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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。
The finite-element method is used to simulate the near-field finite field and the high-order transmission boundary based on the proportional boundary finite element method is used to simulate the far-field infinite field. A dam-foundation dynamic time-domain interaction model is established. The high-order transmission boundary of the model is established by solving the infinite-piece dynamic stiffness matrix using the improved continuous fraction method and expressed as first-order ordinary differential equations in the time domain. It can precisely meet the radiation damping at infinity, with the advantages of global accuracy, local time and fast convergence. The coupling force vector of the near-field finite field and the far-field infinite field at the interface is coupled. By combining the motion equations of the finite field and the infinite field, a standard dynamic equation of the dam-base coupling system is established. Using the direct integral method to solve. The stability of the coupled system depends on the generalized eigenvalue problem of its coefficient matrix. In case of instability, the shift spectrum method is adopted to eliminate the false modal. The results of numerical examples show that the algorithm has good accuracy and efficiency in the time domain.