一种等效的三边形杆件单元
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摘要
基于有限元思想,根据三节点三角形单元与三角形平面杆件单元在受到同样荷载列向量的条件下位移等效原则,构造出一种更为简单适用的等效三角形杆件单元,使二维结构用一维单元进行分析.由于单元的推导不是根据微元体单元应力、应变等效,而是从节点位移等效的这一思路出发,使得本研究单元较以前的等效铰结桁架单元可以满足结构有限元划分单元时对矩形单元的要求.同时截面计算公式中包含了泊松比这一体现材料特性的参数,因而公式更加具有普遍意义.运用本研究方法对钢筋混凝土简支梁及悬臂梁进行计算分析,并将其计算结果与ANSYS计算结果进行比较.研究结果表明,本研究所推导的等效三边形杆件单元计算精度良好,计算结果可靠,可以满足工程应用需要.
Based on the finite element method,a new equivalent triangle element,which is according to the principle of equivalent displacement under the same load between bar element and shell unit with 3-node,is proposed in this paper.The two dimensional structures are analysed by using one-Dimension elements.Because the base theory is different with the principle of equivalent stress/strain between plane bar element(or space bar element)and micro unit,it is feasible to establish triangle element in analyzing plane stress problems by this new model.A concrete and RC simple beam and a RC cantilever beam models are analyzed with this method and ANSYS.The calculation results of both methods are consistent too.The results showed that the proposed method has good analytical precition and reliable results,which can be used in engineering.
Based on the finite element method,a new equivalent triangle element,which is according to the principle of equivalent displacement under the same load between bar element and shell unit with 3-node,is proposed in this paper.The two dimensional structures are analysed by using one-Dimension elements.Because the base theory is different with the principle of equivalent stress/strain between plane bar element(or space bar element)and micro unit,it is feasible to establish triangle element in analyzing plane stress problems by this new model.A concrete and RC simple beam and a RC cantilever beam models are analyzed with this method and ANSYS.The calculation results of both methods are consistent too.The results showed that the proposed method has good analytical precition and reliable results,which can be used in engineering.
引文
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[11]燕斯亮,韩松,张艳军,等.效桁架等参单元模型[J].四川建筑,2009,39(2):164-168.YAN Si-liang,HANG Song,ZHANG Yan-jun,et al.Isoparametric element model of equivalent truss[J].Sichuan Architecture,2009,39(2):164-168.
[12]吴方伯,韩松,尚守平,等.基于有限等参单元的等效平面桁架模型[J].建筑科学与工程学报,2008,25(3):108-114.WU Fang-bo,HAN Song,SHANG Shou-ping,et al.Equivalent plane truss model based on finite isoparametric element[J].Journal of Architecture and Civil Engineering,2008,25(3):108-114.
[13]吴方伯,丁先立,周绪红,等.采用等效平面桁架单元对钢筋混凝土结构进行非线性分析[J].建筑结构学报,2005,26(5):112-117.WU Fang-bo,DING Xian-li,ZHOU Xu-hong,et al.Study on the nonlinear analysis of reinforced concrete structures by equivalent plane truss element method[J].Journal of Building Structures,2005,26(5):112-117.
[14]易广智.框支框架结构受力性能及其转换结构形式改进的研究[D].长沙:湖南大学,2006.YI Guang-zhi.The behaviors of frame structures with transfer story[D].Changsha:Hunan University,2006.
[15]陈逵.有限平面桁架单元法的研究及应用[D].长沙:湖南大学,2005.CHEN Kui.Research on the finite plane truss element method and the application in engineering[D].Changsha:Hunan University,2005.
[2]陈锡栋,杨婕,赵晓栋,等.有限元法的发展现状及应用[J].中国制造业信息化,2010,39(11):6-12.CHEN Xi-dong,YANG Jie,ZHAO Xiao-dong,et al.The status and development of finite element method[J].Manufacture Information Engineering of China,2010,39(11):6-12.
[3]柳春光,刘殿魁.变分法在结构抗震验算中的应用[J].地震工程与工程震动,2002,3(10):12-18.LIU Chun-guang,LIU Dian-kui.Application of variation principles in structural seismic check analysis[J].Earthquake Engineering and Engineering Vibration,2002,3(10):12-18.
[4]龙驭球.有限元法概论[M].北京:人民教育出版社,1978.LONG Yu-qiu.Introduction to finite element method[M].Beijing:People’s Education Press,1978.
[5]沈蒲生.结构分析的计算机方法[M].长沙:湖南科学技术出版社,1993.SHEN Pu-sheng.Computer method of architecture analysis[M].Changsha:Hunan Science and Technology Press,1993.
[6]李录贤,刘书静,张慧华,等.广义有限元方法研究进展[J].应用力学学报,2009,26(1):96-108.LI Lu-xian,LIU Shu-jing,ZHANG Hui-hua,et al.Researching progress of generalized finite element method[J].Chinese Journal of Applied Mechanics,2009,26(1):96-108.
[7]张艳军.有限元法在力学中的数值分析[J].机械管理开发,2010,25(1):197-198.ZHANG Yan-jun.Numerical analysis in mechanics based on finite element method[J].Mechanical Management and Development,2010,25(1):197-198.
[8]邓继华,邵旭东,蔡松柏,等.大转动三角形平面单元有限元分析的共旋坐标法[J].长沙理工大学学报:自然科学版,2010,7(4):32-36.DENG Ji-hua,SHAO Xu-dong,CAI Song-bai,et al.Co-rotational procedure for finite element analysis of trianaular plane element of large rotaion[J].Journal of Changsha University of Science and Technology:Natural Science,2010,7(4):32-36.
[9]徐芝纶.弹性力学[M].北京:高等教育出版社,1990.XU Zhi-lun.Theory of elasticity[M].Beijing:Higher Education Press,1990.
[10]吴方伯,陈坚强,尚守平.等效铰结桁架单元[J].工程力学,2005,22(2):84-88.WU Fang-bo,CHEN Jian-qiang,SHANG Shouping.Equivalent truss elements for plane and space problems[J].Engineering Mechanics,2005,22(2):84-88.
[11]燕斯亮,韩松,张艳军,等.效桁架等参单元模型[J].四川建筑,2009,39(2):164-168.YAN Si-liang,HANG Song,ZHANG Yan-jun,et al.Isoparametric element model of equivalent truss[J].Sichuan Architecture,2009,39(2):164-168.
[12]吴方伯,韩松,尚守平,等.基于有限等参单元的等效平面桁架模型[J].建筑科学与工程学报,2008,25(3):108-114.WU Fang-bo,HAN Song,SHANG Shou-ping,et al.Equivalent plane truss model based on finite isoparametric element[J].Journal of Architecture and Civil Engineering,2008,25(3):108-114.
[13]吴方伯,丁先立,周绪红,等.采用等效平面桁架单元对钢筋混凝土结构进行非线性分析[J].建筑结构学报,2005,26(5):112-117.WU Fang-bo,DING Xian-li,ZHOU Xu-hong,et al.Study on the nonlinear analysis of reinforced concrete structures by equivalent plane truss element method[J].Journal of Building Structures,2005,26(5):112-117.
[14]易广智.框支框架结构受力性能及其转换结构形式改进的研究[D].长沙:湖南大学,2006.YI Guang-zhi.The behaviors of frame structures with transfer story[D].Changsha:Hunan University,2006.
[15]陈逵.有限平面桁架单元法的研究及应用[D].长沙:湖南大学,2005.CHEN Kui.Research on the finite plane truss element method and the application in engineering[D].Changsha:Hunan University,2005.
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