homogenization-method-for-elastic-materials

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1、IntroductionDescriptionofthegeometryProblemsettingImplementation&ResultsBandgapsConclusionAcknowledgementHomogenizationmethodforelasticmaterialsFrantiˇsekSEIFRTFrantiˇsekSEIFRTHomogenizationmethodforelasticmaterialsIntroductionDescriptionofthegeometryProblemse

2、ttingImplementation&ResultsBandgapsConclusionAcknowledgementOutline1Introduction2Descriptionofthegeometry3Problemsetting4Implementation&Results5Bandgaps6ConclusionFrantiˇsekSEIFRTHomogenizationmethodforelasticmaterialsIntroductionDescriptionofthegeometryProble

3、msettingImplementation&ResultsBandgapsConclusionAcknowledgementIntroductionIntroductionstudyofthehomogenizationmethodappliedonelasticmaterials,G.Nguetseng(1989),G.Allaire,D.Cioranescu,P.Donato.Homogenizationmethodsimplifiesdescriptionofbehaviorofheterogeneousma

4、terials,replacementbythe’homogenized’,fictivematerial,homogenizedmaterialshouldbeagoodapproximationoftheoriginalhet.material.FrantiˇsekSEIFRTHomogenizationmethodforelasticmaterialsIntroductionDescriptionofthegeometryProblemsettingImplementation&ResultsBandgapsC

5、onclusionAcknowledgementDescriptionofthegeometryGeometryN×Ncells,cellsizeε,domainΩε-elasticmaterial1,1domainΩε-elasticmaterial2,2referencecellY=[0,1[3.Coordinatessystem(x1,x2)macrocoordinates,Figure:Geometryofthelattice(y1,y2)microcoordinates,(x,y)represents

6、εx+εy.εFrantiˇsekSEIFRTHomogenizationmethodforelasticmaterialsIntroductionDescriptionofthegeometryProblemsettingImplementation&ResultsBandgapsConclusionAcknowledgementStateequationsStateequationsdeflectionoftheloadedlattice,materialcoefficientsεxcijkh(x)=cijkh,

7、(1)εclassicalsenseformulation∂∂uεεk−cijkh(x)=fivΩ,∂xj∂xh(2)εu(x)=0na∂Ω.FrantiˇsekSEIFRTHomogenizationmethodforelasticmaterialsIntroductionDescriptionofthegeometryProblemsettingImplementation&ResultsBandgapsConclusionAcknowledgementStateequationsWeakformul

8、ationFinduε∈H1(Ω)suchthatZ0Zεε1(3)cmnklekl(u)emn(Φ)=f·Φ∀Φ∈H0(Ω).ΩΩCauchytensor1∂vk∂vlekl(v)=+,(4)2∂xl∂xk11H0(Ω)istheSobolevspaceH(Ω)withcompactsupport.FrantiˇsekSEIFRTHomogeni