外文翻译(土木工程专业毕业设计)

附录1外文翻译原文3.2Elasticmodels3.2.1AnisotropyAnisotropicmaterialhasthesamepropertiesinalldirections—wecannotdis-tinguishanyonedirectionfromanyother.Samplestakenoutofthegroundwithanyorientationwouldbehaveidentically.However,weknowthatsoilshavebeendepositedinsomeway—forexample,sedimentarysoilswillknowabouttheverticaldirectionofgravitationaldeposition.Theremayinadditionbeseasonalvariationsintherateofdepositionsothatthesoilcontainsmoreorlessmarkedlayersofslightlydifferentgrainsizeand/orplasticity.Thescaleoflayeringmaybesuffcientlysmallthatwedonotwishtotrytodistinguishseparatematerials,butthelayeringtogetherwiththedirectionaldepositionmayneverthelessbesuffcienttomodifytheproperiesofthesoilindifferentdirections—inotherwordstocauseittobeanisotropic.WecanwritethestiffnessrelationshipbetweenelasticstrainincrementeandstressincrementcompactlyaseD)36.3(whereDisthestiffnessmatrixandhence1Disthecompliancematrix.ForacompletelygeneralanisotropicelasticmaterialutrokftsqnjerqpmidonmlhckjihgbfedcbaD1)37.3(whereeachlettera,b,...is,inprinciple,anindependentelasticpropertyandthenecessarysymmetryofthesti?nessmatrixfortheelasticmaterialhasreducedthemaximumnumberofindependentpropertiesto21.Assoonastherearematerialsymmetriesthenthenumberofindependentelasticpropertiesfalls(Crampin,1981).Forexample,formonoclinicsymmetry(zsymmetryplane)thecompliancematrixhastheform:migdlkkjihfcgfebdcbaD00000000000000001)38.3(andhasthirteenelasticconstants.Orthorhombicsymmetry(distinctx,yandzsymmetryplanes)givesnineconstants:ihgfecedbcbaD0000000000000000000000001)39.3(whereascubicsymmetry(identicalx,yandzsymmetryplanes,togetherwithplanesjoiningoppositesidesofacube)givesonlythreeconstants:cccabbbabbbaD0000000000000000000000001)40.3(Figure3.9:Independentmodesofshearingforcross-anisotropicmaterialIfweaddthefurtherrequirementthat)(2bacandsetEa/1andEvb/，thenwerecovertheisotropicelasticcompliancematrixof(3.1).Thoughitisobviouslyconvenientifgeotechnicalmaterialshavecertainfabricsymmetrieswhichconferareductioninthenumberofindependentelasticproperties,ithastobeexpectedthatingeneralmaterialswhichhavebeenpushedaroundbytectonicforces,byice,orbymanwillnotpossessanyofthesesymmetriesand,insofarastheyhaveadomainofelasticresponse,weshouldexpecttorequirethefull21independentelasticproperties.Ifwechoosetomodelsuchmaterialsasisotropicelasticoranisotropicelasticwithcertainrestrictingsymmetriesthenwehavetorecognisethatthesearemodellingdecisionsofwhichthesoilorrockmaybeunaware.However,manysoilsaredepositedoverareasoflargelateralextentandsymmetryofdepositionisessentiallyvertical.Allhorizontaldirectionslookthesamebuthorizontalsti?nessisexpectedtobedi?erentfromverticalstiffness.Theformofthecompliancematrixisnow:feedcccabcbaD0000000000000000000000001)41.3(andwecanwrite：:/)1(2)(2/1,/1,/,/,/1hhhvhvvvhhhhhEvbafGeEdEvcEvbEa和1DhhhhvhvhvvhvvhvvhhhhhvvhhhhhEvGGEEvEvEvEEvEvEvE/12000000/1000000/1000000/1//000//1/000///1)42.3(Thisisdescribedastransverseisotropyorcrossanisotropywithhexagonalsymmetry.Thereare5independentelasticproperties:vEandhEareYoung’smoduliforunconfinedcompressionintheverticalandhorizontaldirectionsrespectively;hvGistheshearmodulusforshearinginaverticalplane(Fig3.9a).Poisson’sratioshhVandhvVrelatetothelateralstrainsthatoccurinthehorizontaldirectionorthogonaltoahorizontaldirectionofcompressionandaverticaldirectionofcompressionrespectively(Fig3.9c,b).TestingofcrossanisotropicsoilsinatriaxialapparatuswiththeiraxesofanisotropyalignedwiththeaxesoftheapparatusdoesnotgiveusanypossibilitytodiscoverhvGE/1，sincethiswouldrequirecontrolledapplicationofshearstressestoverticalandhorizontalsurfacesofthesample—andattendantrotationofprincipalaxes.Infactweareableonlytodetermine3ofthe5elasticproperties.Ifwewrite(3.42)forradialandaxialstressesandstrainsforasamplewithitsverticalaxisofsymmetryofanisotropyalignedwiththeaxisofthetriaxialapparatus,wefindthat：''/1//2/1ravhhvvhvvhvraEvEvEvE)43.3(Thecompliancematrixisnotsymmetricbecause,inthecontextofthetriaxialtest,thestrainincrementandstressquantitiesarenotproperlyworkconjugate.WededucethatwhilewecanseparatelydeterminevEandhvVtheonlyotherelasticpropertythatwecandiscoveristhecompositestiffness)1/(hhhVE.WearenotabletoseparatehEandhhV(Lingsetal.,2000).Ontheotherhand,GrahamandHoulsby(1983)haveproposedaspecialformof(3.41)or(3.42)whichusesonly3elasticpropertiesbutforcescertaininterdependenciesamongthe5elasticpropertiesforthiscrossanisotropicmaterial.222221/12000000/12000000/120000001//000//1/000///11vvvvvvvvvED)44.3(ThisiswrittenintermsofaYoung’smodulusvEE,theYoung’smodulusforloadingintheverticaldirection,aPoisson’sratiohhVV,togetherwithathirdparameter.Theratioofstiffnessinhorizontalandverticaldirectionsis2/vhEEandotherlinkagesareforced：)1(2//;/vEGGvvhhhvhhvh.Forourtriaxialstress