handling;393
20.11;18.4.1 Optimal Problems in Vehicle Dynamics;393
20.12;18.4.2 Ride Optimization;394
20.13;18.4.3 Handling Optimization;397
20.14;18.5 Minimization of the Maximum Deformation Energy;399
20.15;18.6 Sensitivity Analysis in Flexible Multibody Dynamics;401
20.16;18.7 Demonstrative Example: Flexible Slider-Crank Mechanism;407
20.17;18.7.1 Slider-Crank Mechanism with Flexible Connecting Rod;407
20.18;18.7.2 Rod Deformation Optimization – Integral of the Defor-mation Energy;409
20.19;18.7.3 Maximum Deformation Energy Optimization;411
20.20;18.7.4 Optimization of Local Torsion and Deformation Energy;412
20.21;18.8 Optimization of the Deployment of a Satellite Antenna;414
20.22;18.9 Conclusions;422
20.23;References;423