This paper developed a shape and cross-section optimization method of truss subjected to earthquake excitation for achieving minimum weight design with normal stress and nodal displacement constraints. First, the dynamic responses, their first and second derivatives with respect to design variables are calculated based on Newmark-β method. Second, the inequality constraint problem with time parameter is converted into a sequence of appropriately formed unconstrained problems without time parameter by using the integral penalty function method. The gradient and Hessian matrix of penalty function are calculated by using dynamic response first and second derivatives. Third, Marquardt's method which makes fully use of gradient and Hessian matrix is employed to solve unconstrained problems. Finally, finding optimum design of a 45-bar truss is demonstrated. The results show that optimization methods presented in this paper are an effective and highly efficient approach for minimum weight design.%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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