无网格伽辽金法计算精度的研究

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1、AbstractElement-freeGalerkinMethod(EFGM)isanewnumericalmethodinrecentyears.Itisamoreoftenusedmethodinallmeshlessmethods.Inthispaper,shapefunctionisconstructedbyMovingLeastSquaresMethod.Controlequationsareproducedfromtheweakformofvariationalequation.La

2、grangemultipliersareusedtosatisfydisplacementboundaryconditions,andmakeoutnumericalsolutions.Thismethodsimplifieddataprocessingandimprovedcomputingspeedwithoutgrid.Anditcansolvetheproblemsthatcannotsolvebyfiniteelementmethod.Thispaperincludesfivechapt

3、ers.Chapter1brieflyintroducesthedevelopmentofEFGMandintroducesseveralmeshlessmethods.Inchapeter2,weintroduceEFGM,andstudyshapefunction,weightfunctionandinfluencedomain.Controlequationsareproducedfromtheweakformofvariationalequation.andthenwediscusssev

4、eralmethodsofdealingwithdisplacementboundaiyconditions,moreovergiveEFGMcalculationprocess.InChapter3,wedisscussthefactorsofimpactingthecomputationaccuracyandobtainsomeusefulconclusions.InChapter4,EFGMisappliedtoelasticproblems,andweanalyzeproblemssuch

5、asthebarsubjectedtolinearloading,thecantileverbeamsubjectedtoevenforceandtheeasysupportbeamsubjectedtoevenforce.Thenprogrammingsaregivenaccordingtoeachexample.ThecomputationresultsindicateEFGMhashighprecision.InChapter5,EFGMisappliedtoelectromagneticp

6、roblems.Intheprocessofsolving,themixedtransformationmethodisusedtodealwithdisplacementboundaryconditions.ExamplesarepresentedandtheresultsshowthatEFGMisnotonlyeasytoimplementbutalsowithhighprecisionandgoodstability.KeywordsElement-freeGalerkinmethod;M

7、ovingleastsquares;Computationaccuracy;Lagrangemultiplier;Mixedtransformationmethod;Matlab第1章绪论11.1引言11.2文献综述21.3几种主要的无网格法5L3」光滑质点流体动力学方法(SPH)51.3.2再生核质点法(RKPM)61.3.3无网格伽辽金法(EFGM)81.3.4单元分解无网格方法(PUM)91.4选题的意义及研究内容10第2章无网格伽辽金法理论112.1引言112.2无网格伽辽金法的基木理论1

8、12.2.1移动最小二乘(MLS)112.2.2形函数及其导数142.2.3节点影响域152.2.4权函数162.3无网格伽辽金法的实现过程182.3.1控制方程182.3.2位移边界条件的处理192.3.3无网格伽辽金法的求解流程232.4本章小结24第3章影响无网格伽辽金法计算精度的因素253.1引言253.2基函数对EFGM计算精度的影响263.3权函数对EFGM计算精度的影响273.4影响域半径对EFGM计算精度的影响313.5本章小结35第4章无网格伽辽金法在弹性力学中的