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1.
等效线性化方法是计算结构弹塑性地震反应的实用方法.通过对几种等效线性化方法的比较分析,提出了基于FEMA440 （2005）计算等效刚度和等效阻尼比的等效线性化方法;分别采用静力弹塑性分析方法和等效线性化方法,分析了局部使用高性能纤维增强混凝土新型框架结构的弹塑性地震反应.结果表明,两种方法所得结构的地震反应均比较接近.因此,本文建议的等效线性化方法能够较好地预测新型框架结构的弹塑性地震反应. 相似文献
2.
Bivariate Gaussian mixture–based equivalent linearization method for stochastic seismic analysis of nonlinear structures 
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下载免费PDF全文 To address challenges in stochastic seismic analysis of nonlinear structures, this paper further develops a recently proposed Gaussian mixture–based equivalent linearization method (GM‐ELM). The GM‐ELM uses a Gaussian mixture distribution model to approximate the probabilistic distribution of a nonlinear system response. Using properties of the Gaussian mixture model, GM‐ELM can decompose the non‐Gaussian response of a nonlinear system into multiple Gaussian responses of linear single–degree of freedom oscillators. With the set of the equivalent linear systems identified by GM‐ELM, response statistics as crossing rate and first‐passage probability can be computed conveniently using theories of linear random vibration analysis. However, the original version of GM‐ELM may lead to an inaccurate estimate because of the heuristic parameters of the linear system introduced to supplement insufficient information. To overcome this limitation and define unique equivalent linear systems, this paper proposes a further developed version of GM‐ELM, which uses a mixture of bivariate Gaussian densities instead of univariate models. Moreover, to facilitate the use of elastic response spectra for estimating the mean peak responses of a nonlinear structure, a new response spectrum combination rule is proposed for GM‐ELM. Two numerical examples of hysteretic structural systems are presented in this paper to illustrate the application of the bivariate GM‐ELM to nonlinear stochastic seismic analysis. The analysis results obtained by the bivariate GM‐ELM are compared with those obtained by the univariate GM‐ELM, the conventional equivalent linearization method, the tail equivalent linearization method, and Monte Carlo simulation. The supporting source code and data are available for download at https://github.com/yisangri/GitHub‐bGM‐ELM‐code.git 相似文献
3.
Gaussian mixture–based equivalent linearization method (GM-ELM) is a recently developed stochastic dynamic analysis approach which approximates the random response of a nonlinear structure by collective responses of equivalent linear oscillators. The Gaussian mixture model is employed to achieve an equivalence in terms of the probability density function (PDF) through the superposition of the response PDFs of the equivalent linear system. This new concept of linearization helps achieve a high level of estimation accuracy for nonlinear responses, but has revealed some limitations: (1) dependency of the equivalent linear systems on ground motion intensity and (2) requirements for stationary condition. To overcome these technical challenges and promote applications of GM-ELM to earthquake engineering practice, an efficient GM-ELM-based fragility analysis method is proposed for nonstationary excitations. To this end, this paper develops the concept of universal equivalent linear system that can estimate the stochastic responses for a range of seismic intensities through an intensity-augmented version of GM-ELM. Moreover, the GM-ELM framework is extended to identify equivalent linear oscillators that could capture the temporal average behavior of nonstationary responses. The proposed extensions generalize expressions and philosophies of the existing response combination formulations of GM-ELM to facilitate efficient fragility analysis for nonstationary excitations. The proposed methods are demonstrated by numerical examples using realistic ground motions, including design code–conforming nonstationary ground motions. 相似文献
4.
This paper presents a new direct modeling approach to analyze 3D dynamic SSI systems including building structures resting on shallow spread foundations. The direct method consists of modeling the superstructure and the underlying soil domain. Using a reduced shear modulus and an increased damping ratio resulted from an equivalent linear free-field analysis is a traditional approach for simulating behavior of the soil medium. However, this method is not accurate enough in the vicinity of foundation, or the near-field domain, where the soil experiences large strains and the behavior is highly nonlinear. This research proposes new modulus degradation and damping augmentation curves for using in the near-field zone in order to obtain more accurate results with the equivalent linear method. The mentioned values are presented as functions of dimensionless parameters controlling nonlinear behavior in the near-field zone. This paper summarizes the semi-analytical methodology of the proposed modified equivalent linear procedure. The numerical implementation and examples are given in a companion paper. 相似文献
5.
The seismic performance of existing structures can be assessed based on nonlinear static procedures, such as the Capacity Spectrum Method. This method essentially approximates peak responses of an inelastic single‐degree‐of‐freedom (SDOF) system using peak responses of an equivalent linear SDOF model. In this study, the equivalent linear models of inelastic SDOF systems are developed based on the constant strength approach, which does not require iteration for assessing the seismic performance of existing structures. To investigate the effects of earthquake type and seismic region on the equivalent linear models, four ground‐motion data sets—Japanese crustal/interface/inslab records and California crustal records—are compiled and used for nonlinear dynamic analysis. The analysis results indicate that: (1) the optimal equivalent linear model parameters (i.e. equivalent vibration period ratio and damping ratio) decrease with the natural vibration period, whereas they increase with the strength reduction factor; (2) the impacts of earthquake type and seismic region on the equivalent linear model parameters are not significant except for short vibration periods; and (3) the degradation and pinching effects affect the equivalent linear model parameters. We develop prediction equations for the optimal equivalent linear model parameters based on nonlinear least‐squares fitting, which improve and extend the current nonlinear static procedure for existing structures with degradation and pinching behavior. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
6.
Jacobo Bielak 《地震工程与结构动力学》1978,6(1):17-30
An analysis is made of the steady-state response of a bilinear hysteretic structure supported on the surface of a viscoelastic half-space. The method of equivalent linearization is used to solve the equations of motion, and simplified approximate formulas are obtained for the fundamental resonant frequency of the system and for an effective critical damping ratio. Numerical results indicate that for non-linear hysteretic structures compliance of the soil foundation may lead to larger displacements than would occur if the base were rigid. This behaviour differs from that generally observed for linear systems, for which the effect of soil-structure interaction is to reduce the rigid-base response. 相似文献
7.
A stochastic approach for obtaining reliable estimates of the peak response of nonlinear systems to excitations specified via a design seismic spectrum is proposed. This is achieved in an efficient manner without resorting to numerical integration of the governing nonlinear equations of motion. First, a numerical scheme is utilized to derive a power spectrum which is compatible in a stochastic sense with a given design spectrum. This power spectrum is then treated as the excitation spectrum to determine effective damping and stiffness coefficients corresponding to an equivalent linear system (ELS) via a statistical linearization scheme. Further, the obtained coefficients are used in conjunction with the (linear) design spectrum to estimate the peak response of the original nonlinear systems. The cases of systems with piecewise linear stiffness nonlinearity, along with bilinear hysteretic systems are considered. The seismic severity is specified by the elastic design spectrum prescribed by the European aseismic code provisions (EC8). Monte Carlo simulations pertaining to an ensemble of nonstationary EC8 design spectrum compatible accelerograms are conducted to confirm that the average peak response of the nonlinear systems compare reasonably well with that of the ELS, within the known level of accuracy furnished by the statistical linearization method. In this manner, the proposed approach yields ELS which can replace the original nonlinear systems in carrying out computationally efficient analyses in the initial stages of the aseismic design of structures under severe seismic excitations specified in terms of a design spectrum. 相似文献
8.
The concept of equivalent linearization, in which the actual nonlinear structure is replaced by an equivalent linear single-degree-of-freedom (SDOF) system, is extended for soil-structure systems in order to consider the simultaneous effects of soil-structure interaction (SSI) and inelastic behavior of the structure on equivalent linear parameters (ELP). This is carried out by searching over a two-dimensional equivalent period–equivalent damping space for the best pair, which can predict the earthquake response of the inelastic soil-structure system with sufficient accuracy. The super-structure is modeled as an elasto-plastic SDOF system whereas the soil beneath the structure is considered as a homogeneous half-space and is replaced by a discrete model. An extensive parametric study is carried out for a wide range of soil-structure systems subjected to a suite of 59 ground motions. The effect of SSI on ELP is studied through introducing a set of non-dimensional key parameters, which define the soil-structure system. It is shown that ELP of soil-structure systems result from a trade-off between SSI effect and nonlinear behavior of the structure. The contribution of each of these two factors depends on the characteristics of the soil-structure system which, in turn, are defined by the introduced non-dimensional key parameters. Moreover, the reliability of the predicted response of soil-structure systems and its sensitivity to deviation from optimal ELP is studied in detail, which sheds light on the consequences of using improper pairs of ELP for interacting systems in the framework of performance-based design of structures. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
9.
An algorithmic approach to the total least-squares problem with linear and quadratic constraints 总被引：5，自引：0，他引：5
Proper incorporation of linear and quadratic constraints is critical in estimating parameters from a system of equations.
These constraints may be used to avoid a trivial solution, to mitigate biases, to guarantee the stability of the estimation,
to impose a certain “natural” structure on the system involved, and to incorporate prior knowledge about the system. The Total
Least-Squares (TLS) approach as applied to the Errors-In-Variables (EIV) model is the proper method to treat problems where
all the data are affected by random errors. A set of efficient algorithms has been developed previously to solve the TLS problem,
and a few procedures have been proposed to treat TLS problems with linear constraints and TLS problems with a quadratic constraint.
In this contribution, a new algorithm is presented to solve TLS problems with both linear and quadratic constraints. The new
algorithm is developed using the Euler-Lagrange theorem while following an optimization process that minimizes a target function.
Two numerical examples are employed to demonstrate the use of the new approach in a geodetic setting. 相似文献
10.
通过有限元方法进行非线性动力时程分析获取解析的易损性曲线,计算量大且耗时。本文采用一种简化的计算方法,即基于单自由度的等效线性化模型,对钢筋混凝土框架结构进行地震易损性分析,并研究了该方法在结构高度上的适用性。通过选用5种典型的等效线性化模型对3栋不同高度的钢筋混凝土框架结构进行增量动力分析（IDA）,得到了不同高度的结构在不同强度地震作用下结构的反应和易损性,并与OpenSees程序的计算结果进行对比,研究了等效线性化模型应用于RC框架结构易损性分析在高度上的适用性。分析结果表明:对于10层及以下的框架结构,基于单自由度的等效线性化模型在结构地震易损性分析中具有较好的适用性;对于更高层数的结构,由于高阶振型反应对整体结构反应的影响增大,基于单自由度等效线性化模型的易损性分析结果会出现明显的偏差。 相似文献
11.
The problem of determining linear models of structures from seismic response data is investigated using ideas from the theory of system identification. The approach is to determine the optimal estimates of the model parameters by minimizing a selected measure-of-fit between the responses of the structure and the model. Because earthquake records are normally available from only a small number of locations in a structure, and because of noise in the records, it is necessary in practice to estimate parameters of the dominant modes in the records, rather than the stiffness and damping matrices of the linear model. A new algorithm is developed to determine the optimal estimates of the modal parameters. After tests with simulated data, the method is applied to a multi-storey building using records from the 1971 San Fernando earthquake in California. New information is obtained concerning the properties of the lower modes of the building and the time-varying character of the equivalent linear parameters. 相似文献
12.
A trilinear model is used to simulate the seismic resisting mechanism of a single‐degree‐of‐freedom friction‐damped system to reflect the situation in which both dampers and frame members lose their elastic resistance. The seismic response of the friction‐damped system is normalized with respect to the response of its corresponding linear system by an approach that incorporates a credible equivalent linearization method, a damping reduction rule and the algebraic specification of the design spectrum. The resulting closed‐form solutions obtained for the normalized response are then used to define a force modification factor for friction‐damped systems. This force modification factor, together with the condensation procedure for multi‐degree‐of‐freedom structures, enables the establishment of a quasi‐static design procedure for friction‐damped structures, which is intended for the benefit and use of structural practitioners. A curve‐fitting technique is employed to develop an explicit expression for the force modification factor used with the proposed design procedure; it is shown that this simplification results in satisfactory accuracy. Finally, a design example is given to illustrate the validation of the proposed design procedure. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
13.
通过梳理轨道交通地下结构抗震设计流程,明确抗震设计方法选择的原则和依据。在阐明反应加速度法基本原理基础上,引出土层地震反应分析的一维等效线性化法,并对影响土层地震反应计算结果关键参数进行讨论。针对一维土层地震反应得到的加速度时程提出合理拟合抛物线型二阶基线方程,可以消除加速度时程长周期随机分量引起的漂移问题,经自然积分可以得到消除基线漂移的位移时程;同时阐明数值分析软件Origin Pro有效解决积分得到位移时程的基线漂移问题并得到合理位移分布的途径和方法。以北京地铁3号线体育中心站为例,详细说明反应加速度法相关各个技术环节实现的方法和结果,并指出反应加速度法或位移法所依据的土层地震反应分析和位移时程的确定具有较强专业性,应做专项咨询分析工作;只有一维土层地震反应分析获得的加速度反应谱及时程客观合理,有限元计算所需相应地震动水平的等效剪切模量才可信;积分得到的位移时程需要有效消除基线漂移影响。只有上述相关结果真实客观可信,有限元计算结果才能模拟真实的土层-地下结构地震反应。 相似文献
14.
对一维剪切条计算模型进行改进,提出了土石坝非线性地震反应的简化计算方法。首先将坝体沿坝高离散为一系列的具有不同剪切刚度与阻尼比等参数特性的层状体系,建立了各层的振动控制方程及其边值条件,进而采用数学物理方程方法进行了求解,确定了体系的振动特性,并根据振型叠加原理和Duhamel积分确定了坝体地震反应的线弹性解。采用等价线性化方法考虑坝料的动力非线性性质,通过对线弹性地震响应的反复迭代计算,使得各层土的模量和阻尼比与其相应的剪应变水平相协调,确定出与非线性坝体系统相等效的线性解答,并将所得到的地震响应作为非线性地震响应的近似解。最后,以均质坝和心墙坝作为算例进行了具体的数值计算,将所得结果与有限元数值解进行对比分析,论证了所提方法的适用性和合理性。 相似文献
15.
lvaro A. M. F. Cunha 《地震工程与结构动力学》1994,23(8):837-857
The stochastic equivalent linearization method has been significantly improved during the last two decades, leading to rather efficient and accurate estimates of the first- and second-order statistical moments of the random response process, even when the non-stationarity of the excitation and the hysteretic degrading non-linearities of the structural system are taken into account. The purpose of this paper, apart from presenting a short survey of the most relevant methods developed in this area, indicating their main restrictions, is to call attention to the remarkable possibilities of the equivalent linearization technique as the most powerful approximate method to deal with the seismic response analysis of MDOF non-linear building structures, deserving to be considered by the engineering codes in the near future as an appropriate formulation for that purpose. To illustrate the real interest of this method, several applications concerning a simple shear-building structural model are presented, considering columns with non-linear restoring forces, either bilinear elastic or hysteretic, and the results obtained by some computer programs developed on the basis of the equivalent linearization technique are compared with the estimates achieved by digital simulation in order to check the level of accuracy. Moreover, these results are also used to evaluate limit violation (failure) probabilities, based on the vulnerability function concept. 相似文献
16.
This paper deals with the practical implementation of the statistical equivalent linearization method (EQL) in conjunction with general FE‐analysis to evaluate non‐linear structural response under random excitation. A computational procedure is presented which requires the non‐linear part of the system to be subdivided into suitable sub‐domains (elements). Each element is independently linearized using only a minimum number of co‐ordinates. A local co‐ordinate system is introduced using linear transformations of the global (master) degrees of freedom. Restoring forces and non‐linear constitutive laws are defined by the local co‐ordinates of each element. The linearization coefficients are further transformed back to establish the global linearized system. The procedure has, on one hand, the ability to use any desired linearization criterion and, on the other hand, it can be combined with highly developed procedures to determine the response of arbitrary large FE‐models. To illustrate the applicability of the procedure, two different non‐linear systems are analysed under bi‐directional earthquake excitation. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
17.
Track nonlinear energy sinks (track NESs) have been shown to be an effective and applicable strategy to mitigate structural response in recent years. However, previous studies on track NESs has mainly focused on demonstrating the benefits of track NESs through numerical simulations and experiments, with relatively little attention paid to the analytical understanding of the unique dynamics of track NESs. This study analyzes the responses of a track NES when subjected to impulsive and harmonic excitations by the harmonic balance method. Special attention is given to the cause and effect of the peaking behavior that is a prominent characteristic of the track NES's restoring force–displacement relationship. Analytical results reveal that the special energy–frequency characteristics of track NESs can be, at times, utilized to enhance the energy robustness that is absent in the conventional cubic NESs. Based on the analytical response expression, an equivalent linearization method (ELM) for the track NESs is developed for stochastic analysis. This ELM is numerically validated on the systems with strong nonlinearities. Stochastic optimization built on the ELM is performed to obtain design parameters of the track NES that can lead to minimum response variances of the primary structure. In particular, the proposed optimization procedure can be applied to seismic optimum design in which the seismic excitations are modeled as filtered white-noise ground motions. The analytical techniques provided in this study lay the groundwork for the practical implementation of track NESs as a robust and effective control strategy for engineering structures. 相似文献
18.
以天津滨海某厚层淤泥场地为例,分别采用等效线性化法（LSSRLI-1）和新一代土层地震反应分析SOILQUAKE软件方法在场地危险性计算确定的不同设防水准地震动输入条件下进行了建模土层地震反应计算。计算结果表明：（1）对厚层淤泥软弱场地,与新版区划图结果相比等效线性化法可能会低估场地地震作用,甚至是低估场地设防烈度;（2） SOILQUAKE软件方法在软弱场地设计地震动参数确定时仍能体现一定的放大作用,尤其是强地震动作用下,克服了等效线性化方法在软弱场地计算时出现的设计谱明显矮、宽现象,与当前认识相一致,为软弱场地重大工程设防参数确定提供了参考;（3） SOILQUAKE软件方法在软弱场地设计地震动参数确定较新版区划图结果设防标准有大幅度提高,考虑到相关抗震设防规范的协调性,还需进一步对其他类型软弱场地进行大量强震记录输入计算检验,以便更好的工程应用。 相似文献
19.
Izuru Takewaki 《地震工程与结构动力学》2001,30(9):1345-1360
Earthquake ground motions and their effects on structural responses are very uncertain even with the present knowledge. It is therefore desirable to develop a robust structural design method taking into account these uncertainties. Critical excitation approaches are promising and a new random critical excitation method is proposed for MDOF elastic–plastic shear‐building structures on compliant ground. The power (area of power spectral density (PSD) function) and the intensity (magnitude of PSD function) are fixed and the critical excitation is found under these restrictions. In contrast to linear elastic structures, transfer functions and simple expressions for response evaluation cannot be defined in elastic–plastic structures and difficulties arise in describing the peak responses except by laborious elastic–plastic time‐history response analysis. Statistical equivalent linearization is used to estimate the elastic–plastic stochastic peak responses approximately. The critical excitation responses are obtained for several examples and compared with those of the corresponding recorded earthquake ground motion. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
20.
Fragility curves are found to be useful tools for predicting the extent of probable damage. They show the probability of highway structure damage as a function of strong motion parameters, and they allow the estimation of a level of damage probability for a known ground motion index. In this study, an analytical approach was adopted to develop the fragility curves for highway bridges based on numerical simulation. Four typical RC bridge piers and two RC bridge structures were considered, of which one was a non‐isolated system and the other was an isolated system, and they were designed according to the seismic design code in Japan. From a total of 250 strong motion records, selected from Japan, the United States, and Taiwan, non‐linear time history analyses were performed, and the damage indices for the bridge structures were obtained. Using the damage indices and ground motion parameters, fragility curves for the four bridge piers and the two bridge structures were constructed assuming a lognormal distribution. It was found that there was a significant effect on the fragility curves due to the variation of structural parameters. The relationship between the fragility curve parameters and the over‐strength ratio of the structures was also obtained by performing a linear regression analysis. It was observed that the fragility curve parameters showed a strong correlation with the over‐strength ratio of the structures. Based on the observed correlation between the fragility curve parameters and the over‐strength ratio of the structures, a simplified method was developed to construct the fragility curves for highway bridges using 30 non‐isolated bridge models. The simplified method may be a very useful tool to construct the fragility curves for non‐isolated highway bridges in Japan, which fall within the same group and have similar characteristics. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献