弹性地基上简支多边形薄板问题的准格林函数方法

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1、AbstractComparcd诵thtlleme也odofnumericalanalysissuchasfiniteelementmethod，boundaIyelementmemod缸dme≤hlessmetllod，etc，Greenqu嬲ifunctionInetllodhasitsoWnadVamages．Inrecentye甜s，somedomesticandintemadonaIschoI盯shavercapm柚yimportantfmitsinstIldyofGreenquasimncti

2、onmemod．GreenquasimnctionmethodisfirstproposedbyRVachev'andappliedtosOlVe也epmbkmofbo咖daryvalueofpoissonequation．YhnHOng，etc．popularizemismetllodinvariouskiIldsof盯immeticopemtorS，andappliestosolvemepmblemofpolygormlelasticplateunderdi仃brentedgeconmtions．On

3、thebasisoftheirwork，印plicationofGreenq皿si血nctionlnemodto仙esimple—supponpolygonalminplateonelasticfo喇onarepre∞medinthisdissenatioll，whjchellrichestlleoryOfGreenqu鹊i胁ct沁nandextends印plicati叽sofGreenqllasifimctionmethod．Atmebeginningoftlledissertation，nmtee1锄

4、entmethod，boun如巧elememnle吐10d，etca11dmeiradv彻tagesanddisadvantagesarebrienyin昀duced．Thcdissertationsmnmarizcscharacteristic趾dsuperiorityofGreenquasi如nctionmetlloda11dexplainsmeessenceofGreenqu商鼬lctionmethod．SevemlkindsofeIasticfb咖dationmodel，variouskindso

5、faJlalytical趿dnulllericalmethodsof也eplateOnelasticfoundationatpresentarebriefIyreViewed，andrecentresearchaIlddeVelopmemofGreenquasifhctionmethod盯einn-oduced．chapterlsurveystheapplicationofGreenqu商f洒ctionmethodtoallkindsofarithⅡ1cticoperatorssuchasLaplaceo

6、perator’Hel瑚_lloltzoperatoraIldbihannonicoperator'etc．These耐thmeticoperatorsare嘶delyuSedin也eMechanics锄dPhysicsproblems．Chapter2deaIsGreenq岫siflmctionIncthodoftllebend访gpmblemofthesjmple—supportpolygonaldlinplatcon啪Ill(】erfolllldation．Utilizingintel强ediate

7、variable，thegovemingdi行b∞ntialequationoftllebcIldir培problemofsimpIe·supportp01ygonalt量1inplateonMnklerfouIldationisdividedimotwosimultaneousdi疏rentialequ砒ionsoflowcrorderwhichcoupleeachother．ThroughmechaIlgeofV耐ables，inhomogeneousboundaryconditionofmeorig

8、inalproblemisreducedtotheboulldaIyValuepmblemofhomogeneousboundarycondition．Inordertobeconvenienceforcomparisonofresult，dimensionlessIII广东工业大学工学硕士学位论文quantityisiI遣∞ducedandtbe嘶ginalquestionismmedintodimensionless．Gr