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本文假定水为不可压缩的理想流体,水与坝面、河床表面保持连续,流体作小振幅运动,忽略表面波影响,仅考虑水平方向的加速变地震扰动。本文第一部分,对非直立刚性坝面,运用放松边界条件的变分方法,找出了关于动水压力的Laplace方程的最佳组合状态的级数序列解答,原则上给出了求解任意几何形状坝面动水压力分市的方法。对于斜线及折线形坝断面的二维问题,推导出比较简捷的计算公式。本文给出定量地标志级数近似解答对于精确值收敛程度的离差算式。本文第二部分,在考虑坝的弹性变形与动水压力相互作用的离散化计算中,关于动水压力影响矩阵的求解,提出对于水库上游延伸甚长的情况,可以引用弹性力学及结构力学有限元分析中的子结构方法均基本概念,将水域分成几个子水域联合求解。对于坝踵以外为半无限矩形的情况,本文建议两种方法:“有限差分—有限元联合解法”和“解析法—有限元联合解法”。这样,就减少了离散化计算中的未知元数,在计算机运算中节约了存储,提高了效率。
This article assumes that water is an incompressible ideal fluid, water is continuous with the surface of the dam surface and the surface of the river bed, fluids move at small amplitudes, and surface wave effects are ignored. Only the acceleration-induced seismic disturbance in the horizontal direction is considered. In the first part of this paper, for the non-upright rigid dam surface, using the variational method of relaxation boundary conditions, the series solution of the optimal combination state of the Laplace equation for the hydrodynamic pressure is found. In principle, an arbitrary geometric shape is given. Method for hydrodynamic pressure of dam surface. For the two-dimensional problem of slashed and folded line dam sections, a simpler calculation formula was deduced. This paper presents the deviation formula for the quantitative convergence of the approximate solution of the sign series to the exact value. In the second part of this paper, in the calculation of the discretization of the interaction between the elastic deformation of the dam and the hydrodynamic pressure, the solution to the influence matrix of the hydrodynamic pressure is proposed. It is proposed that the extension of the upstream of the reservoir is very long, and elastic mechanics and limited structural mechanics can be cited. The substructure methods in meta-analysis are all basic concepts, and the waters are divided into several sub-waters for joint solution. For the case of dams with semi-infinite rectangles, we propose two methods: “finite difference-finite element joint solution” and “analysis-finite element joint solution.” In this way, the number of unknown elements in the discretization calculation is reduced, the storage is saved in the computer operation, and the efficiency is improved.