摘要
针对目前结构抗震优化设计方法存在优化效率低下的问题,提出一种高效的框架抗震优化设计方法。在有限元法和Newmark法基础上导出一种高效的层间相对位移对设计变量一阶和二阶导数的算法,建立显含时间参数,以结构质量最小化为目标,同时满足层间相对位移和设计变量约束的优化数学模型,通过积分型内点罚函数将显含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题,利用层间相对位移对设计变量一阶和二阶导数的信息计算罚函数的梯度和海森矩阵,然后利用梯度和海森矩阵构造求解优化设计问题高效有效的优化算法。算例表明该抗震优化方法能获得结构的最优设计,具有简单、下降速度快、不需要进行一维搜索等特点。是一种有效和高效的框架抗震二阶优化方法。
Aiming at the lower efficiency of the current aseismic optimal design methods of structures, an efficient a seismic optimal design method for a frame was developed here. An efficient algorithm for the first and second derivatives of interstorey drift with respect to design variables was derived based on the finite element method and Newmark method. An optimal mathematical model with explicit time parameters was established to realize the minimum weight design of the frame and to satisft the constraints of interstorey drift and design variables. An inequality constraint problem with explicit time parameters was converted into a sequence of appropriately formed unconstrained optimal problems without time parameters using the integral inner point penalty function method. The gradient and Hessian matrix of the penalty function could be achieved using the information of the first and second derivatives of the interstorey drift with respect to design variables. Then, the effective optimal algorithm was constructed to solve the optimal design problem using the gradient and Hessian matrix. Examples indicated that the aeismic optimal design method proposed here can obtain the optimal design of a frame; it has advantages of simplicity, fast descent speed, and excellent convergence rate, it does not need one-dimensional searching, it is an effective aseismic second-order optimization method for a frame.
出处
《振动与冲击》
EI
CSCD
北大核心
2012年第17期99-105,共7页
Journal of Vibration and Shock
基金
广西科学基金资助项目(0832023)
广西工学院博士基金资助项目(03081504)
广西教育厅立项项目(200808LX369)
