简介：ThesufficientconditionsofHoldercontinuityoftwokindsoffractalinterpolationfunctionsdefinedbyIFS(IteratedFunctionSystem)wereobtained.Thesufficientandnecessaryconditionforitsdifferentiabilitywasproved.ItsderivativewasafractalinterpolationfunctiongeneratedbytheassociatedIFS,ifitisdifferentiable.

简介：Byusingthefundamentalequationsofaxisymmetricshallowshellsofrevolution,thenonlinearbendingofashallowcorrugatedshellwithtaperunderarbitraryloadhasbeeninvestigated.ThenonlinearboundaryvalueproblemofthecorrugatedshellwasreducedtothenonlinearintegralequationsbyusingthemethodofGreen'sfunction.Tosolvetheintegralequations,expansionmethodwasusedtoobtainGreen'sfunction.ThentheintegralequationswerereducedtotheformwithdegeneratecorebyexpandingGreen'sfunctionasseriesofcharacteristicfunction.Therefore,theintegralequationsbecomenonlinearalgebraicequations.Newton'siterativemethodwasutilizedtosolvethenonlinearalgebraicequations.Toguaranteetheconvergenceoftheiterativemethod,deflectionatcenterwastakenascontrolparameter.Correspondingloadswereobtainedbyincreasingdeflectiononebyone.Asanumericalexample,elasticcharacteristicofshallowcorrugatedshellswithsphericaltaperwasstudied.Calculationresultsshowthatcharacteristicofcorrugatedshellschangesremarkably.Thesnappinginstabilitywhichisanalogoustoshallowsphericalshellsoccurswithincreasingloadifthetaperisrelativelylarge.Thesolutionisclosetotheexperimentalresults.

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简介：Anewsmoothgapfunctionfortheboxconstrainedvariationalinequalityproblem(VIP)isproposedbasedonanintegralglobaloptimalitycondition.Thesmoothgapfunctionissimpleandhassomegooddifferentiableproperties.TheboxconstrainedVIPcanbereformulatedasadifferentiableoptimizationproblembytheproposedsmoothgapfunction.Theconditions,underwhichanystationarypointoftheoptimizationproblemisthesolutiontotheboxconstrainedVIP,arediscussed.Asimplefrictionalcontactproblemisanalyzedtoshowtheapplicationsofthesmoothgapfunction.Finally,thenumericalexperimentsconfirmthegoodtheoreticalpropertiesofthemethod.

简介：Anaccuratecracksurfaceopeningdisplacementformulaforedgecracksinfinitebodieshasbeenderived,andwassubsequentlyusedtodevelopwide-rangeclosed-formweightfunctionsforedgecracks.Theanalyticalweightfunctionisgeneralandcanbeeasilyusedtodetermineaccuratestressintensityfactorsandcracksurfaceopeningdisplacementsforarbitrarilyloadededgecrackswithhighefficiency.Exampleshavebeengivenforproblemsofedgecrack(s)withanumberoftypicalloadconditionsforillustration.

简介：Aneuralnetwork(NN)isapowerfultoolforapproximatingboundedcontinuousfunctionsinmachinelearning.TheNNprovidesaframeworkfornumericallysolvingordinarydifferentialequations(ODEs)andpartialdifferentialequations(PDEs)combinedwiththeautomaticdifferentiation(AD)technique.Inthiswork,weexploretheuseofNNforthefunctionapproximationandproposeauniversalsolverforODEsandPDEs.ThesolveristestedforinitialvalueproblemsandboundaryvalueproblemsofODEs,andtheresultsexhibithighaccuracyfornotonlytheunknownfunctionsbutalsotheirderivatives.ThesamestrategycanbeusedtoconstructaPDEsolverbasedoncollocationpointsinsteadofamesh,whichistestedwiththeBurgersequationandtheheatequation(i.e.,theLaplaceequation).

简介：Structuraloptimizationforcrashworthinesscriteriaisofparticularsignificanceespeciallyatearlystageofdesign.ThecomparativestudyofKrigingandradialbasisfunctionnetwork(RBFN)wasperformedinordertoimprovethecrashworthinesseffectsofhoneycomb.ImprovingthecrashworthinesscharacteristicofhoneycombwasachievedusingLS-OPTanddomainreductionstrategy.Thisoptimizationisperformedonthebasisofvalidatednumericalsimulationtoestablishtheapproximatedmodeltoillustratetherelationshipbetweentheresponsesanddesignvariables.TheresultsshowedthatKrigingmeta-modelisexcelledinaccuracy,robustnessandefficiencycomparedtoradialbasisfunction(RBF)andcrashworthinesscharacteristicofhoneycombisimprovedby4%.

简介：Theequationofstressintensityfactors(SIF)ofinternallypressurizedthick-walledcylinderwasusedasthereferencecase.SIFequationofrotatingthick-walledcylindercontainingaradialcrackalongtheinternalborewaspresentedinweightfunctionmethod.Theweightfumctionformulaswereworkedoutandcanbeusedforallkindsofdepthofcracks,rotatingspeed,material,sizeofthick-walledcylindertocalculatethestressintensityfactors.Theresultsindicatedthevalidityandeffectivenessoftheseformulas.Meanwhile,therulesofthestressintensityfactorsinrotatingthick-walledcylinderwiththechangeofcrackdepthsandtheratioofouterradiustoinnerradiuswerestudied.Thestudiesarevaluabletoengineeringapplication.

简介：ThedissipationfunctioninturbulentplanePoiseuilleflows(PPFs)andplaneCouetteflows(PCFs)subjecttospanwiserotationsisanalyzed.Itisfoundthat,inthePCFswithoutsystemrotations,themeanpartisconstantwhilethefluctuationpartfollowsalogarithmiclaw,resultinginasimilarlogarithmicskinfrictionlawasPPFs.However,iftheflowsystemrotatesinthespanwisedirection,noobviousdependenceontherotationnumbercanbeevaluated.InthePPFswithrotations,thedissipationfunctionshowsanincreasewiththerotationnumber,whileinthePCFswithrotations,whentherotationnumberincreases,thedissipationfunctionfirstdecreasesandthenincreases.

简介：格林功能方法(GFM)被利用分析在里面飞机强迫了传送液体的弄弯的管子的颤动，在外部刺激和增加的团和抑制比率的randomicity和分发被考虑的地方。Laplace变换被使用，并且有各种各样的边界条件的格林功能随后被获得。数字计算被执行在正切、光线的排水量上验证一些关键参数的现在的解决方案，和效果进一步被调查。有线性、非线性的运动限制的强迫的颤动问题也简短被讨论。方法能被散发学习与管子或更广泛的问题联系的强迫的颤动问题的另外的形式。

简介：ThesolutionsofGreen'sfunctionaresignificantforsimplificationofproblemonatwo-phasesaturatedmedium.UsingtransformationofaxisymmetriccylindricalcoordinateandSommerfeld'sintegral,superpositionoftheinfluencefieldonafreesurface,authorsobtainedthesolutionsofatwo-phasesaturatedmediumsubjectedtoaconcentratedforceonthesemi-space.

简介：Anindependentmethodforpaper[10]ispresented.WeightedlatticepathsareemumeratedbycountingfunctionwhichisanaturalextensionofGaussianmultinomialcoefficientinthecaseofunrestrictedpaths.Convolutionsforpathcountsareinvestigated.whichyieldssomeVandermonde-typeidentitiesformultinomialandq-multinomialcoefficients.

简介：Inthepresentpaper,thecompatibilityequationfortheplanestressproblemsofpower-lawmaterialsistransformedintoabiharmonicequationbyintroducingtheso-calledcomplexpseudo-stressfunction,whichmakesitpossibletosolvetheelastic-plasticplanestressproblemsofstrainhardeningmaterialsdescribedbypower-lawusingthecomplexvariablefunctionmethodlikethatinthelinearelasticitytheory.Byusingthisgeneralmethod,theclose-formedanalyticalsolutionsforthestress,strainanddisplacementcomponentsoftheplanestressproblems’ofpower-lawmaterialsisdeducedinthepaper,whichcanalsobeusedtosolvetheelasto-plasticplanestressproblemsofstrain-hardeningmaterialsotherthanthatdescribedbypower-law.Asanexample,theproblemofapower-lawmaterialinfiniteplatecontainingacircularholeunderuniaxialtensionissolvedbyusingthismethod,theresultsofwhicharecomparedwiththoseofaknownasymptoticanalyticalsolutionobtainedbytheperturbationmethod.

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