多层框架结构区间优化新方法

多层框架结构的设计参数受测量或加工精度影响往往具有一定的误差或不确定性.针对设计参数具有不确定性的多层框架结构,提出一种区间优化新方法.用区间数表征框架结构的不确定设计参数,通过优化框架结构响应区间值的上界,将区间优化问题转化为近似的确定性优化问题.将结构响应Taylor展开式中的一阶导数也看成区间的,可得到框架结构响应更加准确的变化范围. 选择区间设计参数的中值和半径为优化变量,可以得到比传统确定性结构优化更多的优化信息.对一典型四层框架结构进行了具有频率约束的区间优化.结果表明,区间优化不仅能得到与传统结构优化大致相同的设计参数最优值,还能得到当实际工程问题中设计参数取不到理论最优值而有微小波动时,框架结构响应的变化范围,为框架结构的可靠性分析提供理论依据.

A New Interval Optimization Method for Multi-story frame structures

This paper presents a new interval optimization method for the multi-story frame structure with uncertain design parameters. In the proposed method, the uncertain design parameters are characterized as intervals, and the interval optimization problem is transformed into an approximate deterministic one by optimizing the upper bound of the structural interval response. A typical four-story frame structure is then used to perform the interval optimization with frequency constraint. The results show that the proposed interval optimization method may result in optimal design parameters similar to that obtained by the conventional method and may help to obtain the variation range of structural response due to the small variation of optimal design parameters, thus laying theoretical foundations of the reliability analysis of frame structures.