摘要
建立了以杆截面为设计变量、结构重量极小化为目标、具有位移、应力等性态可靠性约束的桁架结构拓扑优化设计数学模型．通过引入可靠性安全系数，并利用结构力学的三个基本方程，将结构的位移和杆件应力可靠性约束等价显示化为设计变量的线性函数，使原基于可靠性的优化模型转化为常规的序列线性规划问题，利用修正的单纯形法求解．算例表明文中提出的方法既简单又有效．
The problem of topology optimization of truss structures based on reliability is studied in this paper. First of all, the structural analysis under the action of random loads is carried out and the mean value and variance of all joint's displacement and bar's stress in the structure are obtained by means of three fundamental equations (equilibrium, physical and geometric) in structural mechanics, as well as the property of moment of random variable. According to this, the mathematical model of topology optimization based on reliability for truss structures is developed, in which the cross sectional areas of bar are taken as design variables, the structure weight is taken as objective function, both the reliability of structural displacement and bar stress are taken as constraint functions. Since the reliability constraints in the preceding optimization model are implicit and complex functions of design variables and they are expressed in form of probability, this leads to the conventional optimization algorithm being difficult to be applied directly. So a treatment method that the reliability constraints are equalized and displayed to the conventional constraints is proposed. By drawing into the reliability safety factor and using the relationship between the internal force and stress, all the reliability constraints of structure's displacement and bar's stress are equivalently displayed as the linear function of design variables. Therefore, the original optimization model based on reliability is transformed into the problem of conventional sequence linear programming and solved with the improved simplex method. For the variation of structural topology, the strategy of degenerate is employed. In addition, a corresponding analysis method for the structure geometric kinematics is used and inserted in the process of structural optimization to avoid insta bility structure. Finally, two examples show that the approach proposed in this paper is simple and efficient.
出处
《力学学报》
EI
CSCD
北大核心
1998年第3期277-284,共8页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金
中国科学院力学研究所LNM开放实验室基金
关键词
结构可靠性
拓扑优化
桁架结构
数学模型
structural reliability, topology optimization, reliability constraints of displacement and stress, linearprogramming, improved simplex method
