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E-raamat: Variational Analysis and Aerospace Engineering

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Variational Analysis and Aerospace EngineeringSuurem pilt
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In recent years, new mathematical methods and tools have been developed and - plied extensively in the ?eld of aerospace engineering, for example, ?nite element method,computational ?uiddynamics, optimization,control,eigenvalues problems. The interaction between aerospace engineering and mathematics has been sign- cant in the past for both engineers and mathematicians and will be even stronger in the future. The School of Mathematics "Guido Stampacchia" of the "Ettore Majorana" FoundationandCentreofScienti cCultureisthemostappropriatesiteforaerospace engineers and mathematicians to meet. The present volume collects the papers p- sented at the Erice Workshop held on September 8-16, 2007, which was organized in order to allow aerospace engineers and mathematicians from Universities, - search Centres, and Industry to debate advanced problems in aerospace engineering requiring extensive mathematical applications. Theeditorsarecon denttocapturetheinterestofpeoplefrombothacademiaand industry, particularly, young researchers working on new frontiers of mathematical applications to engineering. The workshop was dedicated to Angelo Miele, Professor at Rice University in Houston, on the occasion of his 85th birthday. Angelo Miele is both an eminent mathematician and a famous engineer, among other activities, able to conceive new scenarios for space exploration. He has been the advisor of many PhD students at Houston, who became well-known professors in universities worldwide and are speakers at this workshop.
Algorithm Issues and Challenges Associated with the Development of Robust CFD Codes
1(20)
Steven R. Allmaras
John E. Bussoletti
Craig L. Hilmes
Forrester T. Johnson
Robin G. Melvin
Edward N. Tinoco
Venkat Venkatakrishnan
Laurence B. Wigton
David P. Young
Introduction
1(1)
Algorithm Issues Related to the Solution of the Navier-Stokes Equations
2(17)
Grid Adaption and Error Estimation
3(3)
Discretization Issues
6(6)
Higher Order Elements
12(4)
Domain Decomposition and Linear Solver
16(3)
Conclusions
19(2)
References
19(2)
Flight Path Optimization at Constant Altitude
21(12)
Mark D. Ardema
Bryan C. Asuncion
Introduction
21(2)
Singular Optimal Control
23(1)
The Cruise Problem
24(2)
Fanjet Specific Fuel Consumption
26(2)
An Example
28(3)
Conclusions and Discussion
31(2)
References
32(1)
A Survey on the Newton Problem of Optimal Profiles
33(16)
Giuseppe Buttazzo
Introduction
33(4)
Radially Symmetric Profiles
37(3)
The Existence Result
40(9)
References
47(2)
Innovative Rotor Blade Design Code
49(26)
Vittorio Caramaschi
Claudio Monteggia
Introduction
50(1)
Helicopter's Aeromechanics Outlines
51(5)
Helicopter's Rotor Mathematical Model Features and Aeromechanics Codes Worldwide Status
56(1)
AW Aeromechanics Code GYROX II
57(11)
General Procedure
58(1)
Rotor Hub Modelling Features
59(2)
Pylon Modelling Features
61(1)
Rotor Blade Structural Modelling Features
62(1)
Rotor Aerodynamics
63(3)
Solution Algorithms
66(1)
Operational Main Features and Output Data
67(1)
Applications
68(5)
Conclusions
73(2)
Short Term
73(1)
Long Term
74(1)
Fields of Extremals and Sufficient Conditions for the Simplest Problem of the Calculus of Variations in n- Variables
75(16)
Dean A. Carlson
George Leitmann
Introduction
75(1)
Notations and the Problem Definition
76(2)
Leitmann's Direct Method
78(2)
Fields of Extremals
80(4)
Sufficient Conditions for Optimality
84(4)
Conclusion
88(3)
References
88(3)
A Framework for Aerodynamic Shape Optimization
91(16)
Giampiero Carpentieri
Michel J. L. van Tooren
Introduction
91(1)
Adjoint-Based Sensitivity Analysis
92(1)
Optimization Framework
93(7)
Flow Solver
94(2)
Adjoint Solver
96(2)
Shape Parameterization
98(1)
Geometric Sensitivities
99(1)
Optimization Algorithm
99(1)
Optimization Test Cases
100(5)
RAE2822 at M∞ = 0.73 and α = 2°
100(1)
NACA64A410 at M∞ = 0.75 and α = 0°
101(1)
NACA0012 at M∞ = 1.5 and α = 2°
102(1)
ONERA-M6 wing at M∞ = 0.84 and α = 3.06°
103(2)
Conclusions
105(2)
References
106(1)
Optimal Motions of Multibody Systems in Resistive Media
107(20)
Felix L. Chernousko
Introduction
107(1)
Basic Equations
108(2)
Linear Resistance
110(1)
Relative Motions
110(2)
Piecewise Linear Resistance
112(1)
Quadratic Resistance
113(1)
Dry Friction: Velocity-Control Motion
114(6)
Dry Friction: Acceleration Control Motion
120(4)
Generalizations
124(1)
Experiments
124(1)
Conclusions
125(2)
References
125(2)
Instationary Heat-Constrained Trajectory Optimization of a Hypersonic Space Vehicle by ODE-PDE-Constrained Optimal Control
127(18)
Kurt Chudej
Hans Josef Pesch
Markus Wachter
Gottfried Sachs
Florent Le Bras
Introduction
128(2)
Trajectory Optimization Problems with Active Cooling
130(4)
Trajectory Optimization Problem with an Instationary Heat Constraint
134(6)
Conclusions
140(5)
References
142(3)
Variational Approaches to Fracture
145(18)
Gianpietro Del Piero
Fracture as a Minimum Problem
145(2)
The Numerical Solution
147(1)
Energy Barriers and Local Minima
148(3)
Barenblatt's Regularization
151(2)
Two Solution Strategies
153(1)
The Dissipative Model
154(3)
From Surface to Bulk Regularization
157(6)
References
161(2)
On the Problem of Synchronization of Identical Dynamical Systems: The Huygens's Clocks
163(20)
Rui Dilao
Introduction
163(3)
A Model for the Synchronization of the Two Pendulum Clocks
166(2)
A Simple Clock Model
168(1)
Synchronization of Two Pendulum Clocks with Equal Parameters
169(9)
Synchronization of Two Pendulum Clocks with Different Parameters Robustness
178(1)
Conclusions
179(4)
References
180(3)
Best Wing System: An Exact Solution of the Prandtl's Problem
183(30)
Aldo Frediani
Guido Montanan
Introduction
183(1)
The Induced Drag for Lifting Multiwing Systems
184(3)
The Problem of Minimum Induced Drag in a Box Wing
187(9)
Case A: Elliptical Circulations on the Horizontal Wings and Zero on the Vertical Ones
191(1)
Case B: Constant Circulations on the Horizontal Wings and Unknown on the Vertical Ones
192(2)
Final Equations
194(2)
The Optimum Lift Distribution Along the Vertical Wings
196(1)
Results and Conclusions
197(16)
References
199(14)
Numerical Simulation of the Dynamics of Boats by a Variational Inequality Approach
213(16)
Luca Formaggia
Edie Miglio
Andrea Mola
Anna Scotti
Introduction
213(1)
A Vanational Approach to the Floating Body Problem
214(9)
Characteristic Treatment of the Time Derivative
218(1)
Enforcing the Constraint in the Hydrostatic Step
219(1)
The Model for the Dynamics of a Rowing Scull
220(3)
More Realistic Boundary Conditions
223(1)
The Interaction Between the Boat and the Water
223(1)
Numerical Results
224(5)
Sinking and Pitching Motions
224(1)
Reproducing Mean Motion Wave Pattern
225(1)
An Example with the Full Dynamics
226(1)
A Final Detail
226(1)
References
227(2)
Concepts of Active Noise Reduction Employed in High Noise Level Aircraft Cockpits
229(14)
Hatem Foudhaili
Eduard Reithmeier
Passive Versus Active Noise Reduction
230(1)
Active Noise Cancellation
230(4)
Active Structural/Acoustic Control (ASAC)
234(3)
Active Aviation Headsets
237(1)
An Aviation Communication Headset Prototype with Digital Adaptive Noise Reduction
238(2)
Conclusions
240(3)
References
240(3)
Lekhnitskii's Formalism for Stress Concentrations Around Irregularities in Anisotropic Plates: Solutions for Arbitrary Boundary Conditions
243(24)
Sotiris Koussios
Adriaan Beukers
Introduction
243(2)
Governing Equations
245(1)
General Solution
246(1)
Stress, Strain, and Displacements Formulation
247(1)
Formulation of Boundary Conditions
248(2)
Forces
248(1)
Displacements
249(1)
Solution Strategy
250(3)
Series Representation of the Boundary Conditions
250(1)
Transformation into a Single Variable
251(2)
Boundary Conditions Evaluation
253(6)
Homogeneous Part
253(1)
Logarithmic Part
254(2)
Disturbance Field
256(3)
Evaluation of Stresses and Displacements
259(2)
Example
261(3)
Conclusions
264(3)
References
265(2)
Best Initial Conditions for the Rendezvous Maneuver
267(24)
Angelo Miele
Marco Ciarcia
Introduction
268(1)
Algorithm
269(2)
System Description
271(5)
Multiple-Subarc Equations
272(1)
Inequality Constraint
273(1)
Particular Cases
274(1)
Boundary Conditions
274(1)
Performance Index
275(1)
Approaches
276(1)
Minimum Fuel, Time Free
276(1)
Results
277(3)
Minimum Fuel, Time Given
280(7)
Results
282(5)
Conclusions
287(4)
References
288(3)
Commercial Aircraft Design for Reduced Noise and Environmental Impact
291(22)
S. Mistry
Howard Smith
John P. Fielding
Introduction
292(1)
Simple Emission Trade-Off Study
292(3)
Global Warming Costs
292(1)
Noise Costs
293(1)
Local Air Quality Cost (LAQ)
293(1)
Annual Fuel Costs Fro Baseline Aircraft
294(1)
Baseline Aircraft Environmental Costs
294(1)
Summary of Trade-Offs
295(1)
Aircraft Designs for Reduced Noise
295(9)
Background
295(1)
Baseline Aircraft Design and Noise Prediction
296(1)
Low Airframe Noise Design Methodology
297(1)
Low-Noise Aircraft Concept Brainstorming Process
297(2)
Broad Delta Concepts
299(3)
Airframe Approach Noise Prediction
302(1)
Performance Comparison
303(1)
The Cranfield A-6 Greenliner Project
304(7)
Group Design Project Activities
304(1)
Greenliner Description
305(4)
Predicted Performance for the Greenliner
309(2)
Conclusions
311(2)
References
312(1)
Variational Approach to the Problem of the Minimum Induced Drag of Wings
313(30)
Maria Teresa Panaro
Aldo Frediani
Franco Giannessi
Emanuele Rizzo
Introduction
314(1)
Finite Span Wings
314(2)
Problem of Minimum Induced Drag of a Straight Wing: An optimality condition
316(3)
Duality: A New Approach to the Design of Wings
319(6)
Direct Methods
325(18)
Elliptic Distribution
325(2)
Ritz Method
327(15)
References
342(1)
Plastic Hinges in a Beam
343(6)
Danilo Percivale
Franco Tomarelli
Elastic-Plastic Beam
343(4)
Skew-Symmetric Load
347(2)
References
348(1)
Problems of Minimal and Maximal Aerodynamic Resistance
349(18)
Alexander Plakhov
Introduction
349(1)
Translational Motion
350(5)
Translational Motion with Rotation: Two-Dimensional Case
355(12)
Definition of Rough Body and Mam Theorems
355(3)
Problems of Minimal and Maximal Resistance for a Slowly Rotating Body
358(2)
Mathematical Retroreflector
360(1)
Effect of Magnus
361(4)
References
365(2)
Shock Optimization for Airfoil Design Problems
367(12)
Olivier Pironneau
Numerical Optimal Shape Design
367(3)
An Academic Problem
367(1)
Sensitivity Analysis
368(1)
Conceptual Algorithm
369(1)
Automatic Differentiation
370(2)
Principle of Automatic Differentiation
370(1)
Example of Application
371(1)
Differentiability Issues
372(4)
Extended Calculus of Variation
372(1)
Sensitivity Analysis for Burgers' Equation
373(1)
Application to Optimal Control
373(1)
A Simple Example
374(1)
Right and Wrong Schemes
374(2)
Small Disturbances and Automatic Differentiations
376(3)
References
377(2)
Differential Games Treated by a Gradient-Restoration Approach
379(18)
Mauro Pontani
Introduction
379(1)
Zero-Sum Differential Games
380(2)
Numerical Solution of Two-Sided Optimization Problems
382(3)
Transformation into Single-Objective Problem
382(2)
Sequential Gradient-Restoration Algorithm
384(1)
Homicidal Chauffeur Game
385(3)
Formulation of the Problem
385(1)
Method of Solution
386(1)
Numerical Results
387(1)
Orbital Pursuit-Evasion Game
388(7)
Formulation of the Problem
389(1)
Method of Solution
390(2)
Numerical Results
392(3)
Conclusions
395(2)
References
395(2)
Interval Methods for Optimal Control
397(22)
Andreas Rauh
Eberhard P. Hofer
Introduction
398(1)
Optimal and Robust Control of Dynamical Systems
399(4)
Optimal Control of Discrete and Continuous-Time Processes
400(1)
Specification of Robustness in the Time Domain
401(1)
Optimality Cateria for Systems with Uncertainties
402(1)
Interval Arithmetic Optimization Algorithm
403(2)
Parallelization of the Optimization Algorithm
405(1)
Combination with Classical Controller Design
406(1)
Validated Modeling and Simulation of Dynamical Systems with State-Dependent Switchings
407(3)
Optimization Results
410(6)
Interval Algorithm for Structure Optimization
410(3)
Linear State Controller for Improvement of Robustness
413(2)
Interval Algorithm for Parameter Optimization
415(1)
Conclusions and Outlook on Future Work
416(3)
References
417(2)
Application of Optimisation Algorithms to Aircraft Aerodynamics
419(28)
Emanuele Rizzo
Aldo Frediani
Introduction
419(5)
An Algorithm for the Search of Global Minima
424(4)
Test Cases
428(6)
Test Case 1 (Unconstrained): Ackley's Function
428(3)
Test Case 2 (Unconstrained): Rastrigin's Function
431(1)
Test Case 3 (Unconstrained): Rosenbrock's Function
431(1)
Test Case 4 (Unconstrained): Schwefel's Function
432(2)
The AEROSTATE Program: An Application to Aeronautics
434(11)
Minimum Induced Drag of a Wing
435(3)
Minimum Total Drag of a Wing
438(1)
The Trimmed Aircraft
439(2)
The PrandtlPlane
441(4)
Conclusions
445(2)
References
445(2)
Different levels of Optimisation in Aircraft Design
447(14)
Dieter Schmitt
Air Transport System
448(1)
Industrial Process of Aircraft Design
449(3)
Different Levels of Aircraft Design vs. Development Phases
452(3)
Tools Used in Different Phases
455(4)
Conclusion
459(2)
References
459(2)
Numerical and Analytical Methods for Global Optimization
461(16)
Paolo Teofilatto
Mauro Pontani
Introduction
461(2)
Green's Theorem Approach
463(6)
Morse Theory Approach
469(5)
Final Comments
474(3)
References
474(3)
The Aeroservoelasticity Qualification Process in Alenia
477(14)
Vincenzo Vaccaro
Introduction
477(1)
Company Presentation
478(1)
What Is Aeroelasticity
479(1)
Aeroelastic Tradition in Alenia
480(1)
Aeroservoelastic Certification Process
481(10)
Analytical Models
482(2)
Theoretical Background
484(2)
Ground Test
486(1)
Flight Test
486(1)
Research and Future Developments
486(5)
Further Steps Towards Quantitative Conceptual Aircraft Design
491(18)
Michel van Tooren
Gianfranco La Rocca
Teodor Chiciudean
Introduction
491(5)
The Systems Engineering Approach
496(1)
Requirements on Computational Systems
496(1)
The Design and Engineering Engine Concept
497(8)
Describing Design Options
497(4)
The Initiator
501(2)
The Multi-model Generator
503(1)
The Life-Cycle Analysis with Expert Tools
504(1)
The Converger/Evaluator
504(1)
The Agent-Based Framework
504(1)
Results and Discussion
505(2)
Conclusions
507(2)
References
508(1)
Some Plebeian Variational Problems
509
Piero Villaggio
Introduction
509
Mechanical Plebeian Problems
510
Locomotion
513
Peeling and Cooking
515
Conclusions
518
References
518
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