基于精细算法的短肢剪力墙结构弹塑性动力时程分析
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摘要
短肢剪力墙结构体系最早在我国南方地区采用。这种结构体系在理论方面的研究一直滞后于工程应用,尤其是在抗震性能方面的理论研究。因此,有必要建立短肢剪力墙结构的新型力学模型,进行弹塑性的地震反应分析,为我国广大地震区建造这类新型结构体系的高层建筑提供科学依据。
对于不断发展的结构弹塑性动力时程反应分析,精度、稳定性与耗时之间的矛盾日益突出,影响和制约了结构动力反应分析的发展。这就要求或者研究节约存储空间和计算时间的更好隐式方法或者寻求建立具有更高精度和更好稳定性的显式方法。精细时程积分法虽然具有精度高的优点,但是,如果将精细积分法直接应用在结构的动力分析中,则存在矩阵尺度太大的困难。因此,基于精细时程积分法中精细指数矩阵算法的优点,发展新的动力时程方法,并应用在短肢剪力墙结构的地震反应分析中,是一项有意义的工作。论文基于以上内容,进行了以下具体工作:
1.详细地归纳和总结了精细时程积分法的发展和应用现状,为论文新方法的提出提供依据。
2.对精细时程积分法进行了认真、完善的推导,使精细时程积分法更加容易理解。同时,提出该方法的两种逐步积分格式。对基于数值积分的精细时程积分法进行了全面地分析和数值验证,比较、选择出效率较高的数值积分方法。将数值积分引入精细时程积分法积分项的求解,拓宽了精细时程积分法的应用范围。
3.基于指数矩阵的精细算法,将Newmark-β法与更新精细积分法结合,提出Newmark-更新精细直接积分法。提出与参数β取值无关的积分格式。文中详细地推导了该方法的基本公式,并提出了该方法显式和隐式的两种算法。
4.对Newmark-更新精细直接积分法的显式和隐式算法分别提出两种逐步积分格式。对每一种算法的两种积分格式的稳定性进行了分析,通过数值算例对两种算法的精度进行了验证。通过MATLAB软件编程,以及数值算例的分析和比较,结果表明:隐式算法和显式算法的第一种逐步积分格式是条件稳定的,精度较好;而两种算法的第二种逐步积分格式是不稳定的。
5.在Newmark-更新精细直接积分法中,要涉及到计算时间步长内三个时刻点的荷载值。如果荷载是任意的,则难以得到每一时刻点的值。因此,对该算法的隐式方法和显式方法进行了发展,提出显式级数算法和隐式级数算法。运用MATLAB语言研制程序,通过分别绘制谱半径ρ、人工阻尼比(?)、振幅衰减率AD及周期延长率PE与采样频率Ω的关系曲线,对两种级数算法进行稳定性、精度等的特性分析。
6.通过常数荷载和正弦荷载的数值算例验证,进一步分析隐式级数算法和显式级数算法的精度和超越性等特性。提出显式级数算法的全量理论和增量理论。
7.利用MATLAB语言研制了程序SLWPISA,将精细积分法、更新精细积分法和提出的显式级数算法应用在短肢剪力墙结构的弹性和弹塑性地震反应分析中。将计算结果与传统的Newmark-β法和Wilson-θ法的计算结果进行比较。利用研制的程序,可以调用任何地震波(算例中选择了四种地震波)对结构进行响应分析,并可以方便地求出结构在地震作用下的位移、速度、加速度时程曲线,以及各层剪力、层间位移、最大层间位移、最大层间剪力发生的时间等等。
8.算例的计算结果表明:提出的显式级数方法对地震作用是适用的,可行的。由于该算法是显式的(传统的方法是隐式的),不需要计算耦联的方程组,所以应用在大型实际结构的动力反应分析中,更能体现其优越性。同时,在罕遇地震作用下,本文方法和Wilson-θ法的计算结果普遍接近,而其它三种方法的计算结果部分接近,这说明一种特定积分方法的适用性要依赖于非线性类型和非线性程度以及荷载特征等多种因素,因此,一个较好的非线性时程分析程序中必须包括两种或两种以上的积分方法,当一种积分方法不适用时,可方便地选用另一种方法。
9.通过算例的计算结果得出:在设计中短肢剪力墙结构应设底部加强层,在墙肢相交处设置约束边缘构件,使底部加强部位有良好的延性和耗能能力;短肢剪力墙结构的刚度较一般剪力墙小,层间侧移较大,所以在实际工程中,高层建筑结构不应采用全部为短肢剪力墙的剪力墙结构,短肢剪力墙较多时,应布置筒体(或一般剪力墙),形成短肢剪力墙与简体(或一般剪力墙)共同抵抗水平力的剪力墙结构。
The system of short-leg shear wall structure was early used in the southern region of China.The theory study of the system is always fallen behind the engineering application, especially in earthquake-resistant capability.Then it is necessary to establish a new mechanical model and to analyze elastc-plastic seismic response,which can provide the scientific basis for the high-rise buildings with short-leg shear wall in the vast earthquake zone.
The contradiction among the accuracy,stability and time consuming of elasto-plastic time-history analysis is becoming increasingly conspicuous,which conditioned the development of the structural dynamic analysis.That requires to propose better implicit methods saving storage spatial and computing time or explicit methods of high accuracy and better stability.Precise time step integration method(PTSIM)has the advantage of high accuracy but it is difficult to calculate the multi-dimensional matrix if apply the PTSIM directly to structural dynamic analysis.Therefore it is a meaningful work to develop new explicit or implicit dynamic time-history methods based on the advantage of precise exponential matrix algorithm of PTSIM and apply them on seismic analysis of short-leg shear wall structure.Based on those,some work has been done as follows:
1.Summarize the development and application actuality of precise time step integration method in detail,which provide the basis for the proposed method.
2.The PTSIM is much easier to be understood by complete and detailed derivation.Two kinds of integral schemes are proposed.The PTSIM based on numerical integration is analyzed and validated overall,and numerical integration of upper calculation efficiency for PTSIM is selected.By introducing the numerical integral term,application ranges of PTSIM are widen.
3.Based on the precise exponential matrix algorithm,Newmark - RPDTSIM(renewal precise direct time step integration method)is put forward by coupling the Newmark method and RPTSIM.The integral scheme is not related to parameterβ.Basic formulas are introduced and deduced and explicit and implicit algorithms are presented to Newmark-RPDTSIM.
4.Two kinds of integral schemes are respectively proposed to explicit or implicit algorithm of Newrnark-RPDTSIM.The stability and accuracy of the two integral schemes are analyzed.Results prove that the first scheme is conditional stable and better accurate while the second one is unstable by the developed program of MATLAB.
5.Load values of three time points are need to be calculated in Newmark-RPDTSIM.If the load is arbitrary,the values of every time points were difficult to get.Then the explicit and implicit Taylor series algorithms are put forward.The curves between spectralρ,algorithmic damping ratio(?),amplitude decay AD,period elongation PE and sampling frequencyΩare drawn and characteristics of stabilities and accuracies are analyzed by the developed program of MATLAB.
6.With the examples of constant load and sine load,characteristics of accuracy and transcendency for explicit and implicit Taylor series integration methods are further analyzed. The total deformation theory and incremental theory of are put forward explicit integral method with Taylor series.
7.The PTSIM,RPTSIM and the proposed explicit Taylor series method are applied to elastic and elastic-plastic seismic analysis of short-leg shear wall structure whose results are compared with those of Newmark-βmethod and Wilson-θmethod.The developed program SLWPISA of MATLAB is able to draw displacement curve,speed curve and acceleration curve of the building under earthquake actions.Inter-story displacements and the happening time of inter-story maximum displacement and shear force can be gained.
8.The example results show that the explicit integral method with Taylor series is suitable to earthquake action and is reasonable.Because the proposed method is explicit, which means it is not necessary to calculate the coupled equations,it is superior to use the method on large practical structures.The results of the proposed method and Wilson-θmethod are generally approximate,which of the other three methods are partly approximate under the rare earthquake effect.The above analysis shows that the applicability of a specific integral method is rely on many factors of nonlinear types,nonlinear degree and load characteristics. Then a better nonlinear time integration program must consist two or two more integral methods when one method is unsuitable the others can be chosen.
9.The results of example show bottom strengthened stories should be set and restrained edge members should be installed in walls intersection when short-leg shear wall structure is designed.High-rise building should not be all shear wall structures of short-leg shear wall in real engineering because the stiffness of short-leg shear wall structure is smaller than that of general shear wall structure and its inter-story displacement is lager.When short-leg shear wall is more in a high-rise building,barrel or general shear wall should be set.Then the shear wall structure is formed to carry horizontal loads by barrel and short-leg shear wall.
对于不断发展的结构弹塑性动力时程反应分析,精度、稳定性与耗时之间的矛盾日益突出,影响和制约了结构动力反应分析的发展。这就要求或者研究节约存储空间和计算时间的更好隐式方法或者寻求建立具有更高精度和更好稳定性的显式方法。精细时程积分法虽然具有精度高的优点,但是,如果将精细积分法直接应用在结构的动力分析中,则存在矩阵尺度太大的困难。因此,基于精细时程积分法中精细指数矩阵算法的优点,发展新的动力时程方法,并应用在短肢剪力墙结构的地震反应分析中,是一项有意义的工作。论文基于以上内容,进行了以下具体工作:
1.详细地归纳和总结了精细时程积分法的发展和应用现状,为论文新方法的提出提供依据。
2.对精细时程积分法进行了认真、完善的推导,使精细时程积分法更加容易理解。同时,提出该方法的两种逐步积分格式。对基于数值积分的精细时程积分法进行了全面地分析和数值验证,比较、选择出效率较高的数值积分方法。将数值积分引入精细时程积分法积分项的求解,拓宽了精细时程积分法的应用范围。
3.基于指数矩阵的精细算法,将Newmark-β法与更新精细积分法结合,提出Newmark-更新精细直接积分法。提出与参数β取值无关的积分格式。文中详细地推导了该方法的基本公式,并提出了该方法显式和隐式的两种算法。
4.对Newmark-更新精细直接积分法的显式和隐式算法分别提出两种逐步积分格式。对每一种算法的两种积分格式的稳定性进行了分析,通过数值算例对两种算法的精度进行了验证。通过MATLAB软件编程,以及数值算例的分析和比较,结果表明:隐式算法和显式算法的第一种逐步积分格式是条件稳定的,精度较好;而两种算法的第二种逐步积分格式是不稳定的。
5.在Newmark-更新精细直接积分法中,要涉及到计算时间步长内三个时刻点的荷载值。如果荷载是任意的,则难以得到每一时刻点的值。因此,对该算法的隐式方法和显式方法进行了发展,提出显式级数算法和隐式级数算法。运用MATLAB语言研制程序,通过分别绘制谱半径ρ、人工阻尼比(?)、振幅衰减率AD及周期延长率PE与采样频率Ω的关系曲线,对两种级数算法进行稳定性、精度等的特性分析。
6.通过常数荷载和正弦荷载的数值算例验证,进一步分析隐式级数算法和显式级数算法的精度和超越性等特性。提出显式级数算法的全量理论和增量理论。
7.利用MATLAB语言研制了程序SLWPISA,将精细积分法、更新精细积分法和提出的显式级数算法应用在短肢剪力墙结构的弹性和弹塑性地震反应分析中。将计算结果与传统的Newmark-β法和Wilson-θ法的计算结果进行比较。利用研制的程序,可以调用任何地震波(算例中选择了四种地震波)对结构进行响应分析,并可以方便地求出结构在地震作用下的位移、速度、加速度时程曲线,以及各层剪力、层间位移、最大层间位移、最大层间剪力发生的时间等等。
8.算例的计算结果表明:提出的显式级数方法对地震作用是适用的,可行的。由于该算法是显式的(传统的方法是隐式的),不需要计算耦联的方程组,所以应用在大型实际结构的动力反应分析中,更能体现其优越性。同时,在罕遇地震作用下,本文方法和Wilson-θ法的计算结果普遍接近,而其它三种方法的计算结果部分接近,这说明一种特定积分方法的适用性要依赖于非线性类型和非线性程度以及荷载特征等多种因素,因此,一个较好的非线性时程分析程序中必须包括两种或两种以上的积分方法,当一种积分方法不适用时,可方便地选用另一种方法。
9.通过算例的计算结果得出:在设计中短肢剪力墙结构应设底部加强层,在墙肢相交处设置约束边缘构件,使底部加强部位有良好的延性和耗能能力;短肢剪力墙结构的刚度较一般剪力墙小,层间侧移较大,所以在实际工程中,高层建筑结构不应采用全部为短肢剪力墙的剪力墙结构,短肢剪力墙较多时,应布置筒体(或一般剪力墙),形成短肢剪力墙与简体(或一般剪力墙)共同抵抗水平力的剪力墙结构。
The system of short-leg shear wall structure was early used in the southern region of China.The theory study of the system is always fallen behind the engineering application, especially in earthquake-resistant capability.Then it is necessary to establish a new mechanical model and to analyze elastc-plastic seismic response,which can provide the scientific basis for the high-rise buildings with short-leg shear wall in the vast earthquake zone.
The contradiction among the accuracy,stability and time consuming of elasto-plastic time-history analysis is becoming increasingly conspicuous,which conditioned the development of the structural dynamic analysis.That requires to propose better implicit methods saving storage spatial and computing time or explicit methods of high accuracy and better stability.Precise time step integration method(PTSIM)has the advantage of high accuracy but it is difficult to calculate the multi-dimensional matrix if apply the PTSIM directly to structural dynamic analysis.Therefore it is a meaningful work to develop new explicit or implicit dynamic time-history methods based on the advantage of precise exponential matrix algorithm of PTSIM and apply them on seismic analysis of short-leg shear wall structure.Based on those,some work has been done as follows:
1.Summarize the development and application actuality of precise time step integration method in detail,which provide the basis for the proposed method.
2.The PTSIM is much easier to be understood by complete and detailed derivation.Two kinds of integral schemes are proposed.The PTSIM based on numerical integration is analyzed and validated overall,and numerical integration of upper calculation efficiency for PTSIM is selected.By introducing the numerical integral term,application ranges of PTSIM are widen.
3.Based on the precise exponential matrix algorithm,Newmark - RPDTSIM(renewal precise direct time step integration method)is put forward by coupling the Newmark method and RPTSIM.The integral scheme is not related to parameterβ.Basic formulas are introduced and deduced and explicit and implicit algorithms are presented to Newmark-RPDTSIM.
4.Two kinds of integral schemes are respectively proposed to explicit or implicit algorithm of Newrnark-RPDTSIM.The stability and accuracy of the two integral schemes are analyzed.Results prove that the first scheme is conditional stable and better accurate while the second one is unstable by the developed program of MATLAB.
5.Load values of three time points are need to be calculated in Newmark-RPDTSIM.If the load is arbitrary,the values of every time points were difficult to get.Then the explicit and implicit Taylor series algorithms are put forward.The curves between spectralρ,algorithmic damping ratio(?),amplitude decay AD,period elongation PE and sampling frequencyΩare drawn and characteristics of stabilities and accuracies are analyzed by the developed program of MATLAB.
6.With the examples of constant load and sine load,characteristics of accuracy and transcendency for explicit and implicit Taylor series integration methods are further analyzed. The total deformation theory and incremental theory of are put forward explicit integral method with Taylor series.
7.The PTSIM,RPTSIM and the proposed explicit Taylor series method are applied to elastic and elastic-plastic seismic analysis of short-leg shear wall structure whose results are compared with those of Newmark-βmethod and Wilson-θmethod.The developed program SLWPISA of MATLAB is able to draw displacement curve,speed curve and acceleration curve of the building under earthquake actions.Inter-story displacements and the happening time of inter-story maximum displacement and shear force can be gained.
8.The example results show that the explicit integral method with Taylor series is suitable to earthquake action and is reasonable.Because the proposed method is explicit, which means it is not necessary to calculate the coupled equations,it is superior to use the method on large practical structures.The results of the proposed method and Wilson-θmethod are generally approximate,which of the other three methods are partly approximate under the rare earthquake effect.The above analysis shows that the applicability of a specific integral method is rely on many factors of nonlinear types,nonlinear degree and load characteristics. Then a better nonlinear time integration program must consist two or two more integral methods when one method is unsuitable the others can be chosen.
9.The results of example show bottom strengthened stories should be set and restrained edge members should be installed in walls intersection when short-leg shear wall structure is designed.High-rise building should not be all shear wall structures of short-leg shear wall in real engineering because the stiffness of short-leg shear wall structure is smaller than that of general shear wall structure and its inter-story displacement is lager.When short-leg shear wall is more in a high-rise building,barrel or general shear wall should be set.Then the shear wall structure is formed to carry horizontal loads by barrel and short-leg shear wall.
引文
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