基于梯度和海森矩阵计算考虑压杆稳定的桁架动力响应形状优化  

SHAPE OPTIMIZATION OF TRUSS SUBJECTED TO DYNAMIC LOADS USING GRADIENT AND HESSIAN MATRIX

作　　者：刘齐茂[1,2] 燕柳斌[2] 

机构地区：[1]广西工学院土木建筑系,柳州545006 [2]广西大学土木建筑工程学院,南宁530004

出　　处：《机械强度》2011年第4期538-547,共10页Journal of Mechanical Strength

基　　金：广西自然科学基金(0832023);广西工学院博士基金(03081504)资助~~

摘　　要：提出一种在动力作用下,以获取重量最小化设计同时满足强度、刚度和稳定性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导数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导数和二阶导数计算罚函数的梯度和海森矩阵。③使用充分利用梯度和海森矩阵的Marquardt方法,求解无约束优化问题。最后,演示一个十杆桁架的动力响应形状优化设计。结果表明,文中所提方法是一种考虑压杆稳定的桁架在动力作用下有效的形状优化设计方法。A shape optimization method of truss structures subjected to dynamic loads is developed.The objective is to achieve the minimum weight design.The constraints include the strength,stiffness and stability of the truss.The work is arranged as： Firstly,the dynamic responses,their first and second derivatives with respect to design variables are calculated based on Newmarkβ method.Secondly,the inequality time-dependent constraint problem is converted into a sequence of appropriately formed time-independent unconstrained problems using the integral penalty function method.Gradient and Hessian matrix of the penalty function are calculated using the first and second derivatives of dynamic responses with respect to design variables.Thirdly,Marquardt＇s method which makes fully use of gradient and Hessian matrix is employed to solve unconstrained problems.Finally,finding optimum shape design of a ten-bar truss subjected to dynamic loads is demonstrated.The results show that optimization methods presented in this paper are an effective approach for minimum weight design with strength,stiffness and stability constraints.

关 键 词：桁架 形状优化 动力响应 梯度 海森矩阵 

分 类 号：TU311[建筑科学—结构工程]