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本文提出了用于求解稳态地面加速度在拱坝上产生的非耦合动水压力的新型的有限元法。在这个方法中动水压力的控制方程及其边界条件全部从笛卡儿座标空间变换到对称缩聚的园柱极坐标空间;在这过程中,库水——坝体系统的实际轮廓被映射为一个“映象”区域。在这个区域里用一般的有限元法求解变换后的控制方程,并满足变换后的边界条件。因为在映象空间里实际尺寸是被对数缩聚的,所以这个方法适合于处理纵横比大的或非常大的库水——坝体系统,而且是经济有效的。建议的方法可以达到高精度,从所举的例子中可以看出,它能够应用于具有复杂形状的库水——坝体系统。本方法也能适用于研究稳态垂直方向地面加速度所产生的园柱形拱坝上游面的非耦合动水压力。
This paper presents a new finite element method for solving the uncoupled hydrodynamic pressure generated on the arch dam with steady ground acceleration. In this method, the control equation of the hydrodynamic pressure and its boundary conditions are all transformed from the Cartesian coordinate space to the symmetrically condensed cylindrical polar coordinate space; in this process, the actual outline of the reservoir water-dam system is mapped. For a “map” area. In this area, the generalized finite element method is used to solve the transformed control equations and satisfy the transformed boundary conditions. Because the actual dimensions in the image space are logarithmically condensed, this method is suitable for dealing with large or very large reservoir water-dam systems, and is cost-effective. The proposed method can achieve high precision. It can be seen from the examples cited that it can be applied to a reservoir water system with a complex shape - dam system. This method can also be applied to study the uncoupled hydrodynamic pressure on the upstream surface of a cylindrical arch dam generated by the ground acceleration in the steady-state vertical direction.