摘要
中国西部山区铁路的发展使得大量高墩桥梁不断涌现,对于这部分桥梁基本上都超出了规范的要求属于非规则桥梁,具体表现为墩高、墩高差较大、大跨度、曲率半径小等特点。随机振动法是未来抗震分析方法发展的必然趋势,但是由于理论复杂性和计算效率低下而未在实际工程得到充分应用。基于以上两点,本文主要解决的问题就是如何利用随机振动理论来对山区高墩桥梁做抗震分析,同时,使得随机振动法可以在实际工程中应用,不局限于任何固定结构形式,所以本文将高效的虚拟激励法、绝对位移求解法和精细积分法与具有强大前后处理功能的通用有限元软件ANSYS相结合,基于APDL语言进行二次开发,在ANSYS中实现对山区高墩桥梁遭受多维多点平稳／非平稳随机地震激励下的随机响应分析,求解方便,便于在实际工程中应用。
本文首先回顾了国内外大跨度高墩桥梁的发展以及随机振动理论在大跨度桥梁抗震分析中的应用,然后介绍了虚拟激励法在大跨度桥梁动力计算中的作用和应用,以及学者们探索虚拟激励法与通用有限元相结合的过程。从而,说明了随机振动理论在工程中的应用是能实现的和必然的。
第二章为了将多维多点平稳随机理论应用到实际工程中,运用绝对位移直接求解多维多点激励地震动响应方程的方法,从理论上将一维的多点地震激励扩展到三维地震激励模型,避免了计算静力影响矩阵的繁琐,提出了多维多点平稳地震激励在ANSYS快速模拟方法,并通过数值算例验证其计算准确性和精度,将平稳随机振动转换为谐分析,操作方便,可详细地考虑地震动的空间效应(行波效应、场地效应和相干效应)对山区高墩桥梁地震响应的影响。
第三、四章介绍了一个非平稳随机振动理论的分析方法,该方法是运用虚拟激励法来分析遭受多维空间变化地面运动激励的大跨结构的地震响应,同时,研究了局部场地效应对高墩铁路桥梁的地震响应的影响。绝对位移直接求解与虚拟激励法结合克服了传统的虚拟激励法的缺点,其实质的数学理论是一致的。为了将该理论应用到大而复杂的结构抗震分析中,先在通用有限平台上进行应用和验证,然后用来分析局部场地效应和地震动的非平稳性对高墩铁路桥梁的影响。得出的关键性结论将应用到高墩铁路桥梁设计和抗震分析中。
为了进一步提高非平稳随机振动的计算效率,第五章提出了将精细积分方法与多维多点激励的直接求解的虚拟激励法相结合的方法,运用精细积分方法来计算每一个固定频率点下的瞬态分析,仅需计算两个瞬态分析就可以得到所有频率点下的响应时程,迅速地提高了计算效率。同时,提出了在通用有限元软件快速模拟的方法,这样既提高了计算效率,又传承了直接求解多维多点非平稳虚拟激励法的所有优点,节约了自编程序的时间和计算时间,进一步促进随机振动的抗震分析方法在实际工程中的运用。首次正确地推导了单自由度结构,受非均匀调制的非平稳随机振动激励时的解析解,可为以后学者研究非均匀调制的非平稳随机振动验证计算精度所用。以山区高墩桥梁为例,建立了高墩桥梁三维空间模型,分析了非一致场地的空间分布及地形对结构碰撞响应的影响。
Construction of railways is under enormous developments in China, many of them have been built or are now being built in the southwestern region of China. Due to mountainous site topopraphies of the southwest China, many railway bridges are constructed and they usually have high pier, large height differentce, long span and small radius of curvature features in those mountainous areas and called irregular bridges beyond the bridge specification requirements. Stochastic vibration method is an inevitable to replace other seismic analysis approaches in the future, but not be fully applied in the actual projects as a result of theoretical complexity and computational inefficiency. Basd on above resons, How to use stochastic vibration theory(SVT) for aseismic analysis of mountainous high pier bridges subjected to multi-dimensional and multi-support stationary or non-stationary random earthquake excitations will be discussed in this paper and SVT is also employed without the restriction of structural style in actual engineering. Therefore highly efficient pseudo excitation method, absolute displacement solving method, precise integration method and a general finit element roftware ANSYS with powerful modeling capability are combined, and then based on APDL language, it is conducted in ANSYS that aseismic analysis of mountainous high pier bridges subjected to multi-dimensional and multi-support stationary or non-stationary random earthquake excitations and this approachis solved conviently without self-developed program and facilitates the applications of SVT in practical engineering.
The first section of this paper first reviews the major domestic and foreign development history of long-span and high pier bridges and applications of SVT in seismic analysis of long span and high pier bridges, then describes the role and application of pseudo excitation method in the dynamic calculation of long-span bridges, as well as scholars explore the combination process of pseudo excitation method and general-purpose finite element software. Thereby, it is confirmed the feasibility and inevitability of SVT application in the project.
To make stationary stochastic vibration theory used extensively in practical engineering, the second section presents absolute displacement solving response motion equation method of structure under multi-dimensional and multi-support random earthquake loading swiftly extends muti-support excitations input theory from one-dimensional and multi-support to mult-dimensional and multi-support and avoids computing the static influence matrix, which first is implemented in ANSYS at home and abroad. A numerical example is used to testify to the accuracy and precision. This technique will converte stationary excitations into a series of harmonic analyses for detail model of spatially varying ground motions (traveling wave effect, local site effect and coherence effect) acting on mountainous high pier bridges.
The third and fourth sections present a theoretical nonstationary stochastic analysis scheme using pseudo-excitation method (PEM) for seismic analysis of long-span structures under tridirectional spatially varying ground motions, based on which the local site effects on structural seismic response are studied for a high-pier railway bridge. An absolute displacement directly solving scheme of PEM in non-stationary stochastic analysis of structure under tridirectional spatial seismic motions has been proposed to resolve the drawbacks of conventional indirect approach, in conjunction with the derived mathematical scheme in modeling tridirectional nonstationary spatially correlated ground motions. To apply the proposed theoretical approach readily in stochastic seismic analysis of some complex and significant structures, this scheme has been implemented and verified in the general finite element platform, and then been applied to a high pier railway bridge under spatially varying ground motions considering the local site effect and effect of ground motion non-stationarity. Critical conclusions are drawn and can be applied in the actual seismic design and analysis of the high pier railway bridges under tridirectional non-stationary multiple excitations
To further improve the computational efficiency of non-stationary stochastic vibration, the approach of the combination of high-precise integration method employed and directly solving method is proposed to compute expediently transient analysis at every deterministic frequency, the structure response will be achieved only according to two transient analyses, and the computational efficiency is updated greatly. Simultaneously, the non-stationary stochastic vibration implemented in general finite element software not only improves computational efficiency but also inherits all merits of the non-stationary stochastic vibration and saves times of self-developed program and calculation, so that this promotes deeply implements of stochastic vibration technique in seismic analysis. Meanwhile, correct analytic solution is first given of which a structure of single degree of freedom subjects to non-uniformly modulated evolutionary non-stationary random excitations and which confirms the precision of calculations for other scholars. Taking a mountain high pier bridge for example, the establishment of the three-dimensional model of high pier bridge is carried on in ANSYS to study the influence of the collision response for non-uniform distributing spatially varying local site condition and topography.
引文
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