無單元法及其在薄板非線性問題中的應用.pdf

1、青島理工大學碩士學位論文無單元法及其在薄板非線性問題中的應用姓名：王培樂申請學位級別：碩士專業(yè)：結構工程指導教師：張偉星20050601青島理工走學工學碩士學位論文AbstractElementfreemethodisanewnumericalmethodThlSdissertationstudiesindetailthefundamentaltheoriesofElementfreeGalerkinmethod(EFGM)andapp

2、liesittobending，largedeflectiongofelasticthinplatesThecontentsofthisdissertationcandivideintothreeparts：Inthefistpart，thefundamentaltheoriesofMovingLeastSquaresMethod(MLSM)whichisthemathematicalbasisofEFGMarestudiedthoro

3、ughlytheshapefunctionofEFGMarealsodeduced。Severalkeyproblems，suchastheselectionofweightfunctionandbasisfunction，thesizeofinfluenceradiusofnodes，thecollocationofboundaryconditionandthemethodofintegralandimplementationetc，

4、aredeeplyresearchedInthesecondpart，thisdissertationappliedEFGMtosolveelastioplasticproblemandlargedeflectionproblemofthinplatesThecorrespondingstiffnessmatrixofEFGMisderivedusingvariationalprincipleThecorrespondingcomput

5、erprogramsatealsodevelopedNumericalexamplesshowthatthemethodisreasonableandfeasiblePenaltyfunctionisappliedtoen=forcetheessentialboundaryconditionsinthisdissertationThecorrespondingenergyformulasarederivedPenaltyfuncdons

6、olvesthoroughlytheproblemwhichcollocationofboundaryconditionisdifficultbyEFGMResearchshowsthatEFGMsolvingelastio—plasticproblemandlargedeflectionproblemofthinplatesisreasonableandfeasiableNumericalexamplesshowthatEFGMhas

7、theadvantageofsimplebeforeandafterprocesss，highaccmacyinsolvingstaticanddynamicanalysisofplatesInaword，EFGMhasapromisingprospectinengineeringpracticeKeywords：ElementfreeGalerkinMethod(EFGM)；MovingLeastSquareMethod(MLSM)；