基于能量指标的结构形式最优控制设计

Optimal control design of structural form based on energy index

将结构形式视为变化的控制变量,按照结构在安全性和经济性、整体和局部等方面的要求,建立基于能量指标的结构形式最优控制模型。以柱体自由扭转时的最佳单连域横截面问题为例,说明了控制模型的理论求解方法,通过变分法得到的解析解与圣维南所给的一般性结论一致。又以高拱坝体型的静力、动力设计为例,说明了控制模型的数值求解。将拱坝结构的允许形式限定为抛物线、双曲线、椭圆、一般二次曲线、三心圆和对数螺旋线6种坝型分别进行计算,发现坝型为一般二次曲线时得到的控制体型在坝体体积和静力特征响应、动力特征响应上最小,相对于初始体型不仅大幅降低了应力,而且体现了较好的经济性,说明了基于能量响应的性能指标不仅有效而且具有综合的多目标特征。

The structural performance index-strain energy(strain level) is used as the target function to optimize the form of arch dam.For solving the function,the boundary conditions,concrete volume and structure configuration requirements are regarded as the constraint conditions.The derivation of optimal cross section of a cylinder under the action of torsion,which may deduced by analytical method,is used as an example to verified the validity of this method.The application to design of high arch dam by means of numerical computation method shows that the dam with the configuration of quadratic curve is the optimal form possessing the minimum dynamic and static responses.In the optimized arch dam the stress as well as the total volume of concrete are remarkably reduced.