基于修正斜压场理论的钢筋混凝土板、墙非线性有限元全过程分析
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摘要
开裂钢筋混凝土非线性有限元分析已经发展了近40年,取得了不少的成就,但如何准确地模拟混凝土峰值后的反应;如何合理地建立起混凝土在多向受压下对强度增强的模型,如何恰当地利用这些模型采用稳定快速的有限元方法求解这些构件的反应一直是国内外研究者们热衷于解决的课题。特别是在反复加、卸载过程中混凝土和钢筋的应力-应变关系的研究,以及在反复循环荷载过程中单元历史状态的存储更是学者所关注的焦点。
本人在本工作组前面的基础上,基于修正压场理论(Modified Compression Field Theory)的旋转、弥散裂缝模型在FEAPpv平台上编制了钢筋混凝土二维非线性有限元分析程序FEAP程序,主要进行了以下工作:
①在FEAP程序中采用位移控制法模拟钢筋混凝土构件峰值后的反应;
②对比了VT2程序中考虑约束和膨胀的方法,在FEAP程序中采用Mander模型考虑平面外约束钢筋对混凝土强度的增强;
③采用莫尔圆的方法来继承反复循环荷载下单元的历史状态;
④采用FEAP程序对在单调加载下或反复循环加载下大量的板和剪力墙的受力性能进行了模拟分析。
通过本文完成的工作,取得了如下进展:
①模拟了构件峰值后的反应,能更真实地反映开裂混凝土构件的全过程受力性能;
②考虑了平面外约束钢筋对混凝土强度的增强,能更准确地模拟二维开裂混凝土构件的性能反应;
③采用莫尔圆的方法来继承反复循环荷载下单元的历史状态,能够很好的模拟二维开裂混凝土构件在反复循环荷载下的性能反应。
The nonlinear finite element analysis of cracked reinforced concrete has being developed for about 40 years and great success has been achieved. But up to now, three major problems still exist: how to simulate the post-peak response of concrete, how to formulate a rational model of the effect of confinement due to triaxial stress states, and how to utilize these models to get the response of the components and structures with a numerically sound algorithm. These problems have drawn the attention of researchers worldwide. In modeling materials under general loads, effects of unloading and reloading paths of both concrete and reinforcement under reversed cyclic loading and evolution of strains are of crucial importance.
On the basis of the work previously done in our group, the author developed the 2-D nonlinear finite element FEAP program on FEAPpv based on the rotating and smeared crack models proposed in the MCFT(Modified Compression Field Theory), the following work has been carried out in this paper:
1. The post-peak response of a structure was obtained by displacement-controlled loading method.
2. Mander model was implemented in FEAP program to account for confinement on concrete in the same way as that in VT2 .
3. Mohr’s circle was employed to track historical strains experienced during previous loadings.
4. RC panels and walls under monolithic and cyclic loading were analyzed using modified FEAPpv program to verifiy the above-mentioned modeling method.
The following achievements have been obtained:
1. Full-range response of a structure can be accurately simulated by the proposed concrete model using displacement-controlled loading method.
2. Consideration of the confinement on concrete after peak response can improve the accuracy of response of 2-D cracked reinforced concrete.
3. Mohr’s circle is effective to track historical strains, which can be used to simulate the response of RC panel and wall elements under reversed cyclic loading.
本人在本工作组前面的基础上,基于修正压场理论(Modified Compression Field Theory)的旋转、弥散裂缝模型在FEAPpv平台上编制了钢筋混凝土二维非线性有限元分析程序FEAP程序,主要进行了以下工作:
①在FEAP程序中采用位移控制法模拟钢筋混凝土构件峰值后的反应;
②对比了VT2程序中考虑约束和膨胀的方法,在FEAP程序中采用Mander模型考虑平面外约束钢筋对混凝土强度的增强;
③采用莫尔圆的方法来继承反复循环荷载下单元的历史状态;
④采用FEAP程序对在单调加载下或反复循环加载下大量的板和剪力墙的受力性能进行了模拟分析。
通过本文完成的工作,取得了如下进展:
①模拟了构件峰值后的反应,能更真实地反映开裂混凝土构件的全过程受力性能;
②考虑了平面外约束钢筋对混凝土强度的增强,能更准确地模拟二维开裂混凝土构件的性能反应;
③采用莫尔圆的方法来继承反复循环荷载下单元的历史状态,能够很好的模拟二维开裂混凝土构件在反复循环荷载下的性能反应。
The nonlinear finite element analysis of cracked reinforced concrete has being developed for about 40 years and great success has been achieved. But up to now, three major problems still exist: how to simulate the post-peak response of concrete, how to formulate a rational model of the effect of confinement due to triaxial stress states, and how to utilize these models to get the response of the components and structures with a numerically sound algorithm. These problems have drawn the attention of researchers worldwide. In modeling materials under general loads, effects of unloading and reloading paths of both concrete and reinforcement under reversed cyclic loading and evolution of strains are of crucial importance.
On the basis of the work previously done in our group, the author developed the 2-D nonlinear finite element FEAP program on FEAPpv based on the rotating and smeared crack models proposed in the MCFT(Modified Compression Field Theory), the following work has been carried out in this paper:
1. The post-peak response of a structure was obtained by displacement-controlled loading method.
2. Mander model was implemented in FEAP program to account for confinement on concrete in the same way as that in VT2 .
3. Mohr’s circle was employed to track historical strains experienced during previous loadings.
4. RC panels and walls under monolithic and cyclic loading were analyzed using modified FEAPpv program to verifiy the above-mentioned modeling method.
The following achievements have been obtained:
1. Full-range response of a structure can be accurately simulated by the proposed concrete model using displacement-controlled loading method.
2. Consideration of the confinement on concrete after peak response can improve the accuracy of response of 2-D cracked reinforced concrete.
3. Mohr’s circle is effective to track historical strains, which can be used to simulate the response of RC panel and wall elements under reversed cyclic loading.
引文
[1] R. W. Clough, and Edward L. Wilson. Early Finite Element Research at Berkeley. The Fifth U.S. National Conference on Computational Mechanics, August 4-6, 1999: 1-35.
[2] W. F. Chen Plasticity in Reinforced Concrete.New York:McGraw-Hill. 1982..
[3] Esneyder Montoya. Modelling of Confined Concrete. Master of Applied Science. Thesis, Graduate Department of Civil Engineering, University of Toronto. 2000.
[4] D. C. Kent, and R. Park. Flexural Members With Confined Concrete. ASCE Journal of Structural Engineering, V.97, No.ST7, July 1971: 1969-1989.
[5] S. Razvi, and M. Saatcioglu. Confinement Modeling for High-Strength Concrete. ASCE Journal of Structural Engineering, V.125, No.3, March 1999: 281-289.
[6] S. A. Sheikh, and S. M. . Uzumeri. Strength and Ductility of Tied Concrete Columns. ASCE Journal of Structural Engineering, V.106, No.ST5, May 1980: 1079-1112.
[7] B. D. Scott, R. Park and M. J. N. Priestley. Stress-Strain Behavior of Concrete Confined by Overlapping Hoops at Low and High Strain Rates. ACI Structural Journal, V.79, No.1, January-February, 1982: 13-27.
[8] J. B. Mander, M. J. N. Priestley and R. Park. Theoretical Stress-Strain Model for Confined Concrete. ASCE Journal of Structural Engineering, V.114, No.8, August 1988: 1804-1826.
[9] D. Cusson and P. Paultre. Stress-Strain Model for Confined High-Strengh Concrete. ASCE Journal of Structural Engineering, V.121, No.3, March 1995: 468-477.
[10] J. Liu and S. J. Foster. Finite-Element Model for Confined Concrete Column. ASCE Journal of Structural Engineering, V.124, No.9, September 1998: 1011-1017.
[11] J. Xie, J. G. MacGregor and A. E. Elwi. Numerical Inverstigation of Eccentrically Load High-Strength Concrete Tied Columns. ACI Structural Journal, V.93, No.4, July-August, 1996: 449-461.
[12] A. I. Karabinis and P. D. Kiousis. Effects of Confinement on Concrete Columns:Plasticity approach. ASCE Journal of Structural Engineering, V.120, No.9, September 1994: 2747-2767.
[13] B. Chen and S. T. Mau. Recalibration of a Plastic-Fractruing Model for Concrete Confinement. Cement and Concrete Research, V.19, 1989: 143-154.
[14] S. T. Mau , A. E. Elwi and S. Zhou.Analytical Study of Spacing of Lateral Steel and Column Confinement. ASCE Journal of Structural Engineering, V.124, No.3, March 1998: 262-269.
[15] F. Barzegar and S. Maddipudi.Three-Dimension Modeling of Concrete Structrues.Ⅰ:Plain Concrete. ASCE Journal of Structural Engineering, V.123, No.10, October 1997: 1347-1356.
[16] L. Bortoloti.Influence of Concrete Tensile Ductility on Compressive Strength of Confined Concrete. ASCE Journal of Materials, V.6, No.4, April 1994: 542-563.
[17] F.J. Vecchio. Finite Element Modeling of Concrete Expansion and Confinement. ASCE Journal of Structural Engineering, V.118, No.9, September 1992: 2390-2406.
[18] M. A. H. Abdel-Halim and T. M. Abu-Lebdeh. Analytical Study for Concrete Confinement in Tied Columns. ASCE Journal of Structural Engineering, V.115, No.11, Novernber 1989: 2810-2828.
[19] D. Palermo. Behaviour and Analysis of Reinforced Concrete Walls Subjected to Reversed Cyclic Loading. Doctoral Dissertation, Graduate Department of Civil Engineering, University of Toronto. 2002.
[20] F.J. Vecchio. Nonlinear Finite Element Analysis of Reinforced Concrete Membranes. ACI Structural Journal, V.86, No.1, January-February, 1989: 26-35.
[21] F.J. Vecchio. Reinforced Concrete Membrane Element Formulations. ASCE Journal of Structural Engineering, V.116, No.3, March 1990: 730-750.
[22] F.J. Vecchio. Towards Cyclic Load Modeling of Reinforced Concrete. ACI Structural Journal, V.96, No.2, March-April 1999: 132-202.
[23] F.J. Vecchio, and Michael P. Collins. The Modified Compression-Field Theory for Reinforced Concrete Element Subjected to shear. ACI Journal, Proceedings, V.83, No.2, March-April 1986: 219-231.
[24] J.C. Walraven. Fundamental Analysis of Aggregate Interloack. ASCE Journal of Structural Engineering, V.107, No.11, Novermber 1981: 2245-2270.
[25] 吴华. 基于扰动应力场的钢筋混凝土非线性有限元分析. 重庆大学硕士论文,2006.6.
[26] F.J. Vecchio, and Michael P. Collins. Compression Response of Cracked Reinforced Concrete. ASCE Journal of Structural Engineering, V.119, No.12, December, 1993: 3590-3610.
[27] 陈滔. 基于有限单元柔度法的钢筋混凝土框架三维非弹性地震反应分析. 重庆大学博士论文,2003.6.
[28] 朱伯龙, 董振祥. 钢筋混凝土非线性分析. 上海:同济大学出版社,1985.1.
[29] 来武清. 基于修正斜压场的钢筋混凝土二维非线性有限元分析. 重庆大学硕士论文,2005.6.
[30] Robert L. Taylor. A Finite Element Analysis Program Personal Version 2.0 User Manual. Jan 2005.
[31] O.C.Zienkiewicz and R.L. Taylor. The Finite Element Method, volumn 1. McGraw-Hill, Lodon, 5th edition, 2000
[32] O.C.Zienkiewicz and R.L. Taylor. The Finite Element Method, volumn 2. McGraw-Hill, Lodon,5th edition, 2000
[33] J.L. Batoz. and G. Dhatt Incremental Displacement Algorithms for Nonlinear Problems. Int. J. Numerical Methods Engineering, V.14, No.8, 1979: 1262-1267.
[34] 王志军. 考虑软化特性的预应力混凝土框架非线性有限元全过程分析. 重庆大学硕士论文,1991.1.
[35] 江见鲸, 陆新征, 叶列平. 混凝土结构有限元分析. 北京:清华大学出版社,2005.3.
[36] X.B. Pang, and T.T. C, Hsu. Behavior of Reinforced Concrete Membrane Elements in Shear. ACI Structural Journal, V.92, No. 6, November-December 1995: 665-679.
[37] F.J. Vecchio, Michael P. Collins, and J. Aspiotis. High-Strength Concrete Elements Subjected to Shear. ACI Structural Journal, V.91, No.4, June-August, 1994: 423-433.
[38] L.X. Zhang, and T.T.C. Hsu. Behavior and Analysis of 100 MPa Concrete Membrane Elements. ASCE Journal of Structural Engineering, V.124, No.1, 1998: 24-34.
[39] N. J. Stevens, S. M. Uzumeri, and M. P. Collins. Reinforced Concrete Subjected to Reversed Cyclic Shear-Experiments and Constitutive model. ACI Structural Journal, V.88, No.2, March-April 1991: 135-146.
[40] D. Lai. Crack Shear-Slip in Reinforced Concrete Elements. Master of Applied Science. Thesis, Graduate Department of Civil Engineering, University of Toronto. 2001.
[41] R.G. Oesterle et al. Earthquake-Resistant Structural Walls-Tests of Isolated Walls. Report to the National Science Foundation, Construction Technology Laboratories, Portland Cement Association, Skokie, Illinois, November 1976: 315.
[42] A.E. Fiorato, R.G. Oesterle, and W.G. Corley. Behavior of Earthquake Resistant Structural Walls Before and After Repair. ACI Structural Journal, V.91, No.4, September-October, 1983: 403-413.
[43] L.D. Lefas, and M.D. Kotsovos. Strength and Deformation Characteristics of Reinforced Concrete Structural Walls under Load Reversals. ACI Structural Journal, V.87, No.6, November- December 1990: 23-31.
[44] N.J. Stevens,S.M. Uzumeri,M.P. Collins and G.T. Will. Constitutive Model of Reinforced Concrete Finite Element Analysis. ACI Structural Journal, V.88, No.1, January- February 1991: 49-59
[2] W. F. Chen Plasticity in Reinforced Concrete.New York:McGraw-Hill. 1982..
[3] Esneyder Montoya. Modelling of Confined Concrete. Master of Applied Science. Thesis, Graduate Department of Civil Engineering, University of Toronto. 2000.
[4] D. C. Kent, and R. Park. Flexural Members With Confined Concrete. ASCE Journal of Structural Engineering, V.97, No.ST7, July 1971: 1969-1989.
[5] S. Razvi, and M. Saatcioglu. Confinement Modeling for High-Strength Concrete. ASCE Journal of Structural Engineering, V.125, No.3, March 1999: 281-289.
[6] S. A. Sheikh, and S. M. . Uzumeri. Strength and Ductility of Tied Concrete Columns. ASCE Journal of Structural Engineering, V.106, No.ST5, May 1980: 1079-1112.
[7] B. D. Scott, R. Park and M. J. N. Priestley. Stress-Strain Behavior of Concrete Confined by Overlapping Hoops at Low and High Strain Rates. ACI Structural Journal, V.79, No.1, January-February, 1982: 13-27.
[8] J. B. Mander, M. J. N. Priestley and R. Park. Theoretical Stress-Strain Model for Confined Concrete. ASCE Journal of Structural Engineering, V.114, No.8, August 1988: 1804-1826.
[9] D. Cusson and P. Paultre. Stress-Strain Model for Confined High-Strengh Concrete. ASCE Journal of Structural Engineering, V.121, No.3, March 1995: 468-477.
[10] J. Liu and S. J. Foster. Finite-Element Model for Confined Concrete Column. ASCE Journal of Structural Engineering, V.124, No.9, September 1998: 1011-1017.
[11] J. Xie, J. G. MacGregor and A. E. Elwi. Numerical Inverstigation of Eccentrically Load High-Strength Concrete Tied Columns. ACI Structural Journal, V.93, No.4, July-August, 1996: 449-461.
[12] A. I. Karabinis and P. D. Kiousis. Effects of Confinement on Concrete Columns:Plasticity approach. ASCE Journal of Structural Engineering, V.120, No.9, September 1994: 2747-2767.
[13] B. Chen and S. T. Mau. Recalibration of a Plastic-Fractruing Model for Concrete Confinement. Cement and Concrete Research, V.19, 1989: 143-154.
[14] S. T. Mau , A. E. Elwi and S. Zhou.Analytical Study of Spacing of Lateral Steel and Column Confinement. ASCE Journal of Structural Engineering, V.124, No.3, March 1998: 262-269.
[15] F. Barzegar and S. Maddipudi.Three-Dimension Modeling of Concrete Structrues.Ⅰ:Plain Concrete. ASCE Journal of Structural Engineering, V.123, No.10, October 1997: 1347-1356.
[16] L. Bortoloti.Influence of Concrete Tensile Ductility on Compressive Strength of Confined Concrete. ASCE Journal of Materials, V.6, No.4, April 1994: 542-563.
[17] F.J. Vecchio. Finite Element Modeling of Concrete Expansion and Confinement. ASCE Journal of Structural Engineering, V.118, No.9, September 1992: 2390-2406.
[18] M. A. H. Abdel-Halim and T. M. Abu-Lebdeh. Analytical Study for Concrete Confinement in Tied Columns. ASCE Journal of Structural Engineering, V.115, No.11, Novernber 1989: 2810-2828.
[19] D. Palermo. Behaviour and Analysis of Reinforced Concrete Walls Subjected to Reversed Cyclic Loading. Doctoral Dissertation, Graduate Department of Civil Engineering, University of Toronto. 2002.
[20] F.J. Vecchio. Nonlinear Finite Element Analysis of Reinforced Concrete Membranes. ACI Structural Journal, V.86, No.1, January-February, 1989: 26-35.
[21] F.J. Vecchio. Reinforced Concrete Membrane Element Formulations. ASCE Journal of Structural Engineering, V.116, No.3, March 1990: 730-750.
[22] F.J. Vecchio. Towards Cyclic Load Modeling of Reinforced Concrete. ACI Structural Journal, V.96, No.2, March-April 1999: 132-202.
[23] F.J. Vecchio, and Michael P. Collins. The Modified Compression-Field Theory for Reinforced Concrete Element Subjected to shear. ACI Journal, Proceedings, V.83, No.2, March-April 1986: 219-231.
[24] J.C. Walraven. Fundamental Analysis of Aggregate Interloack. ASCE Journal of Structural Engineering, V.107, No.11, Novermber 1981: 2245-2270.
[25] 吴华. 基于扰动应力场的钢筋混凝土非线性有限元分析. 重庆大学硕士论文,2006.6.
[26] F.J. Vecchio, and Michael P. Collins. Compression Response of Cracked Reinforced Concrete. ASCE Journal of Structural Engineering, V.119, No.12, December, 1993: 3590-3610.
[27] 陈滔. 基于有限单元柔度法的钢筋混凝土框架三维非弹性地震反应分析. 重庆大学博士论文,2003.6.
[28] 朱伯龙, 董振祥. 钢筋混凝土非线性分析. 上海:同济大学出版社,1985.1.
[29] 来武清. 基于修正斜压场的钢筋混凝土二维非线性有限元分析. 重庆大学硕士论文,2005.6.
[30] Robert L. Taylor. A Finite Element Analysis Program Personal Version 2.0 User Manual. Jan 2005.
[31] O.C.Zienkiewicz and R.L. Taylor. The Finite Element Method, volumn 1. McGraw-Hill, Lodon, 5th edition, 2000
[32] O.C.Zienkiewicz and R.L. Taylor. The Finite Element Method, volumn 2. McGraw-Hill, Lodon,5th edition, 2000
[33] J.L. Batoz. and G. Dhatt Incremental Displacement Algorithms for Nonlinear Problems. Int. J. Numerical Methods Engineering, V.14, No.8, 1979: 1262-1267.
[34] 王志军. 考虑软化特性的预应力混凝土框架非线性有限元全过程分析. 重庆大学硕士论文,1991.1.
[35] 江见鲸, 陆新征, 叶列平. 混凝土结构有限元分析. 北京:清华大学出版社,2005.3.
[36] X.B. Pang, and T.T. C, Hsu. Behavior of Reinforced Concrete Membrane Elements in Shear. ACI Structural Journal, V.92, No. 6, November-December 1995: 665-679.
[37] F.J. Vecchio, Michael P. Collins, and J. Aspiotis. High-Strength Concrete Elements Subjected to Shear. ACI Structural Journal, V.91, No.4, June-August, 1994: 423-433.
[38] L.X. Zhang, and T.T.C. Hsu. Behavior and Analysis of 100 MPa Concrete Membrane Elements. ASCE Journal of Structural Engineering, V.124, No.1, 1998: 24-34.
[39] N. J. Stevens, S. M. Uzumeri, and M. P. Collins. Reinforced Concrete Subjected to Reversed Cyclic Shear-Experiments and Constitutive model. ACI Structural Journal, V.88, No.2, March-April 1991: 135-146.
[40] D. Lai. Crack Shear-Slip in Reinforced Concrete Elements. Master of Applied Science. Thesis, Graduate Department of Civil Engineering, University of Toronto. 2001.
[41] R.G. Oesterle et al. Earthquake-Resistant Structural Walls-Tests of Isolated Walls. Report to the National Science Foundation, Construction Technology Laboratories, Portland Cement Association, Skokie, Illinois, November 1976: 315.
[42] A.E. Fiorato, R.G. Oesterle, and W.G. Corley. Behavior of Earthquake Resistant Structural Walls Before and After Repair. ACI Structural Journal, V.91, No.4, September-October, 1983: 403-413.
[43] L.D. Lefas, and M.D. Kotsovos. Strength and Deformation Characteristics of Reinforced Concrete Structural Walls under Load Reversals. ACI Structural Journal, V.87, No.6, November- December 1990: 23-31.
[44] N.J. Stevens,S.M. Uzumeri,M.P. Collins and G.T. Will. Constitutive Model of Reinforced Concrete Finite Element Analysis. ACI Structural Journal, V.88, No.1, January- February 1991: 49-59
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