Variational Analysis and Aerospace Engineering: Mathematical Challenges for the Aerospace of the Future

535 Pages·2016·13.59 MB·English

by  Aldo Frediani

Springer Optimization and Its Applications 116
Aldo Frediani
Bijan Mohammadi
Olivier Pironneau
Vittorio Cipolla Editors
Variational
Analysis and
Aerospace
Engineering
Mathematical Challenges for the
Aerospace of the Future
Springer Optimization and Its Applications
VOLUME116
ManagingEditor
PanosM.Pardalos(UniversityofFlorida)
Editor–CombinatorialOptimization
Ding-ZhuDu(UniversityofTexasatDallas)
AdvisoryBoard
J.Birge(UniversityofChicago)
C.A.Floudas(TexasA&MUniversity)
F.Giannessi(UniversityofPisa)
H.D.Sherali(VirginiaPolytechnicandStateUniversity)
T.Terlaky(LehighUniversity)
Y.Ye(StanfordUniversity)
AimsandScope
Optimization has been expanding in all directions at an astonishing rate
during the last few decades. New algorithmic and theoretical techniques
havebeendeveloped,thediffusionintootherdisciplineshasproceededata
rapidpace,andourknowledgeofallaspectsofthefieldhasgrownevenmore
profound.Atthe sametime, oneofthe moststriking trendsin optimization
is the constantly increasing emphasis on the interdisciplinary nature of the
field.Optimizationhasbeenabasictoolinallareasofappliedmathematics,
engineering,medicine,economics,andothersciences.
The series Springer Optimization and Its Applications publishes under-
graduate and graduate textbooks, monographs and state-of-the-art exposi-
tory work that focus on algorithms for solving optimization problems and
alsostudyapplicationsinvolvingsuchproblems.Someofthetopicscovered
include nonlinear optimization (convex and nonconvex), network flow
problems, stochastic optimization, optimal control, discrete optimization,
multi-objectiveprogramming,descriptionofsoftwarepackages,approxima-
tiontechniquesandheuristicapproaches.
Moreinformationaboutthisseriesathttp://www.springer.com/series/7393
Aldo Frediani • Bijan Mohammadi
Olivier Pironneau • Vittorio Cipolla
Editors
Variational Analysis and
Aerospace Engineering
Mathematical Challenges for the Aerospace
of the Future
123
Editors
AldoFrediani BijanMohammadi
DepartmentofCivilandIndustrial MontpellierInstituteAlexanderGrothen
Engineering UniversityofMontpellier
UniversityofPisa Montpellier,France
Pisa,Italy
VittorioCipolla
OlivierPironneau DepartmentofIndustrialandCivil
LJLL-UPMCBoite Engineering
Paris,France UniversityofPisa
AerospaceSection
Pisa,Italy
ISSN1931-6828 ISSN1931-6836 (electronic)
SpringerOptimizationandItsApplications
ISBN978-3-319-45679-9 ISBN978-3-319-45680-5 (eBook)
DOI10.1007/978-3-319-45680-5
LibraryofCongressControlNumber:2016959447
©SpringerInternationalPublishingSwitzerland2016
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Foreword
Thisvolumeisdedicatedto the memoryofPiero Villaggioonbehalfof themany
whohavemethimduringtheearlystagesoftheirscientificformationandwishto
expressthegratitudefortheexampleandthemessageinspiredbyhim.
Piero Villaggio was born in Genova on December 31, 1932. After immersion
in humanistic studies at Liceo Doria, Villaggio completed his degree in Civil
Engineeringin1957withathesisonthemechanicsoffluids.Hisacademiccareer
movedrapidly:hebecameanassistantprofessorattheUniversityofGenovain1959
and was appointedas fullprofessorof Scienza delle Costruzioniat the University
ofPisa in1966,wherehe becamea professoremeritusin 2008.Villaggiowentto
becomeanOrdinaryMemberoftheItalianAccademiadeiLincei.
Villaggio was a distinguished member in the international scientific landscape
and collaborated with numerous eminent figures, particularly scientists from the
ClliffordTruesdellSchoolofContinuumMechanics.
Heheldpositionsofvisitingprofessorinprestigiousinstitutions(JohnsHopkins
University, Heriot-Watt University, University of Minnesota) and served on the
editorial board of various journals. In private, he cultivated intense passions for
mountains,music,historyandphilosophy.Hewasanexpertclimber,amemberof
theacademicsectionofClubAlpinoItalianoandauthoroftechnicalreportswhich
includedtwopapersonthemechanicsofclimbing[122,123].ThepictureinFig.2
portraysVillaggioasayoungandvitalman.VillaggiodiedunexpectedlyonJanuary
4,2014,whilehewasstillactiveinthescientificcommunity.
Asmanyoutstandingfigures,PieroVillaggio’seducationwasacomplexprocess.
Certainly, his work with Guido Stampacchia, in Genova,had a substantial impact
and Villaggio had a sincere sense of esteem and gratitude toward Stampacchia.
Stampacchia introduced Villaggio to the mathematical aspects of the Calculus of
Variationsandtotheweaktheoryofthedifferentialboundaryvalueproblems.
At Istituto Nazionale di Alta Matematica (INDAM) in Rome Villaggio studied
underG.Krall,G.Fichera,C.CattaneoandB.Segre,andwasgiventheopportunity
to meet A. Signorini and M. Picone. While attending INDAM, Villaggio studied
the classics of earlytwentieth centurymechanicsandmodelingproblems,suchas
the theoryof contactby Hertz; the plane elasticity problemsthroughthe complex
v
vi Foreword
variabletechniquedevelopedbyMuskhelishviliandthestressconcentrationaround
holesandnotchesproblemsolvedbyNeuber.
In Pisa, Villaggio worked with Signorini’s former students T. Manacorda and
G.Capriz,togethertheyreestablishedmechanicsbegunbyTruesdell,andformeda
continuummechanicsgroup.
Villaggiocompleted149articles,twomonographsandacritiqueoftheJohannI
andNicolausIIBernoulli’sworks.
Calculus of variations and the weak formulationof the elliptic boundaryvalue
problemscontinuedto growrapidlyat the Pisan schoolof mathematics.Villaggio
realized the importance of foundations of these ideas and played a major role
in expanding them into engineering. Villaggio used calculus of variations in his
early works [1, 8, 9, 14] and in many papers such as the a priori estimates in
elastodynamics[42];theextensiontofinitedeformationsoftheclassicalestimates
of linear elasticity [32]; some maximum modulus theorems for elastic halfspaces
[48];isoperimetricdistributionsofloadsinelastostatics[57]aswellashisarticles
on the extension of Friedrich’s method of the two-side energy bounds to the
unilateralproblems[39,43].
PieroVillaggiopaidspecialattentiontooptimization.Villaggiostudiedvarious
optimization problems and found the optimal shape of an indenter [68, 70]; the
optimalinterfacebetweenan elastic and a rigidhalfspaceglued together[67];the
optimalshapeofanelasticplateloadedonapart(known)ofitsboundaryandfree
ontheremainingpart(unknown)[81,88];theproblemofoptimalpackaging[82];
anoptimalstructuralproblemforabeam[96].Villaggio’sinterestforoptimization
originatedfromworksbyPragerandTaylorattheendof1960s.Towardtheendof
the1970sresearcherssawthatexistence,uniquenessandregularityissuesinknown
solutions. Fixing the matter required looking at weak convergences,relaxation of
functionals,etc.Villaggioappearedtobeawareoftheseissuespromptly[49]andin
apaperwithW.Velte[54]illustratedthepathologiesoftheoptimizationproblems
intheelementarycaseofabarunderaxialloads.
Villiaggio also examined a long series of articles which include contact and
detachmentofbodies,seee.g.[60,74]and[59,108],alongwithfractureandimpact.
Villaggioproposedamodelforafragilefractureincompressioninajointpaperwith
J.Dunwoody[77];thecaseoffracturewithcurvedfracturelineswasstudiedwithR.
Ballariniin[117].ImpactisthetopicofafewarticleswithR.Knops[97,110,140]
and the historic articles [109, 139] are from a plenary lectures given in Genova
(2003)andErice(2010).
The theory of complex variables and its application to planar elasticity distin-
guishedVillaggio’sresearch.Villaggiodedicatedabrilliantpaperattheonsetofhis
career[4]andtwopaperswithM.Leitman[115,142]onanerroneousapplication
oftheanalyticcontinuationtechniquethatispresenteveninworksofauthorslike
Neuber.VillaggioandLeitmanillustratedthe natureof theerrorandindicatehow
it can be removed. Together they provided a solution to the problem of a disk
loadedattheexternalboundaryundervariousloadingconditions,asanapplication.
In the application of the complex variable technique, Villagio wrote a paper with
Knops[138],whereNeuber’serrorstothesolutionsinplaneelasticityproblemsare
emended.
Foreword vii
Apart from the scientific value of his work, a major merit of Villaggio has
been his work between mathematics and engineering. He made the engineering
faculty aware of the technical aspects, built on the work of the classics and on
their extraordinarycapability of simplifying problems.In a passage from [A2] he
explicitly quotes the names of Hertz and Kelvin about this matter. As a personal
contribution,Villaggio called attention to qualitative mathematicsfocussed on the
search for the general properties of solutions to boundary value problems and on
the role of the a priori estimates. Which contributed to create a generation of
engineers,abletoreadtechnicalworksandtousethemtofacenovelproblems.As
amechanician,Villaggiowasopentoaspectsofgeneralityandclaritythatinspired
there-foundedcontinuummechanics.
Villaggio was an attentive observer of the scientific community. In a paper on
mechanicscoveringthepast60years[137]Villaggiopointedouttherisksofpresent
mechanics:theexcessofspecializationandtheabundanceofscientificjournals,that
dealwith“unlikelyproblems”byanevergrowingplethoraofcontributors.Villaggio
calledtosimplicitywhichhasbeenthedistinctivetraitofhislegacy.
Simplicityinspiredhislectures,thatweresharp,conciseandelegantlyillustrated
ontheblackboard.Helovedlecturingandwerememberhimteaching,asinFig.1.
Udine,Italy CesareDavini
viii Foreword
Fig.1 PieroVillaggio,UniversitàMediterraneadiReggioCalabria,Aprile2008.(bycourtesyof
OmiVillaggio)
Foreword ix
Fig.2 Giuseppe Perotti, Piero Villaggio and Mario Micoli at Rosskuppe Peak (Austrian Alps,
Summer1971)
x Foreword
PublicationsbyPiero Villaggio
Articles on Journals
1.“Sul problemavariazionale dellalastracurva asimmetriaassiale”. AttiAcc.Lig.Sc.Lett.
XVI,1–11(1959).
2.“Sullateorianonlinearedellelastresottilielasticheadoppiacurvatura”.Rend.Ist.Lomb.-
Acc.Sc.Lett.94,151–165(1960).
3.“Su unproblema non lineare relativoallatorsione di solidi prismatici”. AttiAcc. Lig.Sc.
Lett.XVIII,l-29(1961).
4.“Problemiditrasmissionedell’elasticitàpiana”.Rend.Ist.Lomb.-Acc.Sc.Lett.95,493–524
(1961).
5.“Suunproblemaelasticopianodellateoriadell’attritovolvente”.Rend.Ist.Lomb.-Acc.Sc.
Lett.95,919–940(1961).
6.“Sui problemi alcontorno persistemi di equazioni differenziali lineari del tipodistabilità
dell’equilibrioelastico”.Ann.Sc.Norm.Sup.Pisa,III,vol.XV,I-II,25–40(1961).
7.“Suunproblemamistorelativoadunsemipianoelasticocollegatoadunanervatura”.AttiIst.
Sc.Costr.Pisa,84,1–16(1961).
8.“Limitiinferioridelcaricocriticodilastreelasticheadoppiacurvatura”.AttiIst.Sc.Costr.
Pisa,86,1–20(1961).
9.“Limitiinferioridelprimomoltiplicatorecriticodilastresottilielastichedirivoluzione”.Atti
Ist.Sc.Costr.Pisa,89,1–19(1961).
10.“Sull’esistenzael’unicitàdisoluzionideiproblemialcontornoinelastoplasticità,Rend.Ist.
Lomb.-Acc.Sc.Lett.,96,112–127(1962).
11.“Suunproblemamistorelativoallastaticadelledighecilindrichespesse”.AttiIst.Sc.Costr.
Pisa,93,1–18(1962).
12.“Tensionideformazioniinflangesottilicircolarielastiche”.AttiIst.Sc.Costr.Pisa,95,1–34
(1962).
13.“Limiti superiori del fattore di concentrazione della tensione intorno a fori ipotrocoidali”.
L’Aerotecnica,vol.VI(3),119–128(1962).
14.“Sualcuneformuledimaggiorazioneperl’energiadideformazionediuncorpoelastico”.Le
Matematiche,XVII,2,21–135(1962).
15.“Suuncriteriodistabilitàcineticadisistemimeccanicisoggettiadazioniimpulsive.”Rend.
Ist.Lomb.-Acc.Sc.Lett.97,96–100(1963).
16.“Condizionidisicurezzaall’instabilitàaerodinamicadilastresottiliinregimesupersonico”.
AttiIst.Sc.Costr.Pisa,96,1–11(1963).
17.“Sulloscorrimentoviscosodelconglomeratoinflessionepura”.AttiIst.Sc.Costr.Pisa,100,
1–14(1963).
18.“Studiodiunsistemaservomotoreperprovedirilassamento”.AttiIst.Sc.Costr.Pisa,101,
1–8(1963).
19.“Limitidicollassoplastico-rigidodiunionichiodate”.Costr.Met.,vol.1,3–11(1964).
20.“Limitidiresistenzadipaliinterrenoplastico-rigido”.IlCemento,vol.10,25–30(1964).
21.“Analisilimitedipiastresottiliappoggiateplastico-rigide”.Giorn.GenioCiv.,vol.3,133–141
(1964).
22.“Lanozionediefficienzateoricaneibullonipretesi”.Costr.Met.,vol.4,284–288(1965).
23.“Alterazioneperturbativadeicarichicriticidilastrepianesottili”.Giorn.GenioCiv.,vol.12,
601–616(1965).
24.“Monodimensionalsolidswithconstrainedsolutions”.Meccanica,vol.II,1,65–68(1967).
25.“StabilityconditionsforElastic-PlasticPrandtl-Reusssolids”.Meccanica,vol.III,1,46–47
(1968).
26.“Stabilitàrispettoalconvessodeidominiplasticidelletravature”.Giorn.GenioCiv.,vol.2–3,
101–109(1968).