A regular variational boundary model for free vibrations of magneto-electro-elastic structures

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Abstract

In thispaperaregularvariationalboundaryelementformulationfordynamicanalysisoftwo-dimensionalmagneto-electro-elasticdomainsispresented.Themethodisbasedonahybridvariationalprincipleexpressedintermsofgeneralizedmagneto-electro-elasticvariables.Thedomainvariablesareapproximatedbyusingasuperpositionofweightedregularfundamentalsolutionsofthestaticmagneto-electro-elasticproblem,whereastheboundaryvariablesareexpressedintermsofnodalvalues.Thevariationalprinciplecoupledwiththeproposeddiscretizationschemeleadstothecalculationoffrequency-independentandsymmetricgeneralizedstiffnessandmassmatrices.Thegeneralizedstiffnessmatrixiscomputedintermsofboundaryintegralsofregularkernelsonly.Ontheotherhand,toachievemeaningfulcomputationaladvantages,thedomainintegraldefiningthegeneralizedmassmatrixisreducedtotheboundarythroughtheuseofthedualreciprocitymethod,althoughthisimpliesthelossofsymmetry.Apurelyboundarymodelisthenobtainedforthecomputationofthestructuraloperators.Themodelcanbedirectlyusedintostandardassemblyproceduresfortheanalysisofnon-homogeneousandlayeredstructures.Additionally,theproposedapproachpresentssomefeaturesthatplaceitintheframeworkoftheweakformmeshlessmethods.Indeed,onlyasetofscatteredpointsisactuallyneededfor thevariableinterpolation,whileaglobalbackgroundboundarymeshisonlyusedfortheintegrationofthe influencecoefficients.Theresultsobtainedshowgoodagreementwiththoseavailableintheliteratureprovingtheeffectivenessoftheproposedapproach.
Original languageEnglish
Pages (from-to)303-312
Number of pages10
JournalEngineering Analysis with Boundary Elements
Volume35
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • General Engineering
  • Computational Mathematics
  • Applied Mathematics

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