基于连分式与有限元法的坝库耦合瞬态分析方法  

DAM-RESERVOIR INTERACTION TRANSIENT-METHOD BASED ON CONTINUED FRACTION FORMULATION AND FEM

作　　者：李上明[1] 吴连军[1] 

机构地区：[1]中国工程物理研究院总体工程研究所,四川绵阳621999

出　　处：《工程力学》2016年第4期9-16,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(10902060;11272299);中国博士后科学基金项目(201003123);中国工程物理研究院科学技术发展基金项目(2011B0201036)

摘　　要：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。To efficiently model the transient responses of a dam-reservoir system under seismic excitations, a continued fraction formulation coupling FEM formulation was proposed. Through combining the dam FEM equation and using the dam-reservoir coupling term, a transient analysis iterative algorithm was presented to obtain the transient responses of a dam-reservoir. The transient responses of a gravity dam under horizontal seismic excitations were analyzed by using the iterative algorithm. The computational efficiency comparison was made between the continued fraction formulation and the dynamic stiffness matrix and the dynamic mass matrix. Numerical example showed the accuracy and efficiency of the iterative algorithm for the transient responses of a dam-reservoir. The presented method inherits the advantages of scaled boundary finite element method （SBFEM）, such as high accuracy and few discretized elements, it also avoids convolution integral, results in an efficiency improvement, and provides an approach with high efficiency for the transient analysis of a dam-reservoir.

关 键 词：有限元 连分式 无限水库 坝库耦合瞬态分析 比例边界有限元法 

分 类 号：O242.21[理学—计算数学] TU312[理学—数学]