A computational procedure for the implementation of equivalent linearization in finite element analysis

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.     

Linearization and first‐order expansion of the rocking motion of rigid blocks stepping on viscoelastic foundation

In structural mechanics there are several occasions where a linearized formulation of the original non‐linear problem reduces considerably the computational effort for the response analysis. In a broader sense, a linearized formulation can be viewed as a first‐order expansion of the dynamic equilibrium of the system about a ‘static’ configuration; yet caution should be exercised when identifying the ‘correct’ static configuration. This paper uses as a case study the rocking response of a rigid block stepping on viscoelastic supports, whose non‐linear dynamics is the subject of the companion paper, and elaborates on the challenge of identifying the most appropriate static configuration around which a first‐order expansion will produce the most dependable results in each regime of motion. For the regime when the heel of the block separates, a revised set of linearized equations is presented, which is an improvement to the unconservative equations published previously in the literature. The associated eigenvalues demonstrate that the characteristics of the foundation do not affect the rocking motion of the block once the heel separates. Copyright © 2008 John Wiley & Sons, Ltd.     

土层非线性地震反应一维时域分析

等效线性化方法在工程中经常被用于土层非线性地震反应一维数值分析,但考虑大震作用将较大峰值加速度时程作为输入时,该方法会引起过大的“共振”效应,造成对地表地震反应的误估。为了更合理的估计非线性地震反应,提出了一种考虑拟合阻尼比、刚度比试验曲线的时域分析方法,并用于响嘡台阵场地土层地震一维非线性反应分析,通过数值模拟结果与实际记录的比较,验证了该方法的可行性。最后,通过数值模拟证明该方法对大震情况下对地表地震反应的估计比等效线性化方法更为合理。     

基于FLAC~(3D)的土层非线性地震反应分析

以唐山响嘡局部场地影响台阵3号测井场地(Ⅱ类场地)作为实验场地,验证用FLAC~(3D)软件方法进行土层地震反应计算的可行性。以天津塘沽某IV类场地为例,在不同地震动强度输入条件下分别采用FLAC~(3D)软件方法和等效线性化程序方法计算该场地地表地震动峰值和反应谱。计算结果表明:在输入地震动强度较小时,两种方法计算得到的结果差别不大;在输入地震动强度较大时,FLAC~(3D)方法克服了等效线性化方法低估地表地震反应(高频部分)和高估土体的非线性所造成的地表反应谱特征周期偏大问题。FLAC~(3D)方法计算得到的结果可能更符合工程实际。     

Gaussian mixture–based equivalent linearization method (GM-ELM) for fragility analysis of structures under nonstationary excitations

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.     

THE EFFECT OF HARD INTERLAYER THICKNESS ONTHE SITE SEISMIC RESPONSE

Studies on the effect of near-surface overburden soil layers on seismic motion have shown that the overburden soil layers have a significant impact on the seismic effect of the site due to the formation age, genetic type, thickness difference, structure, and dynamic characteristics of the soil layers. In this paper, the one-dimensional seismic response analysis of a nuclear power plant site containing a thick hard interlayer was conducted to discuss the influence of the hard interlayer thickness on the site seismic response, so as to provide a basis for determining the seismic motion parameters for seismic design of similar sites. Based on the engineering geological data of a nuclear power plant site, five models of one-dimensional soil-layer seismic response analysis were built, and the equivalent linear method of the one-dimensional site seismic response was applied to analyze the effect of the interlayer thickness on the peak acceleration and the acceleration response spectra of the site seismic response. The seismic response characteristics of the site and influence rules of the hard interlayer thickness are summarized as follows:1)Under different input seismic motion levels, the peak acceleration at the top of the hard interlayer was less than the input peak acceleration, and the peak acceleration at the ground surface of site was greater than the input peak acceleration. 2)Under the same input seismic motion, the ratios of the peak accelerations at the top of hard interlayer to the input peak accelerations were smaller than the ratios of the peak accelerations at the ground surface to the input peak acceleration, and these ratios first decreased and then increased gradually with the increase of the hard interlayer thickness; while for the same hard interlayer thickness, these ratios gradually decreased as the input peak acceleration increasing. 3)For the same input seismic motion, the ratios of the peak accelerations at the ground surface of site to those at the top of the hard interlayer increased gradually as the hard interlayer thickness increased; however, corresponding to different hard interlayer thicknesses, the variation characteristics of ratios which are the peak accelerations at the ground surface of site to those at the top of the hard interlayer were inconsistent with the increase of the input peak acceleration. 4)The hard interlayer had a significant influence on the short-period acceleration response spectrum and the thicker the hard interlayer was, the wider the influence frequency band would be; while for a special hard interlayer thickness, the influence frequency band is certain, and the hard interlayer had little effect on the acceleration response spectrum coordinates outside this frequency band, the longer the period is, the less the influence of the hard interlayer on the acceleration response spectrum coordinates. The seismic response characteristics of the site and influence rules of the hard interlayer thickness indicate that the hard interlayer thickness has a significant impact on the peak acceleration and the acceleration response spectra of the site seismic response, and the hard interlayer has obvious isolation effect at the seismic motion, and the increase of its thickness reduces the nonlinear effect of the site and leads to the wider influence frequency band. Meanwhile, the higher the input peak acceleration is, the stronger the nonlinear effect of the site, and it's remarkable that the soft layer overlying the hard interlayer has a significant amplification effect on the seismic motion.     

求解球面拟合的改进总体最小二乘算法

在球面拟合中,系数矩阵和观测向量的误差同源,均来源于球面点坐标。不同位置有相同元素存在,从理论上讲,这些相同元素应该有相同的改正数,并且非线性形式出现在观测向量中。为此,本文推导了一种改进的总体最小二乘算法,可以很好地克服上述问题。通过算例分析发现,本文方法得到的参数估值更为可靠,证明了本文方法的有效性。     

线性化误差对于UWB系统定位精度影响分析

针对目前常用的超宽带算法,扩展卡尔曼滤波(EK F)在解算过程中产生的线性化误差,对定位结果产生影响,而无损卡尔曼滤波(UKF)算法可以不进行线性化过程进行解算,避免误差的产生.文中首先对UWB定位系统线性化误差进行分析,在此基础上提出UKF和TDOA相结合的定位模型,通过实验比较两种算法的定位精度.实验结果表明U K...     

等效线性化地震反应的震级距离参数调整法及其在地震安全性评价中的应用

传统等效线性化波动法最主要的缺陷之一是,当基岩输入地震动较强时,高频段算得的放大倍率比实际场地的实测结果明显偏低。在地震安全性评价中,该缺陷导致了低估重大工程设计地震动参数的严重后果。为弥补等效线性化方法的上述缺陷,沈建文等(2010)提出了通过震级M和距离R参数修正等效线性化的方法EQLM(M,R)。本文指出应变折减系数对计算结果的重要影响,对土层反应的等效线性化方法EQLM(M,R)做了进一步的讨论。同时结合地震安全性评价的算例,用设定地震确定了震级-距离,用EQLM(M,R)完成了土层反应的计算。     

复杂软土盾构隧道纵向抗震分析

以天津Z2线盾构隧道工程为实例,基于ABAQUS有限元软件,建立三维梁-弹簧模型模拟盾构隧道,采用反应位移法对盾构隧道进行纵向抗震分析.根据盾构隧道接头实际情况,计算环间接头弹簧刚度.将地震作用下的自由场最大水平位移幅值,以简谐波的形式施加到盾构隧道轴向和横向.提出一种同时考虑轴向和横向水平地震动耦联效应的方法,通过调...