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基于梯度和海森矩阵计算在地震作用下桁架的形状优化

Keywords: 桁架,形状优化,动力响应,梯度,海森矩阵

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Abstract:

大型复杂桁架地震响应的形状优化需要大量的计算量,非梯度类算法由于效率低下通常很难成功解决该类问题.本文提出一种在地震作用下以获取质量最小化的二阶优化设计同时满足应力和位移约束的桁架形状优化设计方法.1)在Newmark-β法的基础上导出动力响应及其对设计变量一阶和二阶导数的计算方法;2)通过积分型罚函数将含时间参数的不等式约束问题转变为一系列不含时间参数的无约束问题,并利用动力响应的一阶和二阶导数计算罚函数的梯度和海森矩阵;3)充分利用梯度和海森矩阵的Marquardt方法求解无约束优化问题;演示了一个45杆桁架的形状优化设计.结果表明本文方法是一种桁架在地震作用下有效和高效的形状优化设计方法.

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