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基频约束的框架结构拓扑优化

Keywords: 独立连续映射(ICM)方法,基频约束,框架结构,拓扑优化,线性规划

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Abstract:

目前考虑频率约束的拓扑优化主要集中在连续体结构,以框架结构为研究对象的较少,为了得到满足频率约束的最优框架拓扑结构,需要对满足频率约束的框架结构拓扑优化进行研究.基于独立连续映射(independent,continuousandmapping,ICM)方法,将0-1型离散拓扑变量转化为0,1区间上的连续变量,建立了以重量最小为目标、基频为约束的框架结构拓扑优化模型.在对框架结构频率约束进行性态研究的基础上,引入2组不同的幂函数作为过滤函数,将频率约束近似显式化.将目标和约束均表示为拓扑变量的一阶泰勒展开式,建立线性规划模型,采用运动极限控制拓扑变量步长,避免迭代震荡,保证优化精度.数值算例表明:基于ICM方法的线性规划模型可高效解决基频约束下的框架结构拓扑优化问题.

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