Improved numerical method for time domain dynamic structure-foundation interaction analysis based on scaled boundary finite element method

Based on the reduced set of base function in scaled boundary finite element method (SBFEM), an improved time domain numerical approach for the dynamic structure-foundation interaction analysis was proposed. With reasonable choice of the number of base functions, the degrees of freedom on the structure-foundation interface were reduced and the associated computation for the calculation of convolution integral was greatly reduced. The results of this proposed approach applied to the calculation of a gravity dam and an arch dam. The acceleration frequency response functions were calculated and the influences affected by different reduced set of base functions as well as full set were compared. It was found that a higher degree of reduced set of base functions resulted in a significant increase of computational efficiency but a little bit of loss in accuracy. When the reduced set was decreased by 60%, the efficiency may be increased to up to five times, while the loss of accuracy of peak value of response will be less than 4%. It may be concluded that the proposed approach is suitable for large-scale structure-foundation interaction analysis. __________ Translated from Shuili Xuebao, 2007, 38 (1): 8–14 [译自: 水利学报]     

A semi-analytical solution for characteristics of a dam-reservoir system with absorptive reservoir bottom

In this study, a semi-analytical formulation based on the Scaled Boundary Finite Element Method （SBFEM） was proposed and used to obtain the solution for the characteristics of a two-dimensional dam-reservoir system with absorptive reservoir bottom in the frequency domain. For simplicity, the dam with arbitrary upstream faces was assumed to be rigid and was subjected to a horizontal ground acceleration, while the reservoir with absorptive bottom was assumed to be semi-infinite. The reservoir was divided into two sub-domains： a near-field sub-domain and a far-field sub-domain. The near-field sub-domain with arbitrary geometry was modelled by the Finite Element Method （FEM）, while the effects of the far-field sub-domain which was assumed to be horizontal were described by a semi-analytical formation. The semi-analytical formulation involved the effect of absorptive reservoir bottom, as well as the radiation damping effect of a semi-infinite reservoir. A FEM/SBFEM coupling formulation was presented to solve dam-reservoir coupled problems. The accuracy and efficiency of the coupling formulation were demonstrated by computing some benchmark examples. Highly accurate results are produced even if the near-field sub-domain is very small.     

不同激振方向下动水压力对高面板坝面板动应力的影响

目前关于面板坝与库水动力相互作用的研究较少,而且现有的研究没有考虑库底与岸坡振动所激起的动水压力,即不能精确计算动水压力对高面板坝的影响,难以满足300 m级面板坝的安全评价要求。本文采用比例边界有限元方法计算动水压力,对坝高为300 m的面板坝进行了地震作用下三维有限元动力分析,研究了不同方向地震激励下坝面动水压力的分布规律及其对面板动应力的影响。结果表明:顺河向和坝轴向激励的动水压力最大值相差不大,而竖向激振的动水压力最大值相对较大。顺河向地震作用产生的动水压力对面板动应力有明显影响,而坝轴向地震作用下,动水压力对面板动应力有一定影响;竖向地震作用引起的动水压力对面板的动应力影响较大,不考虑动水压力时会明显低估面板的顺坡向应力最大值及高应力区范围。     

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。     

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.     

基于FEM-SBFEM的坝-库水动力耦合简化分析方法

在坝-库水动力流固耦合分析中,比例边界有限元方法（SBFEM）仅需对流固交界面进行离散,就可以模拟半无限域库水,节省了节点自由度个数,具有较高效率。但采用数值方法处理动水压力时得到的附加质量阵为满阵,进行大规模的面板坝弹塑性动力分析时用于求解方程的时间较多。该文根据动水压力附加质量阵的物理意义与分布特点,提出了一种基于FEM-SBFEM的坝与库水的动力耦合简化计算方法,仅需提供一个保留系数β（0 ≤ β ≤ 1.0）即可实现不同程度的动水压力附加质量阵化简,简单易行;将其应用在面板坝与库水的动力弹塑性耦合计算中,建议了β的取值范围,在保证具有良好精度的前提下大幅提高了计算效率。     

基于SBFEM的地下结构抗震分析

将比例边界有限元法(ScaledBoundaryFiniteElementMethod,以下简称SBFEM)理论应用于地下结构的地震响应分析。首先验证了SBFEM的精确性。根据本文的研究成果,对不均匀介质地下结构地震响应的特点获得了深入的认识,这对地下结构工程的抗震设计将具有重要参考价值。