离散变量桁架非概率可靠性优化设计

Optimization Design of Trusses With Discrete Variables Based on Non-probabilistic Reliability

相较于连续变量优化设计,离散变量优化设计能够给出更符合工程实际需求的结果。本文采用区间变量描述结构不确定参数,提出一种离散变量桁架非概率可靠性优化设计方法。首先,建立了以杆件横截面积为离散设计变量,以桁架重量为目标函数,具有非概率可靠性指标约束的结构优化设计模型。其次,采用分段惩罚函数对离散变量进行连续化处理,得到相应的连续变量优化设计模型。最后,运用了均值点推导了非概率可靠性指标的近似解析公式,并采用序列二次规划法对优化模型进行求解。两个算例分析结果表明所提方法有效的提高了计算效率,为离散变量桁架优化设计提供了一种新的思路。

Discrete variable optimization design can give more results in line with practical engineering requirements than continuous one.By representing structural uncertain parameters as interval variables,a non-probabilistic reliability optimization design method is proposed for a truss with discrete variables.Firstly,a structural optimization design model is established,in which cross-sectional areas,truss weight,and non-probabilistic reliability indices are treated as design variables,objective function,and constrained conditions,respectively.Secondly,a piecewise penalty function is used to deal with the discrete variables,and whereby the corresponding optimization design model with continuous variables is obtained.Finally,the approximate analytical formula of non-probabilistic reliability index is derived by using the mean-value method and the optimization model with continuous variables is solved by the sequential quadratic programming algorithm.The results of two examples show that the proposed method effectively improves the computational efficiency and provides a new idea for the optimal design of discrete variable trusses.