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中文摘要：
研究了带有频率约束的桁架结构拓扑优化问题。首先比较了同为铰结情况下采用两种不同单元-杆单元和梁单元模拟对频率计算结果的影响,发现杆模型会丢失杆件弯曲振动模态,得到的最大自振频率设计往往含有很细截面的杆件,而实际上具有很低的频率。为克服这一困难,并考虑到实际工程结构的结点具有一定的刚性,建议此类优化问题可以采用刚架模型进行分析。讨论了用基结构的方法求解用梁单元模拟的带有频率约束的桁架结构拓扑优化可能会遗漏奇异最优解的问题。为避免丢失奇异最优解,本文将拓扑优化问题按离散变量的优化问题求解,在截面库中添加零截面杆件,采用自动分组的遗传算法进行优化,该方法还可实现杆件的分组优化。为提高计算效率,文中对该算法做了多方面改进。最后,通过一个算例,验证了改进自动分组遗传算法求解带有频率约束的桁架拓扑优化问题的效果。
英文摘要：
Based on the study of topology optimization of skeletal structures with frequency constraints,the paper found that the optimum structure from the truss model which includes some thin bars often had low frequencies and was unreasonable.However,the rigid frame model which was suggested to use may result in the difficulty of singular optimum.Further,the automatic grouping genetic algorithm（AGGA） was improved to overcome the singular difficulty and achieve the optimum topology.At last,the rigid frame model together with improved AGGA was used to optimize a skeletal structure topology with frequency constraints and received good effect.
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