基于力插值的非线性梁柱单元中固定端部求积节点的积分方法
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摘要
构件进入非线性时,塑性区域一般出现在构件的端部,然而目前有限元软件常用的高斯-勒让德积分方法在端部没有求积节点,这将直接影响数值模拟的精度。该文提出在基于力插值的非线性梁柱单元中使用固定端部求积节点的积分方法,并通过OpenSees进行二次开发实现了该方法。实例分析表明,相同的积分点个数,固定一端求积节点的高斯-拉道积分方法和固定两端求积节点的高斯-洛巴托积分方法具有较高的精度,而固定两端求积节点的牛顿-科茨积分方法精度稍低,但均明显优于高斯-勒让德积分方法。建议在非线性分析中采用高斯-拉道积分方法或者高斯-洛巴托积分方法。
The plastic hinge area generally appears at the ends because of the nonlinear material response of beam–column members,but there is no integration point fixed at the end of the element for Gauss-Legendre Integration that is commonly used in FE programs.So an integration method for the fixed integration point at the ends of the element is proposed and developed based on OpenSees.The study case shows that the result of Gauss-Radau integration(it places an integration point at only one end of the element) and Gauss-Lobatto integration(it places an integration point at each end of the element) is better than the result of Newton-Cotes integration(it also places an integration point at each end of the element),but they all perform better than the result of Gauss-Legendre integration.It is suggested to use Gauss-Radau integration or Gauss-Lobatto integration in the nonlinear analysis.
The plastic hinge area generally appears at the ends because of the nonlinear material response of beam–column members,but there is no integration point fixed at the end of the element for Gauss-Legendre Integration that is commonly used in FE programs.So an integration method for the fixed integration point at the ends of the element is proposed and developed based on OpenSees.The study case shows that the result of Gauss-Radau integration(it places an integration point at only one end of the element) and Gauss-Lobatto integration(it places an integration point at each end of the element) is better than the result of Newton-Cotes integration(it also places an integration point at each end of the element),but they all perform better than the result of Gauss-Legendre integration.It is suggested to use Gauss-Radau integration or Gauss-Lobatto integration in the nonlinear analysis.
引文
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[3]Silvia Mazzoni,Frank McKenna,Michael H.Scott and Gregory L.Fenves.OpenSees Users Manual[R].PEER,University of California,Berkeley,2004.
[4]Spacone E,Ciampi V.,Filippou F C.Mixed formulation of nonlinear beam finite element[J].Computers and Structures,1996,58:71―83.
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[11]Amer M Elsouri,Mohamed H Harajli.Seismic repair and strengthening of lap splices in RC columns:carbon fiber–reinforced polymer versus steel confinement[J].Journal of Composites for Construction,2011,15(5):721―729.
[12]禚一,李忠献.钢筋混凝土纤维梁柱单元实用模拟平台[J].工程力学,2011,28(4):102―108.Zhuo Yi,Li Zhongxian.A practical simulation platform of reinforced concrete fiber beam-column element[J].Engineering Mechanics,2011,28(4):102―108.(in Chinese)
[13]Angelo Caratelli,Alberto Meda,Zila Rinaldi,et al.Structural behaviour of precast tunnel segments in fiber reinforced concrete[J].Tunnelling and Underground Space Technology,2011,26(2):284―291.
[14]Rose B,Shing B,Spacone E,Willam K.A reinforced concrete model for analyzing flexural and shear behavior of R/C beam-columns[J].American Society of Civil Engineers,2001:158―174.
[2]杜轲.常用三维结构弹塑性分析软件的应用与比较[D].哈尔滨:中国地震局工程力学研究所,2010.Du Ke.The application and compare of three dimensional structure elastoplastic analysis softwares in common use[D].Harbin:Institute of Engineering Mechanics,2010.(in Chinese)
[3]Silvia Mazzoni,Frank McKenna,Michael H.Scott and Gregory L.Fenves.OpenSees Users Manual[R].PEER,University of California,Berkeley,2004.
[4]Spacone E,Ciampi V.,Filippou F C.Mixed formulation of nonlinear beam finite element[J].Computers and Structures,1996,58:71―83.
[5]Scott M H,Hamutcuoglu O M.Numerically consistent regularization of force-based frame elements[J].International Journal for Numerical Methods in Engineering,2008,76(10):1612―1631.
[6]《现代应用数学手册》编委会.现代应用数学手册:计算与数值分析卷[M].北京:清华大学出版社,2005:285―296.Editorial board of“Modern Applied Mathematics Manual”.Modern Applied Mathematics Manual[M].Beijing:Tsinghua University Press,2005:285―296.(in Chinese)
[7]Abramowitz M,Stegun C A.Handbook of mathematical functions with formulas,graphs,and mathematical tables[M].9th ed,Dover,New York,NY,1972:355―375.
[8]Mo Y L,Wang S J.Seismic behavior of RC columns with various tie configurations[J].Journal of Structural Engineering,ASCE,2000,126:1122―1130.
[9]Camata G,Spacone E,Zarnic R.Experimental and nonlinear finite element studies of RC beams strengthened with FRP plates[J].Composites,2007,1(2):277―288.
[10]Limkatanyu S,Spacone.Frame element with lateral deformable supports:formulations and numerical validations[J].Computers and Structures,2006,8(4):942―954.
[11]Amer M Elsouri,Mohamed H Harajli.Seismic repair and strengthening of lap splices in RC columns:carbon fiber–reinforced polymer versus steel confinement[J].Journal of Composites for Construction,2011,15(5):721―729.
[12]禚一,李忠献.钢筋混凝土纤维梁柱单元实用模拟平台[J].工程力学,2011,28(4):102―108.Zhuo Yi,Li Zhongxian.A practical simulation platform of reinforced concrete fiber beam-column element[J].Engineering Mechanics,2011,28(4):102―108.(in Chinese)
[13]Angelo Caratelli,Alberto Meda,Zila Rinaldi,et al.Structural behaviour of precast tunnel segments in fiber reinforced concrete[J].Tunnelling and Underground Space Technology,2011,26(2):284―291.
[14]Rose B,Shing B,Spacone E,Willam K.A reinforced concrete model for analyzing flexural and shear behavior of R/C beam-columns[J].American Society of Civil Engineers,2001:158―174.
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