简介:Alinear4-nodequadrilateralquasi-conformingplaneelementwithinternalparametersisproposed.Theelementpreservesadvantagesofthequasi-conformingtechnique,includinganexplicitstiffnessmatrix,whichcanbeappliedtononlinearproblems.Theweakpatchtestguaranteestheconvergenceoftheelement.ThenthelinearelementisextendedtothegeometricallynonlinearanalysisintheframeworkofTotalLagrangian(TL)formulation.Thenumericaltestsindicatethatthepresentelementisaccurateandinsensitivetomeshdistortion.
简介:Westudyelectromechanicalfieldsintheanti-planedeformationofaninfinitemediumofpiezoelectricmaterialsof6mmsymmetrywithacircularcylindricalhole.Thetheoryofelectroelasticdielectricswithelectricfieldgradientintheconstitutiverelationsisused.Specialattentionispaidtothefieldsnearthesurfaceofthehole.
简介:Thenonlinearbehaviorofacantileveredfluidconveyingpipesubjectedtoprincipalparametricandinternalresonancesisinvestigatedinthispaper.Theflowvelocityisdividedintoconstantandsinusoidaiparts.Thevelocityvalueoftheconstantpartissoadjustedsuchthatthesystemexhibits3:1internalresonancesforthefirsttwomodes.Themethodofmultiplescalesisemployedtoobtaintheresponseofthesystemandasetoffourfirst-ordernonlinearordinary-differentialequationsforgoverningtheamplitudeoftheresponse.TheeigenvaluesoftheJacobianmatrixareusedtoassessthestabilityoftheequilibriumsolutionswithvaryingparameters.Thecodimension2derivedfromthedouble-zeroeigenvaiuesisanalyzedindetail.Theresultsshowthattheresponseamplitudemayundergosaddle-node,pitchfork,Hopf,homoclinicloopandperiod-doublingbifurcationsdependingonthefrequencyandamplitudeofthesinusoidalflow.Whenthefrequencyofthesinusoidalflowequalsexactlyhalfofthefirst-modefrequency,thesystemhasaroutetochaosbyperiod-doublingbifurcationandthenreturnstoaperiodicmotionastheamplitudeofthesinusoidalflowincreases.