中文摘要：

采用有限元法模拟近场有限域，并采用基于比例边界有限元法的高阶透射边界模拟远场无限域，建立了一种坝-基动力相互作用的时域模型。模型的高阶透射边界由采用改进的连分式法求解无限域动力刚度矩阵建立，在时域里表示为一阶常微分方程组。它能精确满足无限远处的辐射阻尼，具有全局精确、时间局部和收敛速度快等优点。对近场有限域和远场无限域在交界面上的相互作用力向量进行耦合，通过联立有限域和无限域的运动方程，建立了坝-基耦合系统的标准动力学方程，该方程可采用直接积分法进行求解。该耦合系统的稳定性取决于其系数矩阵的广义特征值问题；如果出现不稳定情况，采用移谱法以消除虚假模态。通过算例验算，结果表明该算法在时域里具有良好的计算精度和效率。

英文摘要：

A high-order model based on finite element method （FEM） and the scaled boundary finite element method （SBFEM） for transient dynamic response of dam-foundation systems is presented. The well-established FEM is used for modeling the near-field bounded domains. A local high-order transmitting boundary, which is based on the SBFEM and the improved continued fraction solution for the dynamic stiffness matrix, is used for modeling the dynamic response of the far-field unbounded domains. Such boundary is expressed as a system of first-order ordinary differential equations in the time domain, which can exactly satisfy the radiation boundary condition at infinity and is global in space,local in time and converges rapidly. The bounded and unbounded formulations are coupled via the interaction force vector at the interface. The standard equations of the coupled model in the time domain are obtained by combining the dynamic equations of bounded and unbounded domains, which can be solved by a direct time-domain integration method. The stability of the coupled system depends on the general eigenproblem of the coefficient matrices. Possible spurious modes can be eliminated using the spectral shifting technique. The results of two numerical examples demonstrate that the present approach has excellent accuracy and efficiency.