Highly accurate symplectic element based on two variational principles

(整期优先)网络出版时间:2018-01-11
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Forthestabilityrequirementofnumericalresultants,themathematicaltheoryofclassicalmixedmethodsarerelativelycomplex.However,generalizedmixedmethodsareautomaticallystable,andtheirbuildingprocessissimpleandstraightforward.Inthispaper,basedontheseminalideaofthegeneralizedmixedmethods,asimple,stable,andhighlyaccurate8-nodenoncompatiblesymplecticelement(NCSE8)wasdevelopedbythecombinationofthemodifiedHellinger-Reissnermixedvariationalprincipleandtheminimumenergyprinciple.Toensuretheaccuracyofin-planestressresults,asimultaneousequationapproachwasalsosuggested.NumericalexperimentationshowsthattheaccuracyofstressresultsofNCSE8arenearlythesameasthatofdisplacementmethods,andtheyareingoodagreementwiththeexactsolutionswhenthemeshisrelativelyfine.NCSE8hasadvantagesoftheclearingconcept,easycalculationbyafiniteelementcomputerprogram,higheraccuracyandwideapplicabilityforvariouslinearelasticitycompressibleandnearlyincompressiblematerialproblems.ItispossiblethatNCSE8becomesevenmoreadvantageousforthefractureproblemsduetoitsbetteraccuracyofstresses.