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.

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.

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。

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。

不确定非线性结构动力响应的区间分析方法

研究多自由度非线性不确定参数系统的动力响应问题．以区间数学为基础,将不确定性参数用区间进行定量化,借助一阶Taylor级数,给出了近似估计非线性振动系统动力响应范围的区间分析方法．从数学证明和数值算例两方面,将其与概率摄动有限元法进行了比较,结果显示区间分析方法对不确定参数先验信息具有要求较少、精度较高的优点．

结构可靠度分析的变f序列响应面法及其应用

提出了结构可靠度分析的变f序列响应面法和相应的收敛控制准则 ,并应用于非线性极限状态函数的可靠度计算 .该方法用简单的二次函数逐步逼近原来的复杂函数 ,并由该二次函数计算可靠指标的近似值 .这一方法简化了迭代计算过程 ,减少了迭代次数 ,有效地提高了计算精度和计算效率 ,对于大型复杂结构的可靠度分析较为适宜 ,并可推广应用于动力问题等的可靠度分析 .

基于ANSYS的大跨斜拉桥地震响应分析及性能评估

为研究西部高烈度地区大跨度斜拉桥的地震响应特点,以兰州市南绕城高速公路上一座跨径为177m+360m+177m的结合梁斜拉桥为研究对象,利用有限元软件ANSYS建立其空间计算模型,分析了该桥的动力特性。运用非线性时程分析法计算桥梁结构在50年超越概率10%和2%两种地震水平作用下的地震响应,并以构件的能力需求比评估了该桥的抗震性能。结果表明:地震作用下主梁纵向振动与横向振动基本不耦合,其竖向位移受纵向地震作用影响较大;由于结构的非对称性,5~#塔(南桥塔)的塔顶位移及塔底弯矩均大于4~#塔(北桥塔);在E1和E2两种水平地震作用下,各桥墩和桥塔关键截面以及斜拉索最小能力需求比均大于1,满足抗震性能要求;各桥墩纵桥向能力需求比小于横桥向,而桥塔纵桥向能力需求比大于横桥向,建议在过渡墩和辅助墩上安装减隔震装置,加强其纵桥向抗震性能。

水平土层地震反应分析考虑频率相关性的等效线性化方法

工程场地非线性地震反应分析中,等效线性化方法因原理相对简单、参数获取方便而得到广泛应用。但这种方法算得的地面最大加速度值以及高频段的频响放大倍率与实测结果有较大差异。首先对比分析了几种考虑频率相关性等效线性化方法的原理,对频率相关性的实质进行了初步探讨。在分析具有竖向钻孔地震记录的场地土层应变频谱特征基础上,采用谱平滑化方法进行标准化应变谱曲线拟合,从而得到考虑频率相关性的新方法。通过改造DYNEQ程序得到各种方法的计算程序,并用新方法与其他方法分析了有竖向钻孔地震记录场地的非线性地震反应。分析结果表明:考虑频率相关性后的计算方法比传统方法均有所改善,本文新方法表现出良好的适用性。