曲 哲 | Me 曲 研 | Lab 教 学 | Teaching PQ-Fiber 阅 读 | Reading
PQ-Fiber
基于ABAQUS的用户自定义单轴滞回本构模型库
A collection of user-defined uniaxial hysteretic models for ABAQUS/Standard
PQ-Fiber是与清华大学土木工程系潘鹏教授合作开发的基于ABAQUS开发的一组材料单轴滞回本构模型的集合。它主要可用于: (1)在利用ABAQUS的纤维梁单元(如B21,B31等)模拟钢筋混凝土结构、钢结构等弹塑性响应时,定义钢、混凝土纤维的材料本构; (2)利用ABAQUS的杆单元(如T2D2等)定义具有特残滞回特性的非线性弹簧,如具有硬化特性的橡胶隔震支座、隔震层的边界约束等。
 
我根据自己的研究需要不断地对原程序进行更新与扩充,以使其适应不同分析工作的需要。为便于广大科研与工程设计人员利用ABAQUS进行建筑结构的非线性响应分析,将PQ-Fiber的Fortran源代码公布。 请使用者尊重知识产权。如有问题请通过以下邮箱与我联系:m.quzhe@gmail.com
 
 
PQ-Fiber is the output of a joint work with Prof Pan in Tsinghua University. It is a set of popular user-defined uniaxial hysteretic models for ABAQUS/Standard. It may find its primary applications in: (1) the fiber-based beam element in ABAQUS/Standard (e.g. B21, B31 etc.) to model the hysteretic behvaior of reinforced concrete or steel components. (2) the truss element in ABAQUS/Standard (e.g. T2D2 etc) to define uniaxial springs with special-purpose, such as the nonlinear rubber bearing.
 
The Fortran code is still being extended according to my personal research demands. I am glad to provide the source code here for the free use of all the researchers and engineers who are interested in the numerical simulation of building structures. There is no function limit in the published library but please note it is complied in a 32-bit environment. Please feel free to contact if you have any problem in using it or if you would like to report a bug: m.quzhe@gmail.com
下载
Download
PQ-Fiber_v1.9源代码及示例(单击右键“另存为”)
PQ-Fiber v1.9 source code and an example(right click and "save as...")
下载
Download
PQ-Fiber_v1.9使用手册
PQ-Fiber v1.9 User's Manual (pdf file in Chinese)
v1.9
2019.10
添加了Menegotto-Pinto模型以用于模拟屈曲约束支撑,并可通过为拉压设置不同的应变硬化系数近似模拟屈曲约束支撑的拉压不等强行为 [Qu et al 2017] | Add a Menegotto-Pinto Model with isotropic hardening and separate strain hardening ratios in tension and compression for the simulation of buckling restrained braces [Qu et al 2017]
v1.8
2016.5
公开源代码
Source code is made open
v1.8
2012.7
引入初始刚度比例型阻尼 | Introduce a stiffness-proportional damping
在Trilin模型中计算滞回耗能spd | Calculate hysteretic energy dissipation spd for the model of Trilin
v1.7
2011.12
添加了一个用于模拟混凝土深牛腿的简化模型UCorbel [Qu et al 2015] | Add a specific model for modeling deep RC corbels UCorbel [Qu et al 2015]
添加了一个用于模拟施加了预紧力的高强螺栓受拉行为的的折线型模型UBolt [Qu et al 2015] | Add a model for modeling pre-stressed high-strength bolts UBolt [Qu et al 2015]
v1.6
2011.6
添加了一个基于武田模型(Takeda, 1970)的用于钢筋混凝土构件的三线型滞回模型UTrilin | Add a new model UTRILIN based on the trilinear Takeda model (Takeda, 1970)
恢复了原始的最大点指向型双线性滞回模型,命名为USteel03 | Recover USteel03 which is simiply a bilinear peak-oriented model
v1.5
2011.1
添加了叠层橡胶隔震支座的具有硬化和耗能行为的水平恢复力模型ULRB [Qu et al 2013] | Add a new model ULRB to model the nonlinear behavior of laminated rubber bearing [Qu et al 2013]
添加了具有初始空隙的弹塑性模型UGap,可用于模拟隔震层周边的挡土墙 [Qu et al 2013] | Add a new model UGAP, which is a elastic-plastic spring with initial gaps [Qu et al 2013]
v1.4
2010.3
在USteel02的骨架曲线中引入下降段,当应变超过极限应变eu后按0.5Es的负刚度下降 | Add a descending branch in the skeleton curve of USteel02
改写了USteel02和UConcrete02中计算累积滞回耗能的部分 | Modify the calculation of cumulative energy dissipation in USteel02 and UConcrete02
v1.4
2009.5
重写了UConcrete02 | Rewrite UConcrete02
重写了USteel02 | Rewrite USteel02
为减少捏拢,USteel02在反向再加载时,先按卸载刚度加载至0.2Fmax,再指向Fmax | In reloading, USteel01 first goes to 0.2Fmax along the previous reloading stiffness before pointint to Fmax to reduce some pinching
在USteel02中引入了基于“有效累积滞回耗能”的承载力退化模型[曲哲, 叶列平 2013] | Employ the effective energy-based strength deterioration model [Qu and Ye 2011] in USteel02
v1.3
2007.12
最初公开发布版本,包括三种钢筋模型(随动硬化弹塑性模型USteel01,最大点指向型双线性模型USteel02,拉压不等强弹塑性模型USteel03)和两种混凝土模型(无抗拉强度的混凝土模型UConcrete01, 考虑抗拉强度的混凝土模型UConcrete02)| First public version including 3 steel models and 2 concrete models
1
钢筋混凝土压弯构件的静力往复加载试验

20世纪七八十年代,R. Park与其合作者对矩形截面钢筋混凝土构件的压弯行为做了系统的试验研究 (Ang et al, 1981; Soesianawati et al, 1986; Watson et al 1989; Tanaka et al, 1990)。 现以其中具有代表性的9个试验为基础,讨论PQ-Fiber中的USteel02和UConcrete02模型在模拟钢筋混凝土压弯构件力学行为方面的有效性和局限性。
 
USteel02和UConcrete02模型的参数按《用户手册》的建议取值。
 
首先以Ang et al (1981)的试件No.3和No.4,Tanaka et al (1990)的试件No.5和No.7以及Watson et al (1989)的试件No.5和No.8为例, 考察本文的数值模型对不同轴压比下钢筋混凝土压弯构件滞回行为的模拟效果。这6个试件的轴压比lambda_N的变化范围为0.1~0.7。
 
图1.1-图1.3比较了计算分析与试验得到的滞回曲线。对于轴压比相对较小的Ang et al (1981) 的试件No.3、No.4 以及Tanaka et al (1990) 的试件No.5、No.7,PQFiber能够比较准确的把握往复荷载作用下构件的受力行为。 这不仅表现为比较准确的受力骨架线,也表现为对构件在卸载、再加载过程中的刚度与承载力退化现象的准确模拟。 然而对于轴压比较大的Watson et al (1989) 的试件No.5、No.8,本文模型较多地低估了构件的压弯承载力(图3)。 这说明计算模型在模拟高轴压比钢筋混凝土压弯构件时还有一定的局限性。通过进一步考虑箍筋约束效应对混凝土本构的影响将有助于提高模拟的精度。
 
图1.1 分析结果与Ang et al (1981)试验结果的对比
 
图1.2 分析结果与Tanaka et al (1990)试验结果的对比
 
图1.3 分析结果与 Watson et al (1989) 试验结果的对比
 
即使对于发生弯曲破坏的钢筋混凝土构件,配箍太少也会对其滞回行为有所影响。 USteel02本文模型所考虑的钢筋强度的退化并非钢筋本身的劣化,而是综合反映了钢筋-混凝土界面粘结滑移和混凝土保护层剥落所引起的退化效果。 可以通过钢筋的强度退化间接地模拟箍筋对于构件承载力退化行为的影响。 在Soesianawati et al (1986)的试验中, No 2,No 3和No 4等3个试件基本相同,仅配箍特征值有较大差别。 3个试件的配箍特征值Lambda_v依次减小,分别为0.10、0.07和0.04。
 
图1.4为PQFiber的计算分析结果与这3个试件的滞回曲线试验结果的对比。 由图可见,随着配箍特征值的减小,试件在往复荷载作用下的承载力退化程度加大,这与试验结果的规律相一致。
 
图1.4 分析结果与 Soesianawati et al (1986) 试验结果的对比
 
以上几组试验在施加水平荷载时均采用位移幅值由小到大逐级递增的加载制度。 然而在地震作用下,结构构件的受力历程并非逐级递增,而是具有很大的不确定性。 下面以Takemura et al (1997)完成的一组6个试件的拟静力试验为基础,验证PQFiber对不同加载制度下钢筋混凝土压弯构件力学行为模拟的有效性。
 
Takemura et al (1997)试验的6个试件的尺寸与配筋完全相同,仅加载制度不同。 试验中采用了6种不同的加载制度,如图1.5所示,对应的构件分别编号为TP001~TP006。
 
图1.5 试验采用的加载制度(Takemura et al, 1997)
 
采用PQ-Fiber得到的结果与试验结果的比较如图1.6。 无论对于逐级递增还是逐级递减的加载制度,除TP005外,本文采用的数值模型均能比较准确地把握构件的滞回行为。
 
TP005与TP002均为逐级递增加载且每一级的增幅基本相同,区别仅在于TP002是两侧往复加载,而TP005仅在单侧往复加载。 单侧加载与双侧加载是否对构件的承载力退化行为有显著影响及其影响机理,尚需通过更多的试验研究进行验证。
 


图1.6 分析结果与Takemura et al (1997)试验结果的对比
 
2
足尺钢筋混凝土桥墩的振动台试验
Shaking table test of a full-scale reinforced concrete bridge pier
[Click for more]

模拟的对象是一个足尺的钢筋混凝土桥墩在一组6个地震动作用下的动力响应。 试验体和UC San Diego的室外振动台如图2.1所示。图2.2给出了试验体的主要尺寸和试验体中钢筋混凝土桥墩的配筋。
 
A full-scale reinforced concrete column was subjected to a series of uniaxial simulated earthquake ground motions on the NEES Large High-Performance Outdoor Shake Table at UCSD's Englekirk structural Engineering Center on Sep. 20-21, 2010.
 
The 7315mm ( 24' ) high circular column with a reinforced concrete basement is fixed on the 38' x 25' shaking table. The diameter of the column's cross section is 1219mm (4'). A mass block, composed of five reinforced concrete blocks tied together by pre-stressed steel bars, is installed on top of the column, as can been see in Figure 2.1. Dimensions of the shake table, the test specimen as well as the mass blocks are also provided in Figure 2.2. The diameter of the hole in the central block is 5' , which is 1' larger than that of the column's cross section. The total weight of the mass block is approximately 250 ton.
 
    
图2.1 试验全景与施工照片 [Source]
Figure 2.1. Overview of test setup and photo of specimen under construction
 
图2.2 试验体的尺寸和桥墩配筋
Figure 2.2. Specimen dimensions and pier reinforcement
 

用ABAQUS单元B21建立如图2.3所示的非常简单的有限元模型。桥墩划分为10个单元,基础假设为固结,顶部使用一个250ton的集中质量单元。
 
The circular concrete column is reinforced with 18 #11 deformed steel bars arranged along the perimeter of the cross section, as well as #5 double circular hoops with diameter of 3' 8” at a spacing of 6 inches through the height of the column. There is 2-inch clear cover from the hoops to the concrete surface, indicating an 84.6mm distance from the geometric center of each longitudinal bar to the concrete surface. Double hoop means that there are two butt-welded #5 hoops at each location.
 
A finite element model is established in ABAQUS/Standard 6.7-1 to estimate the seismic response of the above specimen. It uses a total of ten 2-node linear element in plain (B21 in ABAQUS), which is a Timoshenko beam element with reduced integration scheme. The mesh and node numbers are shown in Figure 2.3. As the bottom element is expected to represent by its own the global behavior of the “plastic hinge” at the column base, its size is considered sensitive. Larger bottom element will lead to higher lateral load capacity of the column and smaller will lead to lower capacity. The choice of the element size is tricky but according to the analysis experience, the length of the element is chosen equal to the diameter of the column ( 1219mm ). That's to say that the local responses (e.g. curvature, moment etc.) within this length are averaged to an identical value.
 
图2.3 有限元模型
Figure 2.3. Finite element model in ABAQUS
 

图2.4给出了分析得到的桥墩在一组6个地面运动作用下的位移响应时程。主要分析结果与试验结果的对比及其相对误差如图2.5-图2.6所示。本模型虽然较好的预测了试验体的最大位移和剪力响应,但竖向力和残余位移的预测精度仍然存在不足。 更多分析结果与试验结果的对比,以及其他参赛者的分析结果,请访问[竞赛主页]。
 
The size of the rest of elements is arbitrarily chosen to be 700mm with the exception of the top element, whose length is 496mm to make the overall height of the column to be 7315mm (24 feet).
 
Neither the basement nor the mass blocks on the top are explicitly modeled. The vertical and rotational degrees of freedom of Node 1, which is located at the column-to-basement interface, are restrained and the horizontal degree of freedom is subjected to the enforced acceleration time histories. The mass blocks on the top are modeled by a 250ton lumped mass element at Node 11, which is located at the column-to-central mass block interface, almost the same level as the centroid of the mass blocks.
 
Main results of the simulation are given below. Please refer to the [official website] of the contest for more detailed comparison between the simulation and the test results.
 
图2.4 位移时程分析结果
Figure 2.4. Displacement time history result
 
    
图2.5 主要峰值反应结果
Figure 2.5. Comparison of peak response results
 
图2.6 竖向加速度以及最大轴力
Figure 2.6. Vertical acceleration and maximum axial force
 
3
四层钢框架结构的振动台试验

通过模拟2007年9月在日本E-Defense进行的4层足尺钢框架结构振动台试验(吹田啓一郎 等,2008)检验PQFiber在模拟钢框架结构非线性地震响应方面的表现。 试验数据来自齋藤裕一郎 等(2008),山田哲 等(2008)以及島田侑子 等(2008)。
 
图3.1是该钢框架结构在振动台上准备试验前的照片和简化的有限元模型。建立有限元模型时做以下简化: (1) 忽略试验模型中ALC板外墙、轻质隔墙、铝合金楼梯等非结构构件对结构刚度和承载力的影响,而仅将其作为附加质量; (2) 试验模型中的压型钢板混凝土组合楼板按弹性楼板模拟并忽略次梁;(3) 假设柱底与地面刚性连接。
 
    
图3.1 试验模型和有限元模型
 
试验模型(不包括直接安装在振动台面上的防倒塌支架)和有限元模型的总质量分别为195.5吨和192.9吨,仅相差1.33%。 振动台试验采用日本Takenori地震动记录(鷹取波),同时输入两个水平方向和一个竖向的地震动记录,振幅逐级增大。 图3.2比较了试验过程中在振动台面上记录到的实际输出振动的速度反应谱与有限元分析中采用的地震动记录的速度反应谱,二者相差不大。
 
    
    
图3.2 台面运动反应谱与有限元分析输入地震动反应谱比较
 
计算模型中,结构阻尼采用经典的Rayleigh阻尼,阻尼比为2%。分析中考虑几何非线性的影响。 由分析结果与试验结果的比较可见,无论是结构整体(图3.3)还是构件局部(图3.4),本文分析模型均能比较准确的模拟其地震响应。
 
    
图3.3 试验与计算得到的最大层间位移角
 
    
图3.4 试验与计算得到的底层柱脚的滞回曲线
 
4
三层钢框架结构的振动台试验

Lu et al (2008)通过1:2缩尺模型的振动台试验,检验了一种阻尼墙对结构的减震效果。 下面通过模拟试验中用于对比的纯框架模型在El Centro-NS地震记录输入下的响应,检验PQFiber在模拟钢筋混凝土框架结构地震响应方面的表现。
 
图4.1为安装了阻尼墙结构模型的照片(Lu et al, 2008)及其有限元模型。这里模拟的是未安装阻尼墙的纯框架模型。 模型通过混凝土梁的翼缘考虑现浇混凝土楼板的面外刚度和承载力贡献,通过具有适当刚度的水平弹性斜撑模拟楼板的面内刚度。 混凝土梁的翼缘宽度取值参考我国混凝土规范的建议,对于两侧都有楼板的梁,取为梁跨的1/3和b+12t中的较小值;对于只在一侧有楼板的梁,取为梁跨的1/6,b为梁宽,t为楼板厚度。
 
    
图4.1 试验模型(Lu et al 2008)和有限元模型
 

试验模型和有限元模型的总质量均为15.9吨。振动台试验采用El Centro地震动记录的NS方向分量,沿结构的X方向输入,振幅逐级增大。 计算模型的阻尼采用经典的Rayleigh阻尼,阻尼比取实测的结构初始状态阻尼比2.4%。 分析中考虑几何非线性的影响。分析结果与试验结果的比较如图4.2。可见,PQFiber能够比较准确地预测该钢筋混凝土框架的地震反应。
 
    
图4.2 试验与计算得到的最大位移与变形反应
 
参考文献 | References

Ang B G, Priestley M J N, Park R. 1981. Ductility of reinforced concrete bridge piers under seismic loading. Research Report 81-3, Department of Civil Engineering, University of Canterbury.
 
Lu X L, Zhou Y, Yan F. 2008. Shaking table test and numerical analysis of RC frames with viscous wall dampers. Journal of structural Engineering, ASCE, 134(1): 64-76.
 
Soesianawati M T, Park R, Priestley M J N. 1986. Limited ductility design of reinforced concrete columns. Report 86-10, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.
 
Takemura H, Kawashima K. 1997. Effect of loading hysteresis on ductility capacity of reinforced concrete bridge pier. Journal of structural Engineering, Japan, 43A: 849-858.
 
Tanaka H, Park R. 1990. Effect of lateral confining reinforcement on the ductile behavior of reinforced concrete columns. Report 90-2, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.
 
Watson S. 1989. Design of reinforced concrete frames of limited ductility. Report 89-4, Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.
 
吹田啓一郎, 松岡祐一, 山田哲, 等. 2008. 実大4層建物完全崩壊実験の概要. 日本建築学会大会学術講演梗概集, 833-834.
 
齋藤裕一郎, 吹田啓一郎, 松岡祐一, 等. 2008. 実大4層建物完全崩壊実験における弾塑性加振結果. 日本建築学会大会学術講演梗概集, 835-836.
 
山田哲, 吹田啓一郎, 松岡祐一, 等. 2008. 実大4層建物完全崩壊実験における弾性加振結果, 日本建築学会大会学术讲演梗概集, 837-838.
 
島田侑子, 吹田啓一郎, 松岡祐一, 等. 2008. 実大4層建物完全崩壊実験における崩壊加振結果. 日本建築学会大会学術講演梗概集, 839-840.
声明:本人不对使用者利用本程序得到的分析结果的准确性和可靠性负责。
Disclamer: it is the user's responsibility to interpret and check the reliability of his analysis results. I am not resposible for any results obtained by the herein provided library.
©2004-2021 QU Zhe. All rights reserved.