基于 H ∞范数的输电塔结构动力优化

摘要

目前输电塔结构设计主要基于静力及拟静力工况，以用钢量(总质量)为经济指标进行静力优化，忽略了动力荷载的频率特性。为解决输电塔结构动力优化问题，提出了基于 H ∞范数的优化方法。该方法以系统传递函数的 H ∞范数为优化目标，采用遗传算法对角钢截面进行优化。在计算 H ∞范数时，用串联多质点模型模拟塔架结构以简化计算。同时，引入惩罚函数来调整个体的适应度，从而保证优化结果满足静力工况，不出现杆件失稳且不增加用钢量。以一个实际输电塔结构作为算例进行优化计算，结果表明，该动力优化方法显著降低了输电塔的地震响应，同时保证结构满足静力工况且总质量不超过满应力优化法的用钢量。该方法不需要求解时域响应，计算效率较高。%The current structural optimization method of the transmission tower is based on static loads and quasi-static loads.The optimization objective is chosen as steel consumption (i.e.the total mass). Frequency characteristics of the dynamic load are neglected.In order to solve the dynamic optimization problem of a transmission tower,a method based on H ∞ norm is proposed in this paper.The H ∞ norm is selected as the optimization objective.Genetic algorithm (GA)is used to find the optimal solution.The multi-degree-freedom model is adapted to simplify the tower when calculating its H ∞ norm.In order that the optimized structure satisfied the static loads and that the total mass is not increased,the penalty function is also introduced to adjust the GA fitness.According to the case study,the proposed method effectively reduced the seismic response of a practical tower,with the static load case satisfied and total mass remains the same.This method avoids calculating the response in the time domain,and thus has high computation efficiency.