Developments and Novel Approaches in Nonlinear Solid Body Mechanics PDF
Preview Developments and Novel Approaches in Nonlinear Solid Body Mechanics
Advanced Structured Materials Bilen Emek Abali Ivan Giorgio Editors Developments and Novel Approaches in Nonlinear Solid Body Mechanics Advanced Structured Materials Volume 130 Series Editors Andreas Öchsner, Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Germany Lucas F. M. da Silva, Department of Mechanical Engineering, Faculty of Engineering, University of Porto, Porto, Portugal Holm Altenbach , Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany Common engineering materials reach in many applications their limits and new developments are required to fulfil increasing demands on engineering materials. The performance ofmaterials can beincreasedby combiningdifferent materials to achieve better properties than a single constituent or by shaping the material or constituents in a specific structure. The interaction between material and structure mayariseondifferentlengthscales,suchasmicro-,meso-ormacroscale,andoffers possible applications in quite diverse fields. Thisbookseriesaddressesthefundamentalrelationshipbetweenmaterialsandtheir structure on the overall properties (e.g. mechanical, thermal, chemical or magnetic etc.) and applications. The topics of Advanced Structured Materials include but are not limited to (cid:129) classical fibre-reinforced composites (e.g. glass, carbon or Aramid reinforced plastics) (cid:129) metal matrix composites (MMCs) (cid:129) micro porous composites (cid:129) micro channel materials (cid:129) multilayered materials (cid:129) cellular materials (e.g., metallic or polymer foams, sponges, hollow sphere structures) (cid:129) porous materials (cid:129) truss structures (cid:129) nanocomposite materials (cid:129) biomaterials (cid:129) nanoporous metals (cid:129) concrete (cid:129) coated materials (cid:129) smart materials Advanced Structured Materials is indexed in Google Scholar and Scopus. More information about this series at http://www.springer.com/series/8611 Bilen Emek Abali Ivan Giorgio (cid:129) Editors Developments and Novel Approaches in Nonlinear Solid Body Mechanics 123 Editors Bilen EmekAbali IvanGiorgio Institute of Mechanics Department ofMechanical Technische UniversitätBerlin andAerospace Engineering Berlin, Germany University of RomeLa Sapienza Latina, Italy ISSN 1869-8433 ISSN 1869-8441 (electronic) AdvancedStructured Materials ISBN978-3-030-50459-5 ISBN978-3-030-50460-1 (eBook) https://doi.org/10.1007/978-3-030-50460-1 ©SpringerNatureSwitzerlandAG2020 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained hereinorforanyerrorsoromissionsthatmayhavebeenmade.Thepublisherremainsneutralwithregard tojurisdictionalclaimsinpublishedmapsandinstitutionalaffiliations. ThisSpringerimprintispublishedbytheregisteredcompanySpringerNatureSwitzerlandAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface TheICoNSOM2019,InternationalConferenceonNonlinearSolidMechanics,took placeatPalazzoArgiletum,Rome,Italy,fromJune16toJune19,2019.Over200 participationfromthewholeglobe,theurgeofthisproceedingsbecameclear.With theaidoftheorganizers,MarcoAmabili,Francescodell’Isola,IvanGiorgio,Nicola Rizzi,andLucaPlacidi,thescientificcommunitydidshowagreatinterestallowing ustobringtogetherthisproceedingscollectedintwovolumes: • DevelopmentsandNovelApproachesinNonlinearSolidBodyMechanics • DevelopmentsandNovelApproachesinBiomechanicsandMetamaterials ICoNSoM 2019 Conference has been intended to provide an international oppor- tunity for communicating recent developments in various areas of nonlinear solid mechanics. This monograph consists theory, experiments, and applications in me- chanics,thermodynamics,andmultiphysicssimulationinmanylengthscales. Aseditors,weintendtothankallauthorsfortheircrucialcontributionsaswell asallreviewersfortheirinvaluabletimeandeffort.WedelightedlyacknowledgeDr. ChristophBaumann(SpringerPublisher)forinitiatingthebookproject.Inaddition, wehavetothankDr.MayraCastro(SeniorEditorAppliedSciences;MaterialsSci- ence; Materials Engineering; Nanotechnology and Nanomedicine) and Mr. Ashok Arumairaj(ProductionAdministrator)givingtheirsupportintheprocessofpubli- cation. Brussels,Rome BilenEmekAbali May2020 IvanGiorgio v Contents 1 International Conference on Nonlinear Solid Mechanics 2019: GeneralTopicsandReviewofPlenaryLectures .................. 1 MarcoLaudato,DariaScerrato,Chuong AnthonyTran,andEmilio Barchiesi 1.1 Why Nonlinear Solid Mechanics Deserves an International Conference?.............................................. 1 1.2 PlenaryLectures.......................................... 4 1.2.1 NonlinearMechanicsofDrilling–B.Balachandran..... 4 1.2.2 Surface Elasticity with Applications to Material ModelingattheNano-andMicro-Scales–V.A.Eremeyev 5 1.2.3 TenYearsofGlobalDigitalVolumeCorrelation:What HasBeenAchieved?–F.Hild ....................... 6 1.2.4 GranularMicromechanics:BridgingGrainInteractions andContinuumDescriptions–A.Misra .............. 6 1.2.5 OnSeven-andTwelve-ParameterShellFiniteElements andNon-LocalTheoriesforCompositeStructures–J. N.Reddy ........................................ 7 1.2.6 ExploitingGlobalDynamicstoUnveiltheNonlinear ResponseandActualSafetyofSystemsandStructures –G.Rega ........................................ 8 1.2.7 VibrationsofNonlinearContinuaSubjecttoCombined Harmonic and Stochastic Forces: Linearization ApproximationsandMonteCarloSimulations–P.D. Spanos .......................................... 9 1.3 Conclusions.............................................. 9 References ..................................................... 10 PartI MathematicalToolsforMechanics vii viii Contents 2 Asymptotic Construction of Solutions of Ordinary Differential EquationswithHolomorphicCoefficientsintheNeighborhoodof anIrregularSingularPoint ................................... 17 MariaV.Korovina&VladimirYu.Smirnov References ..................................................... 21 3 PoincareProblemandClassificationofIrregularSingularPoints forLinearDifferentialEquationswithHolomorphicCoefficients.... 23 MariaV.Korovina&VladimirYu.Smirnov References ..................................................... 26 4 Behavior of Solutions of the Cauchy Problem and the Mixed InitialBoundaryValueProblemforanInhomogeneousHyperbolic EquationwithPeriodicCoefficients ............................ 29 HovikA.Matevossian,GiorgioNordo,andAnatolyV.Vestyak 4.1 Introduction.............................................. 29 4.2 NotationandPreliminaries ................................. 31 4.3 MainResults ............................................. 33 References ..................................................... 34 5 ASoftEmbeddingTheoremforSoftTopologicalSpaces ........... 37 GiorgioNordo 5.1 Introduction.............................................. 37 5.2 Preliminaries............................................. 39 5.3 SoftEmbeddingTheorem .................................. 48 5.4 Conclusion............................................... 54 References ..................................................... 54 6 TheDiffusion–VortexProblemsinTermsofStressesforBingham Materials .................................................. 59 DimitriGeorgievskii 6.1 TheGeneralizedDiffusionofVortex ......................... 59 6.2 DiffusionofPlaneVortexLayer.ExtractionofaPlaneoutof Visco-PlasticSpace ....................................... 62 6.3 DiffusionofAxiallySymmetricVortexLayer.Extractionofa ThreadoutofVisco-PlasticSpace ........................... 63 6.4 DiffusionofVortexThread ................................. 64 References ..................................................... 65 7 OntheBehaviorofSolutionsofQuasilinearEllipticInequalities NearaBoundaryPoint....................................... 67 AndrejA.Kon’kov 7.1 Introduction.............................................. 67 7.2 EstimatesofSolutionsnearaBoundaryPoint.................. 70 References ..................................................... 76 Contents ix 8 IntegrableDissipativeDynamicalSystemswithThreeandFour DegreesofFreedom ......................................... 77 MaximV.Shamolin 8.1 Introduction.............................................. 77 8.2 EquationsofGeodesicLines................................ 78 8.3 AFairlyGeneralCase ..................................... 79 8.4 PotentialFieldofForce .................................... 81 8.5 ForceFieldwithDissipation ................................ 82 8.6 StructureofTranscendentalFirstIntegrals..................... 84 8.7 Conclusions.............................................. 84 8.8 ImportantExample:CaseofFour-DimensionalManifold ........ 85 8.8.1 EquationsofMotioninaPotentialForceFieldandFirst Integrals ......................................... 88 8.8.2 EquationsofMotioninaForceFieldwithDissipation andFirstIntegrals ................................. 89 References ..................................................... 91 PartII Modeling,Design,andComputationofNonlinearStructures 9 AVariationalFormulationofClassicalNonlinearBeamTheories ... 95 SimonR.Eugster&JonasHarsch 9.1 Introduction.............................................. 95 9.2 NotationandKinematics ................................... 97 9.3 StrainEnergyFunctional ...................................101 9.4 VirtualWorkContributions.................................103 9.5 PrincipleofVirtualWorkandEquationsofMotion.............107 9.6 ConstrainedBeamTheories.................................109 9.6.1 NonlinearEuler–BernoulliBeam ....................109 9.6.2 NonlinearInextensibleEuler–BernoulliBeam..........110 9.7 ConstrainedandUnconstrainedPlanarBeamTheories ..........110 9.7.1 TimoshenkoBeam.................................111 9.7.2 Euler–BernoulliBeam .............................115 9.7.3 InextensibleEuler–BernoulliBeam...................117 9.8 Conclusion...............................................118 References .....................................................119 10 Finite Element Analysis of Planar Nonlinear Classical Beam Theories ................................................... 123 JonasHarsch&SimonR.Eugster 10.1 Introduction..............................................123 10.2 Notation.................................................125 10.3 VirtualWorkContributionsinParameterSpace ................125 10.3.1 TimoshenkoBeam.................................127 10.3.2 Euler–BernoulliBeam .............................128 10.3.3 ConstraintVirtualWorkContributions................129 10.4 B-SplineShapeFunctions ..................................130 x Contents 10.5 DiscreteKinematics,SemidiscreteVirtualWork,andEquations ofMotion................................................133 10.5.1 TimoshenkoBeam.................................134 10.5.2 Euler–BernoulliBeam .............................136 10.5.3 ConstraintForces..................................138 10.5.4 EquationsofMotionandBilateralConstraints .........140 10.6 NumericalExamples ......................................142 10.6.1 PureBendingofaCantileverBeam ..................142 10.6.2 CantileverBeamSubjectedtoConstantEndLoad ......143 10.6.3 CantileverBeamSubjecttoFollowerEndLoad ........145 10.6.4 Clamped-HingedCircularArchSubjecttoPointLoad...147 10.6.5 Buckling of a Hinged Right-Angle Frame under FollowerPointLoad ...............................150 10.6.6 Natural Frequencies of a Two Sided Pinned Euler–BernoulliBeam .............................152 10.7 Conclusion...............................................155 References .....................................................156 11 Modelling of Two-dimensional Timoshenko Beams in Hencky Fashion.................................................... 159 EmilioTurco 11.1 Introduction..............................................159 11.2 ModellingofTwo-DimensionalTimoshenkoBeams ............160 11.3 NumericallyDrivenDrawingoftheEquilibriumPath ...........164 11.4 Quantitative Analysis of the Influence of the Shear Stiffness Parameter................................................166 11.4.1 TipDeflectionofaCantileverBeam..................167 11.4.2 BucklingofaSimplySupportedBeam................169 11.5 ConcludingRemarksandFutureChallenges...................172 References .....................................................173 12 Nonlinear Phenomena in Granular Solids: Modeling and Experiments................................................ 179 MarcoLaudato 12.1 Introduction..............................................179 12.2 Nonlinear Phenomena in Granular Solids: Modeling and Experiments .............................................180 12.2.1 DeformationandDestructionatDeformationRateof Order103s−1WoodofHardwoodTrees-TatianaYuzhina181 12.2.2 Experimental Study of the Dynamic Properties of ConcreteunderCompressiveLoad-MikhailGonov ....181 12.2.3 DamageProbinginCementedGranularMaterialswith Ultrasound-IoanIonescu ..........................182 12.2.4 TheRoleofFabricintheBehaviorofGranularMaterial -NielsKruyt .....................................182
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