线性分布基床系数弹性地基梁有限单元法改进

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1、第35卷第10期岩土力学Vol.35No.102014年10月RockandSoilMechanicsOct.2014文章编号：1000－7598(2014)10－3027－08线性分布基床系数弹性地基梁有限单元法改进冯又全，杨敏，陈俊岭（同济大学土木工程学院，上海200092）摘要：弹性地基梁法常用于研究土和结构的相互作用，对于均布荷载和边界条件简单的弹地基梁，采用理论解即可方便地进行计算。侧向荷载作用下桩体、嵌入式挡墙一般根据弹性地基梁理论进行分析，并假定基床系数随深度增加。对于基床系数呈线性分布或呈均匀分布但边界条件复杂的弹性地基梁理论求解困难，通常采用有限差分法

2、或有限单元法近似求解。采用有限单元法计算线性分布基床系数弹性地基梁时，若单元划分数量不够，就存在计算精度不足的问题。采用加权余量法推导了更为精确的2节点5次位移函数和相应的单刚矩阵，得出了线性分布荷载作用下挠度的5次多项式近似解，从而实现只需划分很少的单元数，节点位移及单元内位移的分布即可达到较高的计算精度，极大地提高了计算效率，单元内力的分布可直接由位移函数导出，简化了后处理计算程序。关键词：弹性地基梁；线性分布；基床系数；有限单元法；单刚矩阵；位移函数中图分类号：TU470文献标识码：AImprovementoffiniteelementmethodforbeamo

3、nelasticfoundationwithlinearlydistributedcoefficientofsubgradereactionFENGYou-quan，YANGMin，CHENJun-ling（CollegeofCivilEngineering,TongjiUniversity,Shanghai200092,China）Abstract:Theelasticfoundationbeammethodisusuallyusedtoanalyzethesoil-structureinteraction.Forelasticfoundationbeamsunder

4、uniformloadsandsimpleboundaryconditions,theirtheoreticalsolutionscanbeobtainedfromthepreviousresearch.Pilesunderlateralloadsandembeddedretainingwallsaregenerallyanalyzedaccordingtothetheoryofbeamonelasticfoundationandtheircoefficientsofsubgradereactionareassumedtoincreasewiththeincreaseo

5、fthedepth.Forelasticfoundationbeamswithlinearlydistributedcoefficientofsubgradereactionorwithuniformcoefficientofsubgradereactionbutcomplexboundaryconditions,itisdifficulttoobtaintheirtheorysolutions.Inthiscase,finitedifferencemethodorfiniteelementmethodisusedtoobtaintheirapproximatesolu

6、tion.Whenthebeamonelasticfoundationwithlinearlydistributedcoefficientofsubgradereactionisanalyzedbyfiniteelementmethod,thecalculationaccuracyisnotidealifthenumberofelementsarenotenough.A5timespolynomialdisplacementfunctionandcorrespondingstiffnessmatrixofbeamelementwith2nodesarepresented

7、byadoptingweightedresidualmethod.Anapproximatesolutionofthedeflectionofbeamsunderlineardistributionoftheforceisexpressedwithquinticpolynomial.Andthenmoreprecisenodaldisplacementsandthedistributionofelementdisplacementsareachievedbythefewerelements.Therefore,thecomputation