toris,xyyxS()andtheelasticitymatrisisdefinedbyvvvEC()whereEismodulusofelasticityandvisthePoisson’sratio...MeshGenerationandRefinementUnstructuredmeshgenerationprocedureconsistsofsomebasicsteps.Thesearethegenerationsofboundaryandinteriornodesandconnectionofthesenodeswhichhasaspecificnameastriangulationfortriangularfiniteelements.Inthiswork,arandompointgenerationshescanbeconstructedassimple-timesavingroutines,regardingcomplicateddomainswithcomplexboundaries,itisaproblemtofittheboundaryshape.Tocircumventthisdifficulty,unstructuredmeshesareusedtodiscretizethecomplicateddomainswithinternalboundaries(Figure-b).Whileitisatimeconsumingprocedure,unstructuredmeshesarealsosuitableforlocalmeshrefinementandcoarsening.Theaimofthisworkistogetagoodqualityunstructuredmeshwhichwillhavesmallerelementsatthegeometricdiscontinuitiesandbiggerelementsatotherregionsforashearwallframegeometry.Figure.Structured(a)andunstructuredmesh(b).TRIANGULARFINITEELEMENTS..ElementFormulationThefirstadvantageofusingtriangularelementsisthatalmostanyplanegeometrymaybediscretizedusingtriangles.Theseelementshavesixdegreesoffreedom,twotranslationsateachnode(Figure).Becauseofthethreenodes,theelementhaslinearshapefunctionsthatareanadditionalbenefitbecauseofsimplifiedmathematics.However,thesefunctionsgenerateconstantstrainandstressthroughouttheelement.Tosurmountthisdisadvantage,smallerelementsmustbeemployedwherestrainandstressvaryrapidly.Figure.ConstantstraintriangularfiniteelementCSTelementhasdisplacementfunctionsandshapefunctionsasfollows,,,vNvNvNyxvuNuNuNyxu()yxxxyyyxyxAyxNe,()yxxxyyyxyxAyxNe,()yxxxyyyxyxAyxNe,()whereu,uandunodaldisplacementsinxdirectioncorrespondingtonodes,andrespectively.v,vandvnodaldisplacementsinydirectionandN,NandNarelinearshapefunctions.xandyarethecoordinatesofcorrespondingnodesandeAisareaoftheelement.Inthefiniteelementmethod,nodaldisplacementsareobtainedfromthesolutionofthelinearsystemofequations,thatisfKu()where,Kisstiffnessmatrix,uisnodaldisplacementvector,andfisnodalloadvector.StiffnessmatrixmaybecalculatedasSNCSNtAKTe()wheretisthicknessoftheelement,NNNNNNN()anddifferentialoperatoris,xyyxS()andtheelasticitymatrisisdefinedbyvvvEC()whereEismodulusofelasticityandvisthePoisson’sratio...MeshGenerationandRefinementUnstructuredmeshgenerationprocedureconsistsofsomebasicsteps.Thesearethegenerationsofboundaryandinteriornodesandconnectionofthesenodeswhichhasaspecificnameastriangulationfortriangularfiniteelements.Inthiswork,arandompointgeneration分数划分,内部节点在根据指定间距参数划分水平线上生成[]。在三角法步骤中,不同作者提出了许多运算法则,包括简单自动三角法[,],前沿法[,],区域分解法[,]和坐标变换法[]。在现今研究中,问题区域内三角单元是通过Delaunay或空圆法则来得到[-]。根据这个法则,一个三角形外接圆中不能有任何节点,如图。圆区域内节点被从头到尾检查,以获得三个服从空圆法则候选节点。这种法则可以有效排除单元间边界交叉检查。图服从空圆法则三角化(a)和不服从空圆法则三角化最初我们不知道要对有限单元划分多大才能获得所需精度应力分布。因此,对少数初始节点三角化,在像剪力墙内开洞这样几何不连续处周围和剪力墙框架连接点上,就必须插入新节点,重复三角化程序来进行局部网格细化。在这一步骤中,当需要细化时,可以在众多运算法则中采用一种来得到精细网格,这些法则如下。.单节点网格细化.线性或多边形网格细化.中央节点网格细化.Delaunay节点网格细化在有限元分析方法中,所有生成节点和单元都用数字专门编号。当已知一个节点编号时,就很容易查到节点周围单元号。以上述第一种法则为例,一旦这些单元确定下来,它们就形成第一种三角单元,在第一种三角单元附近是第二种三角单元。根据单节点网格细化法则,在第一种三角单元中生成个新三角形单元,在第二种三角单元中生成个新三角形单元,如图-a和-b。线性和多边形局部网格细化法则也是如此,不同于第一中法则是它选择节点以形成直线或封闭多边形。在第三种细化法则中,在一个三角形几何中心处添加一个节点。Delaunay节点网格细化法则中,在一个选择三角形外接圆中心处添加一个节点。图第一种三角单元(a),第二种三角单元(b)和细化后三角单元(c)●代表选择细化点为了改进三角化后三角单元性质,可以采用一种网格滤波程序。在力学所有分支中,三角单元形状是有限单元法中一个重要因素,特别是在固体力学中,近似等边三角形被认为是很好一个形状[];在计算流体动力学问题时,关系到边界层及其震动,薄长三角形单元可以提供更好解答[]。为了获得较好性质三角形单元,我们使用了拉普拉斯算子滤波法,这种方法利用周围三角形来进行节点重新配置,如图所示。通过迭代法使节点移至与其连接节点形状质心[],通常一次或两次迭代就可足够,但迭代也可继续直到每次节点移动都满足一个收敛距离。图节点移动前(a),周围节点(b),节点移动后(c)新节点坐标由下式确定。uyxyx,,()niiunu(),yyxxuiii()式中,n代表周围节点个数,下标代表初始位置。.剪力墙框架问题为完成一个有限元分析,我们考虑了一个和梁柱连接带有开窗剪力墙模型,用非结构网格法进行网格生成和细化。该剪力墙框架结构在顶部加载,但荷载被分配给框架顶部几个节点上,所需几何尺寸如图-a。边界节点由直接法生成,以柱宽度作为间距参数,少数初始节点采用随机程序生成,如图-b。采用线性网格细化法则来对梁和柱处网格细化;采用单节点网格细化法则来对开窗、梁和剪力墙连接处尖角部位进行网格细化,得到最终网格如图。用最终网格计算出变形形状和应力分布如图。图剪力墙尺寸和荷载(a)和初始节点生成(b)图细化后有限元网格图有限元分析后图表结果.结论为了得到梁和柱、梁和剪力墙连接处应力分布精确解,我们用Matlab软件编了一个有限元程序。由于内部开洞存在,这个问题区域几何形状非常复杂,尽管如此,该结构还是用非结构有限元网格细化方法进行了离散。)在集合不连续区域,采用了小三角单元对有限元网格进行了细化,在小三角形和大三角形处采用了平滑过渡,采用了空圆法则和拉普拉斯滤波法,获得了较好性质等边三角形单元。)Ansys结果和实际横向位移和剪应力大致吻合,表和表列出了在荷载P=N下横向位移和剪应力结果比较。表.开洞剪力墙侧移计算结果位置Ux方向侧移(m)Ux方向侧移(m)误差()mN...mN...mN:节点在m高度mN:节点在m高度表.图所示节点剪应力xy位置剪应力(Pa)剪应力(Pa)误差()P...P...P...P...)本文介绍运算法则属于半自动法,也有一种自动网格生成法可适用于任意内部开洞区域,不过在区域网格细化时需要一本结果手册。)实际上,本文工作为我们提供了一个更深发展跳板来得到一个适合剪力墙框架结构计算有限元程序。shescanbeconstructedassimple-timesavingroutinesregardingcomplicateddomainswithcomplexboundaries,itisaproblemtofittheboundaryshape.Tocircumventthisdifficulty,unstructuredmeshesareusedtodiscretizethecomplicateddomainswithinternalboundaries(Figure-b).Whileitisatimeconsumingprocedure,unstructuredmeshesarealsosuitableforlocalmeshrefinementandcoarsening.Theaimofthisworkistogetagoodqualityunstructuredme附录英文原文及翻译StressDistributionInaShearWall–FrameStructureUsingUnstructured–RefinedFiniteElementMeshABSTRACTAsemi-automaticalgorithmforfiniteelementanalysisispresentedtoobtainthestressandstraindistributioninshearwall-framestructures.Inthestudy,aconstantstraintrianglewithsixdegreesoffreedomandmeshrefinement-coarseningalgorithmswereusedinMatlabenvironment.Initiallytheproposedalgorithmgeneratesacoarsemeshautomaticallyforthewholedomainandtheuserrefinesthisfiniteelementmeshatrequiredregions.Theseregionsaremostlytheregionsofgeometricdiscontinuities.Deformation,normalandshearstressesarepresentedforanillustrativeexample.Consistentdisplacementandstressresultshavebeenobtainedfromcomparisonswithwidelyusedengineeringsoftware.KeyWords:Shearwall,FEM,Unstructuredmesh,Refinement..INTRODUCTIONInthelasttwodecades,shearwallsbecameanimportantpartofourmidandhighriseresidentialbuildingsinTurkey.Aspartofanearthquakeresistantbuildingdesign,thesewallsareplacedinbuildingplansreducinglateraldisplacementsunderearthquakeloadssoshear-wallframestructuresareobtained.Sincethe’sseveralapproacheshavebeenadoptedtosolvedisplacementsandstressdistributionofshearwallstructures.Continuousmediumapproaches,andframeanalogymodelsaretheexamplesoftheseapproaches[-].Inthepastandtoday,numericalsolutionmethodsarethemaineffortareabecauseoftheaccuracyofsolutionandtheeaseofusageinDandDanalysisofshearwalls[-].Shearwallswithopenings,coupledshearwallsandcombinedshearwallframestructurescanbemodeledasthinplateswheretheloadingisuniformlydistributedoverthethickness,intheplaneoftheplate.ThisDdomaincanbesubdividedintoafinitenumberofgeometricalshapes.Inthefiniteelementmethod(FEM),thesesimpleshapedelementssuchastrianglesorquadrilaterals(inD)arecalledelements.Theconnectionoftheseindividualelementsatnodesandalonginterelementboundariescoveringthewholeproblemdomainiscalledfiniteelementmeshorgrid.Intheliteraturemeshescanbegroupedintotwomaincategoriessuchasstructuredandunstructuredmeshes.Structuredmeshesareconstructedwithgeometricallysimilartriangularorquadrilateralelements.Theyaresuitableespeciallyforproblemswithsimplegeometryandboundaryshapes(Figure-a).Althoughstructuredmeshescanbeconstructedassimple-timesavingroutines,regardingcomplicateddomainswithcomplexboundaries,itisaproblemtofittheboundaryshape.Tocircumventthisdifficulty,unstructuredmeshesareusedtodiscretizethecomplicateddomainswithinternalboundaries(Figure-b).Whileitisatimeconsumingprocedure,unstructuredmeshesarealsosuitableforlocalmeshrefinementandcoarsening.Theaimofthisworkistogetagoodqualityunstructuredmeshwhichwillhavesmallerelementsatthegeometricdiscontinuitiesandbiggerelementsatotherregionsforashearwallframegeometry.Figure.Structured(a)andunstructuredmesh(b).TRIANGULARFINITEELEMENTS..ElementFormulationThefirstadvantageofusingtriangularelementsisthatalmostanyplanegeometrymaybediscretizedusingtriangles.Theseelementshavesixdegreesoffreedom,twotranslationsateachnode(Figure).Becauseofthethreenodes,theelementhaslinearshapefunctionsthatareanadditionalbenefitbecauseofsimplifiedmathematics.However,thesefunctionsgenerateconstantstrainandstressthroughouttheelement.Tosurmountthisdisadvantage,smallerelementsmustbeemployedwherestrainandstressvaryrapidly.Figure.ConstantstraintriangularfiniteelementCSTelementhasdisplacementfunctionsandshapefunctionsasfollows,,,vNvNvNyxvuNuNuNyxu()yxxxyyyxyxAyxNe,()yxxxyyyxyxAyxNe,()yxxxyyyxyxAyxNe,()whereu,uandunodaldisplacementsinxdirectioncorrespondingtonodes,andrespectively.v,vandvnodaldisplacementsinydirectionandN,NandNarelinearshapefunctions.xandyarethecoordinatesofcorrespondingnodesandeAisareaoftheelement.Inthefiniteelementmethod,nodaldisplacementsareobtainedfromth 附录英文原文及翻译StressDistributionInaShearWall–FrameStructureUsingUnstructured–RefinedFiniteElementMeshABSTRACTAsemi-automaticalgorithmforfiniteelementanalysisispresentedtoobtainthestressandstraindistributioninshearwall-framestructures.Inthestudy,aconstantstraintrianglewithsixdegreesoffreedomandmeshrefinement-coarseningalgorithmswereusedinMatlab®enviro