一种新的求解坝面动水压力的半解析方法

基于比例边界有限元理论,推导了综合考虑库水可压缩性和库底边界吸收的坝面动水压力方程,提出了一种新的求解坝面动水压力的半解析方法,并通过算例验证了这种方法的精度和效率。结果表明,与传统方法相比,这种方法具有精度高、计算工作量小的优点。     

不同高度重力坝动水压力分析及Westergaard修正公式研究

对5种不同高度的重力坝进行了地震作用下坝体-库水系统耦合计算,将所得结果与Westergaard公式解析解相比较发现,两种方法得到的动水压力结果沿坝高度上的分布有很大不同,流固耦合结果在坝面上有上部偏大,下部偏小的趋势;随着坝体高度的增加流固耦合模型的这种趋势越为明显,坝面上出现动水压力最大值的位置也逐渐升高。据此,对Westergaard公式做出修正,考虑到多方面因素对动水压力的影响,对原公式引入了坝体高度修正项、坝体弹性修正项、库底吸收修正项。修正的Westergaard公式解与流固耦合结果及以往文献的试验和计算结果吻合良好。     

库底淤砂视为液固两相介质时挡水坝的动水压力

将库底淤砂视作液固两相介质,基于Biot理论建立了淤砂动力问题的基本方程,联合水体的动力方程,采用加权残量法进行了相应问题的解,分析了不同地震干扰频率、不同淤砂厚度等因素对挡水坝动水压力的影响。研究结果表明：淤砂对坝面动水压力的不利影响主要反映在厚淤砂和高频振动方面,需引起足够重视。     

用FE／LT方法求液固耦合动力响应

本文首先对液固耦合问题进行了Ｌａｐｌａｃｅ变换，然后给出了Ｌａｐｌａｃｅ空间的泛函和对应的变分原理，依据这个变分原理，对液固耦合系统进行有限元离散，给出有限元方程，为了提高反演的计算效率，文中采用了快速富利叶变换（ＦＦＴ）技术，最后，选用二维坝库系统的地震响应进行了试算，坝上动水压力的时程曲线与有关文献的结果进行了比较，计算结果表明本文提供的“采用有限元与Ｌａｐｌａｃｅ数值逆变变换结合求解液固耦合     

深水桥梁墩水耦合振动试验研究与数值计算

为研究深水桥墩动力特性以及动水压力分布规律,开展了本次墩水耦合振动台试验。通过比较试验结果与ANSYS-CFX计算结果验证了试验数据的有效性。通过数值拟合得到了动水压力沿桥墩截面周边以及水深的变化规律。提出附加刚度法对有水桥墩弹性振动问题进行数值模拟,结果表明:附加刚度法计算结果与试验结果相符,且能较好的解释实验原理;桥墩基频会随着水深的增加而增大,桥墩的响应随着水深的增加而减小;附加刚度法能较好地模拟深水桥梁墩水耦合弹性振动行为。     

基于SBFEM的竖向地震重力坝动水压力算法研究

考虑库水的可压缩性和库底的吸收作用,在比例边界有限元方法的框架中推导并求解了在竖向激励下重力坝所受到的动水压力,实现了在地震作用下重力坝-库水相互作用的全方向求解,在频域和时域中均实现了对坝面动水压力的求解。数值算例结果表明,方法具有极高的精度,同时还发现在一定的条件下,垂直激励下动水压力响应对坝水系统存在较为重要的影响,此外,还对库水的压缩性以及库底的吸收作用对坝面的动水压力的影响也进行了研究。     

动水压下减震连续梁桥随机优化及减震性能研究

地震作用下,跨海桥梁桥墩和周围水体的动力相互作用将对桥梁结构的动力响应产生较大影响。建立了考虑动水压力的2自由度连续梁桥简化分析模型,推导了其组合刚度和附加质量;提出了以墩顶位移方差最小为目标的黏滞阻尼器参数随机优化的Lyapunov方法。在此基础上,通过对设置黏滞阻尼器的某跨海连续梁桥简化模型进行了阻尼器参数优化,研究了动水压力和地震耦合作用下连续梁桥的减震性能。研究结果表明:动水压力增大了桥梁的地震反应,对桥梁的动力响应特性有较大影响。采用黏滞阻尼器可有效减小跨海连续梁桥的地震反应,改善桥梁结构抗震安全性能。     

基于连分式与有限元法的坝库耦合瞬态分析方法EI北大核心CSCD

为高效模拟地震激励下坝库耦合瞬态响应,建立了无限水库的连分式与有限元法的耦合公式。结合坝体有限元公式,利用坝库耦合项,发展了坝库耦合瞬态分析迭代算法。利用该算法分析了水平向地震激励下重力坝的瞬态响应。比较了基于连分式法、动态刚度矩阵法、动态质量矩阵法模拟坝库耦合问题的计算效率。数值算例表明该耦合算法模拟坝库耦合瞬态响应的正确性及高效性。该方法继承了比例边界有限元法的精度高、离散单元少等特点,又避免了其卷积积分,提升其计算效率,为坝库耦合瞬态响应提供了一种高效分析方法。     

基于连分式与有限元法的坝库耦合瞬态分析方法

为高效模拟地震激励下坝库耦合瞬态响应,建立了无限水库的连分式与有限元法的耦合公式。结合坝体有限元公式,利用坝库耦合项,发展了坝库耦合瞬态分析迭代算法。利用该算法分析了水平向地震激励下重力坝的瞬态响应。比较了基于连分式法、动态刚度矩阵法、动态质量矩阵法模拟坝库耦合问题的计算效率。数值算例表明该耦合算法模拟坝库耦合瞬态响应的正确性及高效性。该方法继承了比例边界有限元法的精度高、离散单元少等特点,又避免了其卷积积分,提升其计算效率,为坝库耦合瞬态响应提供了一种高效分析方法。     

基于ABAQUS的动水压力波双渐近透射边界单元及应用

高阶双渐近透射边界能够在全频范围内迅速逼近准确解,具有很高的计算精度和计算效率。基于大型通用有限元软件ABAQUS提供的用户子程序接口UEL开发了动水压力波双渐近透射边界单元,实现了有限元-双渐近透射边界时域耦合分析模型。双渐近透射边界单元的刚度矩阵和阻尼矩阵均为常矩阵,在分析计算中仅需计算一次,因此可以预先求解再读入ABAQUS以提高计算效率。通过数值算例验证了双渐近透射边界单元程序的正确性,并将其应用到大坝-库水动力相互作用分析。算例分析结果表明,双渐近透射边界单元具有良好的稳定性和计算精度,适用于实际大坝的地震响应分析。     

基于比例边界有限元法动态刚度矩阵的坝库耦合分析方法

针对坝体在水平向激励下的瞬态耦合问题和基于比例边界有限元法,推导了等横截面半无限水库的动态刚度矩阵,其值用贝赛尔函数计算。基于该动态刚度矩阵,建立了有限元法与比例边界有限元法的耦合方程,分析了水平向激励下任意几何形状的半无限水库的瞬态响应。其中,半无限水库分解成用有限元离散的任意几何形状的近场域和用比例边界有限元法模拟的远场域即等横截面半无限水库。通过比较动态刚度矩阵和动态质量矩阵模拟等横截面半无限水库的计算效率,发现它们计算精度相同,但动态刚度矩阵效率更高。数值算例表明了所发展的动态刚度矩阵与其耦合方程的正确性。     

Diagonalization procedure for scaled boundary finite element method in modeling semi‐infinite reservoir with uniform cross‐section

To improve the ability of the scaled boundary finite element method (SBFEM) in the dynamic analysis of dam–reservoir interaction problems in the time domain, a diagonalization procedure was proposed, in which the SBFEM was used to model the reservoir with uniform cross‐section. First, SBFEM formulations in the full matrix form in the frequency and time domains were outlined to describe the semi‐infinite reservoir. No sediments and the reservoir bottom absorption were considered. Second, a generalized eigenproblem consisting of coefficient matrices of the SBFEM was constructed and analyzed to obtain corresponding eigenvalues and eigenvectors. Finally, using these eigenvalues and eigenvectors to normalize the SBFEM formulations yielded diagonal SBFEM formulations. A diagonal dynamic stiffness matrix and a diagonal dynamic mass matrix were derived. An efficient method was presented to evaluate them. In this method, no Riccati equation and Lyapunov equations needed solving and no Schur decomposition was required, which resulted in great computational costs saving. The correctness and efficiency of the diagonalization procedure were verified by numerical examples in the frequency and time domains, but the diagonalization procedure is only applicable for the SBFEM formulation whose scaling center is located at infinity. Copyright © 2009 John Wiley & Sons, Ltd.     

Space-time finite element procedure with block-iterative algorithm for dam-reservoir-soil interaction during earthquake loading

This paper presents a time-discontinuous Galerkin space-time finite element method for the seismic analysis of dam-reservoir-soil system. For the reservoir domain an auxiliary variable q, a first-order time derivative of hydrodynamic pressure is introduced as the primary unknown. Similarly, velocity is taken as the primary unknown in the solid domain. In this approach, secondary unknowns (displacement and pressure) are computed in a postprocessing step by consistent time integration of the primary unknowns. This arrangement leads to a system of linearly coupled algebraic equations, which is solved with a block-iterative algorithm. In each iteration of the algorithm, two smaller linear systems, ie, one for velocity field and another for the auxiliary field, are solved separately and coupling between these two fields is enforced through iterations. Afterwards, numerical performance of the proposed scheme is demonstrated by solving some benchmark dam-reservoir interaction problems. It is shown that very few iterations are required for the convergence. Lastly, the method is employed to analyze the effects of dynamic interactions on the response of concrete dam to the earthquake loading.     

Seismically induced, non-stationary hydrodynamic pressure in a dam-reservoir system

Stochastic seismic analysis of hydrodynamic pressure in a dam-reservoir system is presented in this paper. The analysis is conducted assuming infinite reservoir compressible fluid and modeling seismic acceleration as a normal zero-mean stochastic process obtained by Penzien filter. The non-homogeneous boundary conditions associated to the problem have been incorporated into the equation of pressure wave scattering in the form of a forcing function turning the non-homogeneous boundary value problem into an homogeneous one. Solution obtained via modal analysis in time-domain is coupled with the use of classical Itô stochastic differential calculus to characterize the stochastic hydrodynamic pressure field. Both cases of hydrodynamic pressure acting along the upstream face of the dam in presence of stationary and non-stationary seismic accelerations have been considered.     

重力坝动水压力模型试验的数值重构研究

由于试验设备及模型材料的限制,在重力坝动力模型试验中采用在坝体模型上游安置水箱内盛满水的方法模拟重力体-库水系统相互作用的效果存在误差。为此,采用流固耦合模型对重力坝动水压力模型试验进行数值重构分析的方法,研究了用上游水箱中盛满水模拟地震作用下原型库水对坝体动力作用产生误差的原因。研究结果表明,水箱内水体密度及可压缩性是导致试验中坝体-水库系统相互作用效果偏小的两个原因,其水体密度偏小更为主要因素。据此,提出了修正上述误差的三种可行且准确的方法。     

基于比例边界有限元法和有限元法的水下结构瞬态分析方法

针对冲击波作用下水下结构与无限声学水域的流固耦合问题,建立了基于比例边界有限元法和有限元法的瞬态分析方法。无限水域用比例边界有限元法离散,而水下结构等有限域用有限元法模拟。该方法利用声学近似法将无限水域施加给水下结构的载荷分解成冲击波载荷和散射波载荷。冲击波载荷由水下冲击波理论确定,而散射波载荷由比例边界有限元法估值。为改善比例边界有限元法动态质量矩阵的计算效率,发展了动态质量矩阵的时域递推公式。数值算例分析结果表明了所发展的瞬态分析方法和时域递推公式的正确性。     

Explicit time-domain transmitting boundary for dam-reservoir interaction analysis

An explicit time-domain transmitting boundary for the analysis of dam-reservoir interactions is presented. This transmitting boundary is a semi-analytical solution of the governing wave equation of the far field of the reservoir. By using this transmitting boundary, the radiation condition and water compressibility can readily be incorporated in the time-domain analysis of dam-reservoir systems. Therefore, the finite element method can be used to accurately analyse a dam-reservoir system including the semi-infinite reservoir while maintaining its efficiency in time-domain analysis. Numerical results have excellent agreement with the available analytical solution. Results also show that the proposed explicit transmitting boundary is more efficient computationally than the implicit transmitting boundary presented by Tsai and Lee.     

Transient analysis of three-dimensional dynamic interaction between multilayered soil and rigid foundation

The study of dynamic soil-structure interaction is significant to civil engineering applications, such as machine foundation vibration, traffic-induced vibration, and seismic dynamic response. The scaled boundary finite element method (SBFEM) is a semi-analytical algorithm, which is used to solve the dynamic response of a three-dimensional infinite soil. It can automatically satisfy the radiation boundary condition at infinity. Based on the dynamic stiffness matrix equation obtained by the modified SBFEM, a continued fraction algorithm is proposed to solve the dynamic stiffness matrix of layered soil in the frequency-domain. Then, the SBFEM was coupled with the finite element method (FEM) at the interface to solve the dynamic stiffness matrices of the rigid surface/buried foundation. Finally, the mixed-variable algorithm was used to solve the three-dimensional transient dynamic response of the foundation in the time domain. Numerical examples were performed to verify the accuracy of the proposed algorithm in solving the dynamic stiffness matrix of the infinite domain in the frequency domain and the dynamic transient displacement response of the foundation in the time domain. Compared with the previous numerical integration technique, the dynamic stiffness matrix in the frequency domain calculated by using the proposed algorithm has higher accuracy and higher efficiency.