【作者】 胡志强；

【导师】 林皋； 陈健云；

【作者基本信息】 大连理工大学 ， 水工结构工程， 2004， 博士

【摘要】 本文的目的是提出一种能够综合考虑坝-基动力相互作用的有横缝高拱坝动力响应分析方法。针对这一目的,对摩擦接触问题的求解方法、结构-无限地基动力相互作用时域分析方法以及时域数值积分方法进行了较为深入的研究,通过数值试验的比较,最终选择了在精度、效率、收敛性、稳定性都能较好满足工程要求的分析方法。具体内容主要包括以下三方面:1、 首先,为了模拟有横缝拱坝在静、动力荷载作用下的接触非线性响应,针对非光滑方程组方法在三维摩擦接触问题中的应用作了较为深入地研究。对于摩擦接触问题,可以采用“试验-误差”型迭代法和数学规划法来求解,后者具有严格的数学基础,且可以进行收敛性分析。非光滑方程组方法是在非光滑分析理论和算法迅速发展的基础上所提出的一种精确、高效、收敛性好的方法,其中,摩擦接触条件被写成非光滑方程组的形式。本文首先介绍了两种形式的非光滑方程组方法(陈万吉、陈国庆提出的非光滑方程组方法、Christensen等提出的B-可微方程组方法),并对其中一种形式-B可微方程组形式提出了不需计算柔度阵的新的求解方法。然后将非光滑方程组方法推广应用到动力接触和弹塑性静力接触问题中。在动接触问题的求解中,通过考虑碰撞时的动量和动能守恒条件,使计算结果更为合理,其中采用的数值积分方法是隐式的Newmark方法。通过数值算例验证了算法的有效性。2、 其次,本文采用了在地基外侧施加以多次透射公式(廖振鹏)所表示的人工边界条件,来实现波动能量向无穷远处的逸散,从而可在拱坝动力分析中考虑坝-基动力相互作用的影响。人工边界条件的引入会导致数值积分的不稳定,通过对一些数值积分的数值试验,发现Hughes提出的预报-校正显式积分算法也可以与多次透射公式结合,并能够在一定条件下保证数值积分的稳定性和正确性。基于动摩擦接触问题和坝-基动力相互作用的时域分析所采用的不同的数值积分算法,本文采用Hughes提出隐-显式积分算法将这两种算法耦合在一起,作为拱坝的动力响应的分析方法,从而实现了在拱坝地震响应分析中能够综合考虑横缝和坝-基动力相互作用的影响。3、 最后利用所提出的拱坝动力分析方法对溪洛渡、小湾拱坝进行了地震响应分析,并讨论了横缝布置间距、横缝布置位置对坝体应力分布、应力大小和横缝张开度的影响。本文的计算结果可为高拱坝抗震安全性评价提供参考。更多还原

【Abstract】 The purpose of this paper is to provide a practical numerical method to simulate the seismic response of the arch dam with the consideration of effects of contraction joints and dam-foundation interaction. Therefore, the studies on frictional contact problems, structure-foundation dynamic interaction analysis in time domain and the time integration algorithms are carried out by large amount of numerical tests. Finally, some approaches which can be satisfied with the need of practical engineering in the aspects of accuracy, efficient, convergence property and stability are presented. The contents of the paper include the following three aspects.1. Firstly, the study on the applications of the Non-smooth Equations method (simply denoted by NEQ) in three-dimensional frictional contact problems has been carried out in order to simulate the response of the arch dam with contraction joints under static and seismic loads. The effects of contraction joints on the response of the arch dam belong to the contact nonlinear problems. There are two solution methods to the contact problem, one is the "trial-error" iteration method and the other is Mathematical Programming which has rigorous mathematical theoretical foundation and in which the convergence analysis can be performed. NEQ which is proposed on the base of fast development of the theory of Non-smooth analysis has the property of high accuracy, high efficient and good convergence. In this paper, two kind of NEQ are introduced, one is proposed by Chen Wanji et al. and the other is B-differential Equation proposed by Christensen. And a new solution method to the B-differential Equation method in which the contact flexibility matrix is not computed any more is presented. The generations of the NEQ to dynamic elastic contact problems and the static elastoplastic contact problems is studied. In the solution of dynamic elastic contact problems, the conservation of momentum and kinetic energy at the time of impact are taken into consideration to obtain a reasonable results, and the implicit Newmark time integration algorithm is used. Some numerical examples demonstrate the valid of algorithms.2. Secondly, in order to consider the effect of dam-foundation dynamic interaction, the artificial boundary condition (ABC) expressed by Multi Transmitting Formula (MTF) of the second order is implemented on the external boundary of the system of dam-foundation to simulate the energy of scattered wave dissipates to infinite. Numerical instability will occur when the ABCs are introduced in the numericalintegration. Through the numerical tests, it is found that Prediction-Correction explicit integration algorithm can be used to integrate the dynamic differential equations with MTF stably and accurately. For the implicit Newmark method is used in the simulation of dynamic contact among the contraction joints and explicit integrator algorithm in the analysis of dam-foundation interaction, so the Implicit-Explicit integration algorithm by Hughes which couple these two algorithm, implicit Newmark and explicit Prediction-Correction algorithm is adopted to analyze effects of the contraction joints and dam-foundation dynamic interaction on seismic response of the arch dam.3. Finally, the dynamic analysis method mentioned in 2 is used to analyze the seismic responses of Xi Luo Du and Xiao Wan arch dams. The effects of space and locations of the joints on the stress distribution and magnitude of the dam body and the joint opening are discussed. The results by the method proposed in this paper provide reference to the aseismic safety assessment of high arch dam.更多还原