中文摘要：

结构-地基动力相互作用是结构地震响应分析及安全评估的一个非常重要课题。基于比例边界有限元法，提出了一种新颖的结构-地基动力相互作用的时域模型，即采用比例边界有限元子域模拟近场有限域部分，采用高阶透射边界模拟远场无限域部分。通过采用连分式展开和引入辅助变量，有限域的动力方程采用高阶的静力刚度矩阵和质量矩阵表示。高阶透射边界精确满足无限远处的辐射边界条件，具有全局精确、时间局部和收敛速度快等优点。它是基于改进的连分式法求解无限域动力刚度矩阵而建立的，在时域里表示为一阶常微分方程组。通过联立有限域和无限域的运动方程，建立了结构-地基相互作用的标准动力学方程，采用Newmark法可直接求解。3个算例结果表明，该算法在时域里比黏弹性边界更精确、有效。

英文摘要：

Structure-foundation dynamic interaction plays an important role in the earthquake response analysis and safety assessment of structures. A novel computational model for structure-foundation dynamic interaction in the time domain based on the scaled boundary finite element method is presented. The near field bounded domain is modelled by the subdomains of the scaled boundary finite element method; and the far-field unbounded domain is represented by the high order transmitting boundary. By using the continued-fraction expansion and introducing auxiliary variables, the dynamic equation of the bounded domain is expressed in high order static stiffness and mass matrices. The high order transmitting boundary can exactly satisfy the radiation boundary condition at infinity. This open boundary is global in space, local in time and converges rapidly as the order increases. The high order transmitting boundary is based on the improved continued-fraction solution for the dynamic stiffness matrix of the unbounded domain; and the equation is a system of first-order ordinary differential equations in the time domain. Then the standard equation of structure-foundation interaction in the time domain is obtained by combining the dynamic equations of the bounded and unbounded domains, which can be solved by the Newmark method directly. The results of three numerical examples demonstrate that the proposed method is more accurate and efficient than the viscoelastic boundary in the time domain.