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。

A SIMPLIFIED DAM-RESERVOIR DYNAMIC COUPLING ANALYSIS METHOD BASED ON FEM-SBFEM

In the dam-reservoir dynamic fluid-structure coupling analysis, the scaled boundary finite element method (SBFEM) can simulate the semi-infinite reservoir water by discretizing only the interface of the fluid and the structure to save the number of node degrees of freedom and have higher efficiency. However, because the hydrodynamic pressure additional mass matrix is full, a large-scale elasto-plastic dynamic analysis of CFRD takes too much time for solving the equation. According to the physical meaning and distribution characteristics of the additional mass matrix of the hydrodynamic pressure by SBFEM, a simplified dam-reservoir dynamic coupling analysis method based on FEM-SBFEM is proposed. Only a retention coefficient β (0 ≤ β ≤ 1.0) is needed to simplify the hydrodynamic pressure additional mass matrix in different degrees, which is simple and easy. The simplified method is applied to the calculation of the dynamic elasto-plastic coupling of CFRD and reservoir water. The value range of β is suggested to improve the computational efficiency with good accuracy.