简介：Thispaperdemonstratestheplanestressstateandthestressfreethermo-elasticdeformationofFGMthickplateunderthermalloading.First,theSneddon-LocketttheoremontheplanestressstateinanisotropicinfinitethickplateisgeneralizedforacaseofFGMprobleminwhichallthermo-mechanicalpropertiesareoptionalfunctionsofdepthco-ordinate.TheproofisbasedonapplicationoftheIljushinthermo-elasticpotentialtodisplacementtypesystemofequationsthatreducesittotheplanestressstateproblem.Thenanexistenceofthepurelythermaldeformationisprovedintwoways:first,itisshownthattheuniquesolutionfulfilsconditionsofsimultaneousconstanttemperatureandlineargradationofthermalexpansioncoefficient,second,proofisbaseddirectlyonstresstypesystemofequationswhichstraightforwardlyreducestocompatibilityequationsforpurelythermaldeformationifonlystressfieldishomogeneousindomainandatboundary.Finally,coupleexamplesofapplicationtoanengineeringproblemarepresented.