拱坝优化及GRG法的应用

Optimization of Arch Dam and Application of GRG Method

本文探讨拱坝优化设计中的数学模型与优化方法。首先,采用空间曲面函数描述拱坝(称为曲面模型)。通过给定凸性约束条件以保证坝体光滑保凸,避免出现以往模型中近岸坡边梁的内凹现象;倒悬度计算可用方向导数精确求解;坝体稳定性不再用中心角或推力角控制,而是用可利用岩石厚度和抗滑所需岩石厚度之比作为安全度控制。其次,优化方法采用了广义简约梯度法(GRG法),计算结果表明,它用于拱坝优化设计是可行的、有效的。第三,提出并验证了一种新的应力分析近似技术—分载线性化法。

In this paper, a modelling of arch dam and an efficient algorithm for optimization are discussed. First, we adopt the curved surface function to specify the shape of arch dam. The convex conservation condition is introduced as a constraint to guarantee the smooth and convexity of upper stream surface of dam, and to avoid the concave appearance near the abutments which may occur in the conventional model. Moreover, the overhang degree of dam can be calculated precisely with a direction derivative. The stability of abutments are controlled by the ratio of utilizable rock thickness to the minimum rock thickness required instead of centre-angle or push-force-angle. Sacond, the generalized gradient method (GRG) is used as an optimum algorithm. Results show that it is reliable, efficient method for optimal design of arch dam. Finally, numerical tests indicate that quantities of loads shared by the crown cantilever is linear to design variables within some ranges. So, a new approximate approach-shared load linearization method is proposed in cooperation with GRG to reduce computational efforts.1