Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

Effective stress analysis method of seismic response for high tailings dam

Based on the analysis method for tailings dam in upstream raising method presently used in metallurgy and nonferrous metals tailings depository in the world, an effective stress analysis method of seismic response for high tailings dam was developed according to the results of engineering geological exploration, static and dynamic test and stability analysis on Baizhishan tailing dam 113.5 m high. The law of generation, diffusion and dissipation of seismic pore water pressure during and after earthquake was investigated, and the results of tailings dam’s acceleration, seismic dynamic stress and pore water pressure were obtained. The results show that the seismic stability and liquefaction resistance of high tailings dam are strengthened remarkably, and the scope and depth of liquefaction area at the top of dam are reduced greatly. The interior stress is compressive stress, the stress level of every element is less than 1.0 and the safety coefficient of every element is greater than 1.0. The safety coefficient against liquefaction of every element of tailing dam is greater than 1.5 according to the effective stress analysis of seismic response by finite element method. The calculated results prove that liquefaction is the main reason of seismic failure of high tailing dams, and the effect of seismic inertia forces on high tailing dams’ stability during earthquake is secondary reason.

Study of Nonlinear Seismic Response and TMD Primary Control of the Cable-Stayed Bridge Section of the Third Macao-Taipa Bridge

The practical design of the cable-stayed bridge of the 3rd Macao-Taipa bridge is investigated by the finite element analysis program ANSYS, and 3-D elements BEAM188 and BEAM4 are adopted to create a dynamic calculation model. In order to analyze the material nonlinear seismic response of the cable-stayed bridge, the nonlinear behaviors of the ductile plastic hinges of the bridge towers are taken into account by employing the nonlinear rotational spring element COMBIN40. To simulate a major earthquake, three earthquake records were chosen using a wave-choosing program and input into the bridge structure along longitudinal and transversal directions. Comparisons of the linear and nonlinear seismic responses of the cable-stayed bridge are performed. In addition, a study of TMD primary control is carried out using element MASS21 and element COMBIN14, and it is indicated that the effects of mitigation monitoring are evident.

Arc-length technique for nonlinear finite element analysis

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

Pushover analysis procedure for systems considering SSI effects based on capacity spectrum method

This paper presents a new procedure to transform an SSI system into an equivalent SDOF system using twice equivalence. A pushover analysis procedure based on the capacity spectrum method for buildings with SSI effects （PASSI） is then established based on the equivalent SDOF system, and the modified response spectrum and equivalent capacity spectrum are obtained. Furthermore, the approximate formulas to obtain the dynamic stiffness of foundations are suggested. Three steel buildings with different story heights （3, 9 and 20） including SSI effects are analyzed under two far-field and two near-field historical records and an artificial seismic time history using the two PASSI procedures and the nonlinear response history analysis （NLhRHA） method. The results are compared and discussed. Finally, combined with seismic design response spectrum, the nonlinear seismic response of a 9-story building with SSI effects is analyzed using the PASSI procedures, and its seismic performance is evaluated according to the Chinese ＇Code for Seismic Design of Buildings. The feasibility of the proposed procedure is verified.

Research on wind-induced responses of a large-scale membrane structure

The wind-induced responses of a large-scale membrane structure, Expo Boulevard, are evaluated in this study. To obtain the wind pressure distribution on the roof surface, a wind tunnel test is performed. A brief analysis of wind pressure on the membrane roof is conducted first and then an analysis of the wind-induced responses of the structure is carried out using a numerical integral method in the time domain. In the process of calculation, the geometrical nonlinearity is taken into account. Results indicate that mean, RSM and peak values of the structure responses increase nonlinearly while the approaching flow velocity increases. Strong nonlinear characteristics are observed in the displacement responses, whereas the responses of nodal stress and cable axial force show minimal nonlinear properties when the membrane structure is subjected to wind loads. Different values of the damping ratio only have a minimal impact on the RSM response of the structure because the background component is a dominant part of the total dynamic response and the resonant component is too small. As the damping ratio increases from 0.02 to 0.05, the RMS responses of vertical displacement, nodal stress and cable axial force decrease by 8.1%, 6.7% and 17.9%, respectively. Since the mean component plays a significant role in the wind-induced response, the values of the gust response factor are not high for Expo Boulevard.

A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

规则波浪中圆筒型浮式生产储装置参数激励非线性响应研究

目前常见的提升圆筒型浮式生产储装置(Floating production storage and offloading vessels,FPSO)垂荡性能的方法是通过增加刚度使垂荡固有周期增大到20 s以上,远离常见波浪周期,但这使得垂荡固有周期与纵摇固有周期的比值接近1∶2,可能会导致参数激励现象的发生。因此本文针对此类圆筒型FPSO系统的参数激励非线性运动展开研究。考虑规则波建立了系统单自由度参数激励纵摇方程,本文中采用多尺度法求解运动方程的一次近似解析解,基于Lyapunov定理分析解的稳定性,以分析规则参数激励下圆筒型FPSO纵摇失稳的机理。最后,结合多尺度法与数值方法进行参数敏感性分析。结果表明,使参数激励周期与纵摇固有周期的比值远离1/2、降低参数激励幅值和增大纵摇阻尼的3种方式均能够有效避免大幅参数激励的发生。

独塔非对称钢-混混合梁斜拉桥抗震性能研究

【目的】研究独塔非对称钢-混混合梁斜拉桥的抗震性能,并探明非对称结构地震响应的差异。【方法】以长沙香炉洲大桥西汊航道桥为依托,采用MidasCivil软件建立非对称钢-混混合梁斜拉桥全桥有限元模型,分别采用反应谱法和非线性时程分析法对其进行地震响应分析,并重点研究了结构非对称性对斜拉桥辅助墩、过渡墩及其桩基抗震性能的影响。【结果】独塔非对称钢-混混合梁斜拉桥的动力特性和地震响应规律呈现出明显的非对称性,非对称布置的两过渡墩和两辅助墩在地震作用下的内力响应存在较大差异,结构的非对称性对横向地震更加敏感,在抗震设计时应予以重视;除两过渡墩桩基外,长沙香炉洲大桥按照静力计算设计的结构尺寸及配筋形式均能满足各工况地震作用下的抗震性能目标;塔身、墩身在横向+竖向地震作用下的安全储备均大于纵向+竖向地震的,桩基在横向+竖向地震作用下的安全储备几乎都小于纵向+竖向地震的;受结构非对称性的影响,边跨的27#过渡墩桩基总是先于主跨的31#过渡墩桩基发生破坏;在横向地震作用下,受群桩承台影响横向各排桩基地震轴力有较大差异。【结论】从经济性和抗震合理性角度出发,应对独塔非对称钢-混混合梁斜拉桥进行差异化的抗震设计,研究成果可为非对称斜拉桥及其他非对称桥梁结构的抗震设计提供有益参考。

基于非线性结构分析的架空输电线路风致位移响应研究

高压输电线路的稳定性和可靠性是影响电网安全稳定运行的重要因素。因此,开展输电塔线体系的风致响应研究,一直是输电工程技术领域的研究热点。以220 kV输电线路为例,进行了脉动风场的数值模拟,分析了塔线体系的振动形态,重点研究了风载荷作用下导线的振动形态以及在不同工况下由导线振动引起的位移变化。深入分析了输电线路的瞬态动力学响应,包括对架空输电线路的模态分析、风载荷下的振动过程以及不同工况下塔线的位移变化。结果表明:铁塔与导线的振动主要为一阶模态、二阶模态低频振动;导线的振动模式主要影响塔线体系的振动,不同时刻下振动位移的最大值对系统安全运行有更严重的影响。研究分析结果对输电线路的防风抗灾、安全稳定运行具有指导意义。

自由场位移修正值R在地下结构抗震设计中的应用

地下结构抗震设计中,土和结构之间的相对位移普遍采用反应位移法和非线性动力时程分析法。但是反应位移法参数过多、求解过程繁琐,非线性动力时程分析法耗时较长,不利于设计工作者快速得到可靠设计参数。本文基于地铁结构抗震设计的案例,在传统设计方法之外,研究了一种简便计算方法,即通过自由场位移修正值R快速准确地计算出土和结构之间的相对位移,并将该方法与传统方法进行了对比,发现计算结果较接近,为地下结构的抗震设计提供了参考。

Evaluation of site response characteristic using nonlinear method （Case study： Babol, Iran）

In this the present study, an attempt has been made to evaluate the seismic hazard considering local site effects by carrying out detailed geotechnical site characterization in Babol, Iran. Use of geotechnical data and synthesis of drilling data extracted from the Babol＇s subsurface database have enabled authors to determine the geotechnical properties of each site. These data are consisted of twenty five boreholes up to depth of 40 m. Based on the obtained data from geotechnical investigation the study area is divided to five zones. Dynamic analysis was performed in time domain, using fully nonlinear model by PLAXIS. A series of analysis in the study area showed the site period, ranging from 0.4 to 0.8 s. Finally the obtained response spectra from fully nonlinear method were compared with site response spectra of Iran＇s 2800 （earthquake） code.

内嵌牛顿迭代的线性隐式算法及其在结构非线性动力分析中的应用

将牛顿迭代法的思想引入平均加速度法,对方程式以加速度项作为迭代变量进行内嵌一次牛顿迭代处理,推导出了一种新型的线性隐式数值积分方法。然后通过离散控制理论和根轨迹法分析了新算法在求解含非线性恢复力和非线性阻尼力的结构运动方程时维持稳定的条件,并利用一个单自由度剪切型结构,检验了新算法的非线性稳定性。最后通过数值模拟,考察了新算法对于非线性多自由度结构体系的适用性和可靠性。

剂量反应Meta分析中常见的统计学问题

剂量反应Meta分析(dose-response Meta-analysis,DRMA)是基于多项提供剂量反应关系数据的原始研究,对其剂量反应结果进行定量合并后得出综合剂量反应直线或曲线的一类Meta分析,广泛应用于循证证据产生及临床决策等方面。目前已发表DRMA结果的可靠性和文章质量水平不一,而且国际上暂无DRMA的统一报告规范。本研究系统梳理了DRMA的本质、各步骤统计方法及常见统计分析问题,以期从统计学角度提高国内学者对DRMA的整体理解,为提高DRMA的整体质量奠定一定理论基础。

单侧主缆刚度损伤悬索桥的模态分析及1:1内共振

悬索桥缆索在长期服役状态下损伤很难避免,单侧主缆刚度损伤会使系统出现主梁竖弯与扭转自由度间的耦合,这可能会进一步对悬索桥的模态和大振幅下的非线性响应造成影响.为此,建立了考虑单侧主缆刚度受损的七自由度悬索桥横截面模型,模态分析发现单侧主缆刚度损伤会使得系统前两阶固有频率曲线由交叉变为跃迁,导致两个本身相互独立的模态发生耦合.以此为基础,考虑悬索桥主缆刚度有损伤和未损伤两种工况,运用拓展的增量谐波平衡法(EIHB)计算系统在内共振条件下的非线性振动.研究结果表明:单侧主缆刚度有损伤的悬索桥在外部简谐激励下发生1∶1内共振,系统能量表现出明显的转移现象;竖向和扭转简谐激励下,有损伤的悬索桥较未损伤工况响应幅值有所减小,但出现了两个共振响应峰值,对激励频率更为敏感.数值结果与利用Runge-Kutta法计算得到的结果吻合一致,验证了EIHB法的准确性.

等效线性化法和非线性法对不同类别场地土层地震反应分析的影响

等效线性化法和非线性法是土层地震反应分析的主要方法,二者考虑土体的非线性特性方法是不相同的.文章在实际钻孔模型的基础上,构造了含软弱、硬夹层及不含夹层的不同场地类别的计算模型,分析对比了等效线性化法和非线性法对不同类别场地土层地震反应分析的影响.等效线性化法选用了国内主要使用的LSSRLI-1程序,非线性法选用了国际上多使用的DEEPSOIL软件.结果表明:对于含软弱夹层和软弱场地(如Ⅲ、Ⅳ类场地)的工况,等效线性化法和非线性法分析结果差异较大,应选用非线性法程序计算分析或采用多种分析程序对比确定;对于不含夹层土体较硬(如Ⅱ类场地)的工况,两种方法分析结果差异较小,二者均可采用;对于含硬夹层的工况,二者计算所得的峰值和反应谱差异与无夹层的工况类似,但二者计算的不同深度的最大剪应变差异较大,在实际使用中亦应采用多种分析程序对比确定.同时,文中浅析了两种程序分析结果差异的缘由,对不同土层地震反应分析程序的选取、使用及改进提供些许价值.

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。

连续梁桥纵向地震碰撞反应参数研究

针对连续梁桥在地震作用下伸缩缝处的碰撞现象,建立了考虑支座非线性和墩柱弹塑性的碰撞模型。在此基础上,应用非线性时程方法研究了纵向地震作用下连续梁桥相邻联的非同向振动和伸缩缝处的碰撞效应。分析结果表明:影响碰撞反应的主要因素是相邻联的周期比和基本周期的大小,相邻联的质量比、伸缩缝间隙大小以及墩柱的弹塑性等因素对连续梁桥地震碰撞反应也有重要影响。同时还发现:碰撞对高度不同向振动的相邻联影响较大,当相邻联的周期比T1/T2>0.7时,碰撞对连续梁桥纵向地震反应的影响较小。

浮体与系泊系统的耦合动力分析

浮体与系泊系统的耦合动力分析对各种新型海洋平台和海洋结构物的应用具有重要意义。在浮体和系泊系统的时域耦合分析中,研究并提出了一种预报浮体和系泊系统非线性运动响应和缆索张力的分析技术。考虑瞬时物面变化引起的各种非线性因素,在时域内建立浮体的非线性运动方程并求解,其中,入射波力和静恢复力按瞬时物面条件计算,辐射力和绕射力按浮体在瞬时平均湿表面为平衡位置做简谐振荡运动来计算;考虑系泊缆索受到的非线性流体动力及大位移,采用三维弹性梁理论将缆索模型化,把缆索看作是等拉伸、等弯曲刚度的细长结构,并采用非线性有限元法对缆索的运动方程进行求解;将浮体的分析方法和系泊缆索的分析方法结合,建立了浮体和系泊系统非线性运动响应和缆索张力的耦合计算方法;对缆索,使用高阶单元,只需要较少的单元就可以得到收敛解;对耦合动力分析方程,采用隐式、显式混合的数值格式,最终将方程化为显式格式进行求解,并且合理排列和控制求解次序,这样大大提高了计算效率。对系泊浮体的固有周期、各种工况下大幅非线性运动、缆索张力等进行了计算,并进行对比研究,可以看出,该文的方法既适用于缆索小变形条件下,也适用于缆索大变形条件下浮体与系泊系统的耦合动力分析。