横观各向同性功能梯度圆板和环板的轴对称问题

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1、浙江大学博士学位论文横观各向同性功能梯度圆板和环板的轴对称问题姓名：李翔宇申请学位级别：博士专业：结构工程指导教师：陈伟球;丁皓江20070401浙江大学博士论文2007李翔宇AbstractAsaspecialkindofinhomogeneousmaterials9functionallygradedmaterials(FGMs)，whichsuccessfullyunifythemicro-structuresandfunctions，aresuperiortothetraditionallaminatedcompositematerials,andhavebeoomeapr

2、omising舶ldofmaterialscienceinthepresentcentury．Materialsciencehasstriddenfugth@rwhentheconceptofFGMisintroducedintoPiezoelectricityandMagneto-electro-elasticity．Whilechangingcompletelytheideaofmaterial／structuraldesign,FGMsalsoresultingreatopportunitiesaswellascriticalchallengesforscientificre

3、search．Inthethree-dimensional(3D)analysesavailableinliterature，thefollowingtwoFGMmodelshavebeenfrequentlyemployedfordescribingtheirdaomogeneityofFGM：(1)allmaterialconstantsvaryinthe$ameparticularform；or(2)itisapproximatedbyalaminatecomposedofmanythinLayers．ThefirstfailsduetothediversityofFGMs，

4、andthesecondisalwaysapproximateandmaybecomelessefficientforcertainproblems．Inthiswork,3DstaticanalysesofaxisymmetricproblemsofFGMcircular／annularplateswith缸ansVerseisotropyaresystematicallyconducted．Thestressfimctionsordisplacementsareexpressedintermsofpowerserieswithrespecttotheradialvariable

5、，诵也thecoefficientsbeingfunctionsoftheaxialvariable．Theanalyticalsolutions，obtainedthroughastep-by·stepintegrationscheme，satisfyexactlythebasicequationsandboundaryconditionsontheupperandlowersurfaces，butapproximatelythecylindricalboundaryconditionsintheSaintVenant’Ssense．Thecontributionsofthewo

6、rkinclude(1)3DanalyticalsolutionsofanFGMelasticcircularplatesubjecttoauniformlydistributedloadOrbendingmomentatitsedge；．(2)3Dpiezoelasticsolutionsofafunctionallygradedpiezoelectriccircularplatesubjectedtomechanicalorelectricload；(3)3Dsolutionsofauniformlyloadedfunctionallygradedmagneto-electro

7、-elasticcircularplate；(4)Thegeneralizationofthemethodtofunctionally伊adedpiezoelectric／Hmagneto-elcc仃o．-e]asticannularplatesubjecttoauniformmechanicalload．Allanalyticalsolutionscanaccountforthearbitraryvariationsofthematerialparametersal