能力谱方法的混沌动力学分析

能力谱方法是一种简化的结构抗震非线性分析方法,ATC-40等文件采用它来预测结构的力和位移需求.然而,ATC-40能力谱方法对一些非弹性系统的求解出现不收敛现象.现利用混沌动力学理论对ATC-40能力谱方法的收敛问题进行分析.ATC-40能力谱方法等效线性化迭代求解非弹性体系的位移,形成一个离散非线性映射或差分方程.对于这一离散动力系统,随着控制参数的变化,给出了动力系统迭代解的分岔图,展示了解的周期振荡、倍周期分岔、混沌等复杂动力学现象,阐明了能力谱方法迭代过程周期振荡解产生的原因.计算了动力系统的Lyapunov指数,从而判定系统解的运动状态和稳定性.最后指出了实现能力谱法等迭代算法收敛振荡控制的途径--混沌控制.     

应用ATC-40能力谱法评估结构目标位移

基于性能的抗震设计思想已得到国际上的普遍认可,其发展的一种趋势是建立简单的非线性方法确定结构非线性行为。非线性静力方法作为计算结构非线性行为的一种方法在工程界已得到普遍应用,其中ATC-40使用的能力谱法及改进的能力谱法是简化的非线性静力分析的主要方法。本文通过实例详细介绍并对比研究了这两种方法,发现ATC-40能力谱法低估了结构变形,改进的能力谱法(用非弹性设计谱建立需求谱)提供了相对较为准确的值。     

框架结构损伤识别的改进直接解析法

在一般直接解析法的基础上进行模态截尾误差的改进,从而大大降低了测量模态数目,而且识别效果也很好,但迭代次数多且收敛比较慢,本文通过改进方程解法来提高其速度。作者将约束最小二乘法迭代迅速的特点和极小最小二乘法搜索寻优功能相结合,提出了一种混合迭代求解方法,改进的方法充分组合了一般方法的搜索能力强和约束最小二乘法求解精度高的优点,从而解决了改进模态截尾误差后迭代收敛慢的问题。通过对五层两跨的平面框架结构进行损伤识别数值模拟分析后表明改进的方程解法是有效的,与一般的方法相比,算法收敛速度明显加快,求解精度明显提高,验证了改进后方法的可行性与准确性。     

振戎中学食堂楼耗能减震分析与设计(Ⅱ)－能力谱法与地震损伤性能控制设计

本文针对云南洱源县振戎中学食堂钢筋混凝土耗能减振体系，首先建立了耗能减振结构构件的恢复力模型；其次，结合文献[10]提出的“三水准”地震损伤性能目标和文献[11]中的简化设计方法以及ATC-40报告中的能力谱法，对此结构在大震下的地震损伤性能进行了分析和设计验算；最后考察了耗能减振装置对结构损伤性能的控制效果。     

二维核磁共振变参量迭代快速反演方法

核磁共振二维谱应用在储层流体识别与评价中具有快速直观识别流体类型、储层参数估算精度高的特点,使之能高效率的完成测井资料解释工作,然而拥有稳健、可靠及计算快速的反演方法是获取高质量核磁共振二维谱的关键所在.通过对二维核磁共振子空间类型反演方法的大量研究,在奇异值截断公式上进行了分析和改进,使得反演方程组的奇异值矩阵能保留下更多的奇异值,为反演结果的保真性奠定基础,并对其进行分组处理使反演方程组的条件数降低,从而提高求解的稳定性;在迭代计算中提出变参量迭代算法,使求解更合理、快速及高效.在数值模拟中,变参量迭代快速反演方法能够准确地还原30×30、60×80扩散弛豫二维构造谱,计算用时都在1分钟内;在油水试验中,变参量迭代快速反演方法反演出的扩散—弛豫二维谱能够正确识别所测流体类型,含油饱和度估算结果的相对误差为0.6%,绝对误差为0.79%.变参量迭代快速反演方法能够快速有效得处理二维核磁共振数据,反演出的扩散一弛豫二维谱质量高,二维谱应用于解释中所得到的结论可靠性高,表明该方法具有一定应用价值.     

性态点的数值解法

目前求解性态点处位移的方法均为图形方法，而且多数需迭代才能完成。本文提出一种求解性态点处位移的数值方法。并将本文方法与能力谱法求出的位移值进行比较。比较结果说明本文所提方法不但正确而且求法简单。     

能力谱方法在桥梁抗震性能评估中的应用研究

位移延性是桥梁抗震性能的重要指标之一,以Pushover分析为基础的能力谱方法能够考察结构在地震下的弹塑性位移响应,是抗震性能评估的一种有效手段.文中阐述了能力谱法的基本原理,说明了基于弹塑性反应谱的能力谱方法在求解性能点时不需要进行迭代计算;基于弹性设计反应谱建立了相对应的弹塑性反应谱,结合某实桥,将能力谱方法和增量动力分析方法进行了对比,并根据不同的地震基本烈度和场地土类型进行了抗震性能评估.分析认为,能力谱方法计算简便,对结构1阶振型的地震响应占主导时,具有较好的精度,并能够基于设计反应谱来考察结构的弹塑性抗震性能,可用于桥梁抗震性能的评估.     

考虑迭代相关及相位谱的人工地震波反应谱拟合

针对传统频域法拟合人工地震波过程中迭代效率低下的问题,本文提出使用考虑迭代相关的拟合方法与考虑相位谱的拟合方法相结合的综合方法,分别以 《公路桥梁抗震设计规范》 中的设计谱和核电厂设备抗震需求谱为拟合对象,对比了改进的综合方法与传统方法的优劣。结果显示:改进的综合方法对于目标设计谱的拟合精度较传统方法有明显提升,尤其是在反应谱的高频段和低频段;改进方法对于 《公路桥梁抗震设计规范》 中设计谱的拟合效果好于对核电厂设备抗震需求谱的拟合效果。      

对应地震反应谱的当量功率谱密度函数的数值算法

提出根据地震反应谱曲线求解当量功率谱密度函数曲线的一种数值算法,为结构随机地震反应分析中确定和计算地面运动功率谱密度提供依据。在相对位移谱与结构相对位移响应峰值的均值之间建立联系;在现有迭代方法的基础上,对算法公式作进一步的推导和整理,将迭代计算转变为线性方程组的求解计算,进而避免迭代方法的不收敛。通过对数值计算结果的分析发现,由于规范反应谱曲线存在斜率突变,采用本文算法计算出的功率谱密度曲线在规范反应谱曲线的两端和分段转折点处会出现倍周期分岔甚至混沌现象。为此建议适当增加低频范围内离散频率点的数目,且采取整体光滑的反应谱曲线,从而提高计算结果的稳定性。     

基于现行抗震规范的胡聿贤模型参数研究

回顾了地震地面加速度随机过程模型,根据随机振动理论采用迭代方法求解出与我国现行《建筑抗震设计规范》(GB50011-2001)设计反应谱相对应的功率谱密度函数,选用胡聿贤功率谱密度函数拟合上述功率谱密度函数,运用非线性拟合技术给出了与规范对应的胡聿贤功率谱参数,可供这种模型作为地震地面运动输入时选用。     

振戎中学食堂楼耗能减震分析与设计（Ⅱ）—能力谱法与地震损伤性能控制设计

本文针对云南洱源县振戎中学食堂钢钢筋混凝土耗能减振体系，首先建立了耗能减振结构构件的恢复力模型，其次，结合文献[10]提出的“三水准”地震损伤性能目标和文献[11]中的简化设计方法以及ＡＴＣ－４０报告中的能力谱法，对此结构在大震下的地震损伤性能进行了分析和设计验算，最后考察了耗能关振装置对结构损伤性能的控制效果。     

A comparative study of the ATC-40 recommended and numerically derived M-(ψ) relationship

Nonlinear static analysis procedures are key tools in evaluating the performance of existing buildings and verifying the design of seismic retrofits in seismically active regions.In this procedure,nonlinear force-displacement or moment-curvature (M-(4)) behavior needs to be defined.In the ATC-40 document,values of M-~ have been proposed to model elements in a nonlinear procedure.However,these values need to be investigated to determine if they are representative of actual values.In this paper,an attempt has been made to numerically derive M-（4） curves to simulate actual performance.Then,these curves are compared with the ATC-40 recommended curves with respect to various parameters.The study indicated that ATC-40 suggested values are conservative in nature in most situations.     

A comparative study of the ATC-40 recommended and numerically derived M-φ relationship

Nonlinear static analysis procedures are key tools in evaluating the performance of existing buildings and verifying the design of seismic retrofits in seismically active regions. In this procedure, nonlinear force-displacement or moment-curvature (M-φ) behavior needs to be defined. In the ATC-40 document, values of M-φ have been proposed to model elements in a nonlinear procedure. However, these values need to be investigated to determine if they are representative of actual values. In this paper, an attempt has been made to numerically derive M-φ curves to simulate actual performance. Then, these curves are compared with the ATC-40 recommended curves with respect to various parameters. The study indicated that ATC-40 suggested values are conservative in nature in most situations.     

Evaluation of ASCE-41, ATC-40 and N2 static pushover methods based on optimally designed buildings

Alternative static pushover methods for the seismic design of new structures are assessed with the aid of advanced computational tools. The current state-of-practice static pushover methods as suggested in the provisions of European and American regulations are implemented in this comparative study. In particular the static pushover methods are: the displacement coefficient method of ASCE-41, the ATC-40 capacity spectrum method and the N2 method of Eurocode 8. Such analysis methods are typically recommended for the performance assessment of existing structures, and therefore most of the existing comparative studies are focused on the performance of one or more structures. Therefore, contrary to previous research studies, we use static pushover methods to perform design and we then compare the capacity of the outcome designs with reference to the results of nonlinear response history analysis. This alternative approach pinpoints the pros and cons of each method since the discrepancies between static and dynamic analysis are propagated to the properties of the final structure. All methods are implemented in an optimum performance-based design framework to obtain the lower-bound designs for two regular and two irregular reinforced concrete building configurations. The outcome designs are compared with respect to the maximum interstorey drift and maximum roof drift demand obtained with the Incremental Dynamic Analysis method. To allow the comparison, also the life-cycle cost of each design is calculated; i.e. a parameter that is used to measure the damage cost due to future earthquakes that will occur during the design life of the structure. The problem of finding the lower bound designs is handled with an Evolutionary type optimization algorithm.     

静力弹塑性分析(Pushover Analysis)的基本原理和计算实例

阐述了美国两本手册FEMA273／274和ATC-40中关于静力弹塑性分析的基本原理和方法，给出了利用ETABS程序进行适合我国地震烈度分析的计算步骤，并用一框剪结构示例予以说明，表明Pushover方法是目前对结构进行在罕遇地震作用下弹塑性分析的有效方法。     

大跨预应力混凝土框架结构的静力弹塑性(pushover)分析

基于美国规范ATC-40和N2方法,建立了大跨预应力混凝土框架结构竖向地震反应的静力弹塑性(pushover)分析方法。编制了预应力混凝土构件截面弯矩-曲率的计算程序。这些为评价大跨预应力混凝土框架结构的竖向抗震能力提供了有益的参考。结合具体工程实例进一步说明了该方法的实施步骤。     

An improved capacity spectrum method for ATC‐40

In order to account for the non‐linear behavior of structures via non‐linear static procedure, the capacity spectrum method has been adopted by ATC‐40 for evaluation and retrofit of reinforced concrete buildings. For elastic‐perfectly‐plastic SDOF systems, the accuracy of the capacity spectrum method depends only on the acceleration response spectrum chosen to form the demand spectrum and the adopted model for calculating the equivalent viscous damping ratios. According to this method, the pseudo‐acceleration response spectrum (PS_a) is used to create the demand diagram. It is found that the ATC‐40 procedure, using its Type A hysteretic model, may be inaccurate especially for systems with damping ratios greater than 10% and periods longer than 0.15sec. In order to improve the accuracy of the capacity spectrum method, this study proposes to use the real absolute acceleration response spectrum (S0._a) instead of the PS_a to establish the demand diagram. The step‐by‐step procedure of the improved method and examples are implemented in this paper to illustrate the calculations of earthquake‐induced deformations. In addition, three selected models of equivalent viscous damping are also compared in this paper to assess the accuracy of the model used in the ATC‐40 procedure. Results show that the WJE damping model may be used by the capacity spectrum method to reasonably predict the inelastic displacements when the ductility demand (μ) of the structures is less than 4, whereas the damping model proposed by Kowalsky can be implemented when μ>4.0. Alternatively, the damping model proposed by Kowalsky may be used to calculate the equivalent viscous damping for the entire range of ductility. Copyright © 2003 John Wiley & Sons, Ltd.     

基于改进能力谱方法的位移反应估计

本文阐述了Pushover分析中改进能力谱方法的概念和实施步骤；对不同场地条件下四个中、低层框架结构采用改进能力谱方法估计的目标位移和非线性时程反应分析结果进行了比较，分析，并提供了不同场地条件下两种方法的相对误差，为该方法的实际应用提供了一些参考依据。     

A mathematical basis for the convergence of the capacity spectrum method

The capacity spectrum method is adopted by the ATC‐40 document for evaluating the inelastic deformation demands of reinforced concrete structures. Several studies have shown that the iterative procedure needed in the method may not give convergent outcomes in some cases. This paper focuses on the convergence of the capacity spectrum method in the constant velocity region of the response spectrum. The results obtained from the examples discussed in this study show that the convergent characteristics of this method depend on the elastic period, the hysteretic damping model, the yield displacement and the ductility ratio of the system analyzed. The capacity spectrum method can converge only for the case that the absolute value of the first derivative of the government equation derived from the demand and capacity diagrams of structures is smaller than 1.0. Copyright © 2004 John Wiley & Sons, Ltd.