A coupled hygro-elastic 3D model for steady-state analysis of functionally graded plates and shells

This3Dcoupledhygro-elasticmodelproposesthe three-dimensional (3D) equilibriumequations associated withthe3DFickdiffusionequationfor spherical shells. Theprimaryunknownsof theproblemarethedisplacementsandthemoisturecontent.Thiscoupled3Dexactshell modelallowstounderstandtheeffectsofthemoisturefieldin relationwiththeelasticfieldonstressesanddeformationsin differentplatesandshells.Thismodel isspecificallydevelopedforconfigurationsincludingfunctionallygradedmaterial (FGM) layers. Fourdifferent geometries areanalyzed using anorthogonalmixed curvilinear reference system. Themainadvantageof thisreferencesystemforspherical shellsisthedegenerationoftheequationstothoseforsimpler geometries. The solvingmethod is theexponentialmatrix methodinthethicknessdirection.Theclosed-formsolution ispossiblebecauseofsimplysupportedsidesandharmonic formsfordisplacementsandmoisturecontent.Themoisture contentamplitudesaredirectlyappliedatthetopandbottom outerfacesthroughsteady-statehypotheses.Thefinalsystem isbasedonasetofcoupledhomogeneoussecond-orderdifferentialequations.Themoisturefieldeffectsareevaluated forthestaticanalysis intermsofdisplacement, strain,and stress components. After preliminaryvalidations, used to betterunderstandhowtoproperlydefinethecalculationof thecurvature-relatedtermsandFGMproperties, fournew benchmarksareproposedforseveral thicknessratios,geometrical data, FGMconfigurations, andmoisture values imposedattheexternalsurfaces.Fromtheresults,itisclear theaccordancebetweentheuncoupledhygro-elasticmodel andthisnewcoupledhygro-elasticmodelwhenthe3DFick diffusionlawisemployed.Botheffectsconnectedwiththe thicknesslayerandtheembeddedmaterialareincludedin the 3Dhygro-elastic analyses proposed. The 3Dcoupled hygro-elasticmodel is simpler than the uncoupled one becausethe3DFickdiffusionlawdoesnothavetobeseparatelysolved.