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Variational Analysis and Aerospace Engineering

E-BookPDF1 - PDF WatermarkE-Book
518 Seiten
Englisch
Springer New Yorkerschienen am21.08.20092009
This proceedings volume consists of papers presented at the Variational Analysis and Aerospace Engineering conference held in Erice, Italy in September 2007 at the International School of Mathematics, Guido Stampacchia. The workshop provided a platform for aerospace engineers and mathematicians (from universities, research centers and industry) to discuss the advanced problems requiring an extensive application of mathematics. Important mathematical methods have been developed and extensively applied in the field of aerospace engineering. Topics and contributions at the workshop concentrated on the most advanced mathematical methods in engineering such as computational fluid dynamics methods, the introduction of new materials, theory of optimization, optimization methods applied in aerodynamics, theory of structures, space missions, flight mechanics, theories of control, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful. This work is dedicated to Professor Angelo Miele, an eminent mathematician and engineer, on the occasion of his 85th birthday.mehr
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KlappentextThis proceedings volume consists of papers presented at the Variational Analysis and Aerospace Engineering conference held in Erice, Italy in September 2007 at the International School of Mathematics, Guido Stampacchia. The workshop provided a platform for aerospace engineers and mathematicians (from universities, research centers and industry) to discuss the advanced problems requiring an extensive application of mathematics. Important mathematical methods have been developed and extensively applied in the field of aerospace engineering. Topics and contributions at the workshop concentrated on the most advanced mathematical methods in engineering such as computational fluid dynamics methods, the introduction of new materials, theory of optimization, optimization methods applied in aerodynamics, theory of structures, space missions, flight mechanics, theories of control, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful. This work is dedicated to Professor Angelo Miele, an eminent mathematician and engineer, on the occasion of his 85th birthday.
Details
Weitere ISBN/GTIN9780387958576
ProduktartE-Book
EinbandartE-Book
FormatPDF
Format Hinweis1 - PDF Watermark
FormatE107
Erscheinungsjahr2009
Erscheinungsdatum21.08.2009
Auflage2009
ReiheSpringer Optimization and Its Applications
Reihen-Nr.33
Seiten518 Seiten
SpracheEnglisch
IllustrationenXXVI, 518 p. 300 illus. in color.
Artikel-Nr.1439334
Rubriken
Genre9200

Inhalt/Kritik

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;527mehr

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