Buttazzo / Frediani Variational Analysis and Aerospace Engineering

1. Auflage 2009
ISBN: 978-0-387-95857-6
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 518 Seiten

Autoren/Hrsg.

Buttazzo, Giuseppe

Frediani, Aldo

Inhaltsverzeichnis

1;Preface;7
2;Acknowledgments;8
3;Contents;9
4;Contributors;18
5;Algorithm Issues and Challenges Associated with the Development of Robust CFD Codes ;23
5.1;Steven R. Allmaras, John E. Bussoletti, Craig L. Hilmes, Forrester T. Johnson, Robin G. Melvin, Edward N. Tinoco, Venkat Venkatakrishnan, Laurence B. Wigton and David P. Young;23
5.1.1;Introduction;23
5.1.2;Algorithm Issues Related to the Solution of the Navier--Stokes Equations;24
5.1.2.1;Grid Adaption and Error Estimation;25
5.1.2.2;Discretization Issues;28
5.1.2.3;Higher Order Elements;34
5.1.2.4;Domain Decomposition and Linear Solver;38
5.1.3;Conclusions;41
5.1.4;References;41
6;Flight Path Optimization at Constant Altitude ;42
6.1;Mark D. Ardema and Bryan C. Asuncion;42
6.1.1;Introduction;42
6.1.2;Singular Optimal Control;44
6.1.3;The Cruise Problem;45
6.1.4;Fanjet Specific Fuel Consumption;47
6.1.5;An Example;49
6.1.6;Conclusions and Discussion;52
6.1.7;References;53
7;A Survey on the Newton Problem of Optimal Profiles ;54
7.1;Giuseppe Buttazzo;54
7.1.1;Introduction;54
7.1.2;Radially Symmetric Profiles;58
7.1.3;The Existence Result;61
7.1.4;References;68
8;Innovative Rotor Blade Design Code
;70
8.1;Vittorio Caramaschi and Claudio Monteggia
;70
8.1.1;Introduction
;96
8.1.2;Helicopter’s Aeromechanics Outlines
;97
8.1.3;Helicopter’s Rotor Mathematical Model Features
and Aeromechanics Codes Worldwide Status
;99
8.1.4;AW Aeromechanics Code GYROX II
;101
8.1.5;Applications
;105
8.1.6;Conclusion;109
9;Fields of Extremals and Sufficient Conditions for the Simplest Problem of the Calculus of Variations in n-Variables ;96
9.1;Dean A. Carlson and George Leitmann;96
9.1.1;Introduction;96
9.1.2;Notations and the Problem Definition;97
9.1.3;Leitmann's Direct Method;99
9.1.4;Fields of Extremals;101
9.1.5;Sufficient Conditions for Optimality;105
9.1.6;Conclusion;109
9.1.7;References;109
10;A Framework for Aerodynamic Shape Optimization ;111
10.1;Giampiero Carpentieri and Michel J.L. van Tooren;111
10.1.1;Introduction;111
10.1.2;Adjoint-Based Sensitivity Analysis;112
10.1.3;Optimization Framework;113
10.1.3.1;Flow Solver;114
10.1.3.2;Adjoint Solver;116
10.1.3.3;Shape Parameterization;118
10.1.3.4;Geometric Sensitivities;119
10.1.3.5;Optimization Algorithm;119
10.1.4;Optimization Test Cases;120
10.1.4.1;RAE2822 at M=0.73 and = 2;120
10.1.4.2;NACA64A410 at M=0.75 and = 0;121
10.1.4.3;NACA0012 at M=1.5 and = 2;122
10.1.4.4;ONERA-M6 wing at M=0.84 and = 3.06;123
10.1.5;Conclusions;125
10.1.6;References;126
11;Optimal Motions of Multibody Systems in Resistive Media ;127
11.1;Felix L. Chernousko;127
11.1.1;Introduction;127
11.1.2;Basic Equations;128
11.1.3;Linear Resistance;130
11.1.4;Relative Motions;130
11.1.5;Piecewise Linear Resistance;132
11.1.6;Quadratic Resistance;133
11.1.7;Dry Friction: Velocity-Control Motion;134
11.1.8;Dry Friction: Acceleration-Control Motion;140
11.1.9;Generalizations;144
11.1.10;Experiments;144
11.1.11;Conclusions;145
11.1.12;References;145
12;Instationary Heat-Constrained Trajectory Optimization of a Hypersonic Space Vehicle by ODE--PDE-Constrained Optimal Control ;147
12.1;Kurt Chudej, Hans Josef Pesch, Markus Wächter, Gottfried Sachs and Florent Le Bras;147
12.1.1;Introduction;148
12.1.2;Trajectory Optimization Problems with Active Cooling;150
12.1.3;Trajectory Optimization Problem with an Instationary Heat Constraint;154
12.1.4;Conclusions;160
12.1.5;References;162
13;Variational Approaches to Fracture ;165
13.1;Gianpietro Del Piero;165
13.1.1;Fracture as a Minimum Problem;165
13.1.2;The Numerical Solution;167
13.1.3;Energy Barriers and Local Minima;168
13.1.4;Barenblatt's Regularization;171
13.1.5;Two Solution Strategies;173
13.1.6;The Dissipative Model;174
13.1.7;From Surface to Bulk Regularization;177
13.1.8;References;181
14;On the Problem of Synchronization of Identical Dynamical Systems: The Huygens's Clocks ;183
14.1;Rui Dilão;183
14.1.1;Introduction;183
14.1.2;A Model for the Synchronization of the Two Pendulum Clocks;186
14.1.3;A Simple Clock Model;188
14.1.4;Synchronization of Two Pendulum Clocks with Equal Parameters;189
14.1.5;Conclusions;199
14.1.6;References;200
15;Best Wing System: An Exact Solution of the Prandtl's Problem ;202
15.1;Aldo Frediani and Guido Montanari;202
15.1.1;Introduction;202
15.1.2;The Induced Drag for Lifting Multiwing Systems;203
15.1.3;The Problem of Minimum Induced Drag in a Box Wing;206
15.1.3.1;Case A: Elliptical Circulations on the Horizontal Wings and Zero on the Vertical Ones;210
15.1.3.2;Case B: Constant Circulations on the Horizontal Wings and Unknown on the Vertical Ones;211
15.1.3.3;Final Equations;213
15.1.4;The Optimum Lift Distribution Along the Vertical Wings;215
15.1.5;Results and Conclusions;216
15.1.6;References;218
16;Numerical Simulation of the Dynamics of Boats by a Variational Inequality Approach ;231
16.1;Luca Formaggia, Edie Miglio, Andrea Mola and Anna Scotti;231
16.1.1;Introduction;231
16.1.2;A Variational Approach to the Floating Body Problem;232
16.1.2.1;Characteristic Treatment of the Time Derivative;236
16.1.2.2;Enforcing the Constraint in the Hydrostatic Step;237
16.1.2.3;The Model for the Dynamics of a Rowing Scull;238
16.1.2.4;More Realistic Boundary Conditions;241
16.1.3;The Interaction Between the Boat and the Water;241
16.1.4;Numerical Results;242
16.1.4.1;Sinking and Pitching Motions;242
16.1.4.2;Reproducing Mean Motion Wave Pattern;243
16.1.4.3;An Example with the Full Dynamics;244
16.1.4.4;A Final Detail;244
16.1.5;References;245
17;Concepts of Active Noise Reduction Employed in High Noise Level Aircraft Cockpits ;246
17.1;Hatem Foudhaili and Eduard Reithmeier;246
17.1.1;Passive Versus Active Noise Reduction;247
17.1.2;Active Noise Cancellation;247
17.1.3;Active Structural/Acoustic Control (ASAC);251
17.1.4;Active Aviation Headsets;254
17.1.5;An Aviation Communication Headset Prototype with Digital Adaptive Noise Reduction;255
17.1.6;Conclusions;257
17.1.7;References;257
18;Lekhnitskii's Formalism for Stress Concentrations Around Irregularities in Anisotropic Plates: Solutions for Arbitrary Boundary Conditions ;259
18.1;Sotiris Koussios and Adriaan Beukers;259
18.1.1;Introduction;259
18.1.2;Governing Equations;261
18.1.3;General Solution;262
18.1.4;Stress, Strain, and Displacements Formulation;263
18.1.5;Formulation of Boundary Conditions;264
18.1.5.1;Forces;264
18.1.5.2;Displacements;265
18.1.6;Solution Strategy;266
18.1.6.1;Series Representation of the Boundary Conditions;266
18.1.6.2;Transformation into a Single Variable;267
18.1.7;Boundary Conditions Evaluation;269
18.1.7.1;Homogeneous Part;269
18.1.7.2;Logarithmic Part;270
18.1.7.3;Disturbance Field;272
18.1.8;Evaluation of Stresses and Displacements;275
18.1.9;Example;277
18.1.10;Conclusions;280
18.1.11;References;281
19;Best Initial Conditions for the Rendezvous Maneuver ;282
19.1;Angelo Miele and Marco Ciarcià;282
19.1.1;Introduction;283
19.1.2;Algorithm;284
19.1.3;System Description;286
19.1.3.1;Multiple-Subarc Equations;287
19.1.3.2;Inequality Constraint;288
19.1.3.3;Particular Cases;289
19.1.3.4;Boundary Conditions;289
19.1.3.5;Performance Index;290
19.1.3.6;Approaches;291
19.1.4;Minimum Fuel, Time Free;291
19.1.5;Results;292
19.1.6;Minimum Fuel, Time Given;295
19.1.6.1;Results;297
19.1.7;Conclusions;302
19.1.8;References;303
20;Commercial Aircraft Design for Reduced Noise and Environmental Impact ;305
20.1;S. Mistry, Howard Smith, and John P. Fielding;305
20.1.1;Introduction;306
20.1.2;Simple Emission Trade-Off Study;306
20.1.2.1;Global Warming Costs;306
20.1.2.2;Noise Costs;307
20.1.2.3;Local Air Quality Cost (LAQ);307
20.1.2.4;Annual Fuel Costs Fro Baseline Aircraft;308
20.1.2.5;Baseline Aircraft Environmental Costs;308
20.1.2.6;Summary of Trade-Offs;309
20.1.3;Aircraft Designs for Reduced Noise;309
20.1.3.1;Background;309
20.1.3.2;Baseline Aircraft Design and Noise Prediction;310
20.1.3.3;Low Airframe Noise Design Methodology;311
20.1.3.4;Low-Noise Aircraft Concept Brainstorming Process;311
20.1.3.5;Broad Delta Concepts;313
20.1.3.6;Airframe Approach Noise Prediction;316
20.1.3.7;Performance Comparison;317
20.1.4;The Cranfield A-6 Greenliner Project;318
20.1.4.1;Group Design Project Activities;318
20.1.4.2;Greenliner Description;319
20.1.4.3;Predicted Performance for the Greenliner;323
20.1.5;Conclusions;325
20.1.6;References;326
21;Variational Approach to the Problem of the Minimum Induced Drag of Wings ;327
21.1;Maria Teresa Panaro, Aldo Frediani, Franco Giannessi and Emanuele Rizzo;327
21.1.1;Introduction;328
21.1.2;Finite Span Wings;328
21.1.3;Problem of Minimum Induced Drag of a Straight Wing: An optimality condition;330
21.1.4;Duality: A New Approach to the Design of Wings;333
21.1.5;Direct Methods;339
21.1.5.1;Elliptic Distribution;339
21.1.5.2;Ritz Method;341
21.1.6;References;356
22;Plastic Hinges in a Beam ;357
22.1;Danilo Percivale and Franco Tomarelli;357
22.1.1;Elastic--Plastic Beam;357
22.1.2;Skew-Symmetric Load;361
22.1.3;References;362
23;Problems of Minimal and Maximal Aerodynamic Resistance ;363
23.1;Alexander Plakhov;363
23.1.1;Introduction;363
23.1.2;Translational Motion;364
23.1.3;Translational Motion with Rotation: Two-Dimensional Case;369
23.1.3.1;Definition of Rough Body and Main Theorems;369
23.1.3.2;Problems of Minimal and Maximal Resistance for a Slowly Rotating Body;372
23.1.3.3;Mathematical Retroreflector;374
23.1.3.4;Effect of Magnus;375
24;Shock Optimization for Airfoil Design Problems ;380
24.1;Olivier Pironneau;380
24.1.1;Numerical Optimal Shape Design;380
24.1.1.1;An Academic Problem;380
24.1.1.2;Sensitivity Analysis;381
24.1.1.3;Conceptual Algorithm;382
24.1.2;Automatic Differentiation;383
24.1.2.1;Principle of Automatic Differentiation;383
24.1.2.2;Example of Application;384
24.1.3;Differentiability Issues;385
24.1.3.1;Extended Calculus of Variation;385
24.1.3.2;Sensitivity Analysis for Burgers' Equation;386
24.1.3.3;Application to Optimal Control;386
24.1.3.4;A Simple Example;387
24.1.3.5;Right and Wrong Schemes;387
24.1.4;Small Disturbances and Automatic Differentiations;389
24.1.5;References;390
25;Differential Games Treated by a Gradient-Restoration Approach ;391
25.1;Mauro Pontani;391
25.1.1;Introduction;391
25.1.2;Zero-Sum Differential Games;392
25.1.3;Numerical Solution of Two-Sided Optimization Problems;394
25.1.3.1;Transformation into Single-Objective Problem;394
25.1.3.2;Sequential Gradient-Restoration Algorithm;396
25.1.4;Homicidal Chauffeur Game;397
25.1.4.1;Formulation of the Problem;397
25.1.4.2;Method of Solution;398
25.1.4.3;Numerical Results;399
25.1.5;Orbital Pursuit-Evasion Game;400
25.1.5.1;Method of Solution;402
25.1.5.2;Numerical Results;404
25.1.6;Conclusions;407
25.1.7;References;407
26;Interval Methods for Optimal Control ;409
26.1;Andreas Rauh and Eberhard P. Hofer;409
26.1.1;Introduction;410
26.1.2;Optimal and Robust Control of Dynamical Systems;411
26.1.2.1;Optimal Control of Discrete- and Continuous-Time Processes;412
26.1.2.2;Specification of Robustness in the Time Domain;413
26.1.2.3;Optimality Criteria for Systems with Uncertainties;414
26.1.3;Interval Arithmetic Optimization Algorithm;415
26.1.4;Parallelization of the Optimization Algorithm;417
26.1.5;Combination with Classical Controller Design;418
26.1.6;Validated Modeling and Simulation of Dynamical Systems with State-Dependent Switchings;419
26.1.7;Optimization Results;422
26.1.7.1;Interval Algorithm for Structure Optimization;422
26.1.7.2;Linear State Controller for Improvement of Robustness;425
26.1.7.3;Interval Algorithm for Parameter Optimization;427
26.1.8;Conclusions and Outlook on Future Work;428
26.1.9;References;429
27;Application of Optimisation Algorithms to Aircraft Aerodynamics ;431
27.1;Emanuele Rizzo and Aldo Frediani;431
27.1.1;Introduction;431
27.1.2;An Algorithm for the Search of Global Minima;436
27.1.3;Test Cases;440
27.1.3.1;Test Case 1 (Unconstrained): Ackley's Function;440
27.1.3.2;Test Case 2 (Unconstrained): Rastrigin's Function;443
27.1.3.3;Test Case 3 (Unconstrained): Rosenbrock's Function;443
27.1.3.4;Test Case 4 (Unconstrained): Schwefel's Function;444
27.1.4;The AEROSTATE Program: An Application to Aeronautics;446
27.1.4.1;Minimum Induced Drag of a Wing;447
27.1.4.2;Minimum Total Drag of a Wing;450
27.1.4.3;The Trimmed Aircraft;451
27.1.4.4;The PrandtlPlane;453
27.1.5;Conclusions;457
27.1.6;References;457
28;Different levels of Optimisation in Aircraft Design ;459
28.1;Dieter Schmitt;459
28.1.1;Air Transport System;460
28.1.2;Industrial Process of Aircraft Design;461
28.1.3;Different Levels of Aircraft Design vs. Development Phases;464
28.1.4;Tools Used in Different Phases;467
28.1.5;Conclusion;471
28.1.6;References;471
29;Numerical and Analytical Methods for Global Optimization ;472
29.1;Paolo Teofilatto and Mauro Pontani;472
29.1.1;Introduction;472
29.1.2;Green's Theorem Approach;474
29.1.3;Morse Theory Approach;480
29.1.4;Final Comments;485
29.1.5;References;485
30;The Aeroservoelasticity Qualification Process in Alenia ;487
30.1;Vincenzo Vaccaro;487
30.1.1;Introduction;487
30.1.2;Company Presentation;488
30.1.3;What Is Aeroelasticity;489
30.1.4;Aeroelastic Tradition in Alenia;490
30.1.5;Aeroservoelastic Certification Process;491
30.1.5.1;Analytical Models;492
30.1.5.2;Theoretical Background;494
30.1.5.3;Ground Test;496
30.1.5.4;Flight Test;496
30.1.5.5;Research and Future Developments;496
31;Further Steps Towards Quantitative Conceptual Aircraft Design ;500
31.1;Michel van Tooren, Gianfranco La Rocca and Teodor Chiciudean;500
31.1.1;Introduction;500
31.1.2;The Systems Engineering Approach;505
31.1.3;Requirements on Computational Systems;505
31.1.4;The Design and Engineering Engine Concept;506
31.1.4.1;Describing Design Options;506
31.1.4.2;The Initiator;510
31.1.4.3;The Multi-model Generator;512
31.1.4.4;The Life-Cycle Analysis with Expert Tools;513
31.1.4.5;The Converger/Evaluator;513
31.1.4.6;The Agent-Based Framework;513
31.1.5;Results and Discussion;514
31.1.6;Conclusions;516
31.1.7;References;517
32;Some Plebeian Variational Problems ;518
32.1;Piero Villaggio;518
32.1.1;Introduction;518
32.1.2;Mechanical Plebeian Problems;519
32.1.3;Locomotion;522
32.1.4;Peeling and Cooking;524
32.1.5;Conclusions;527
32.1.6;References;527