桁架结构非概率可靠性形状优化设计

Non-probabilistic reliability-based shape optimization design of truss structures

采用区间变量描述不确定参数,提出一种桁架结构非概率可靠性形状优化方法。建立了以截面尺寸和节点坐标为设计变量,以结构重量为目标函数,具有非概率可靠性指标约束的桁架结构形状优化数学模型。采用量纲归一化对截面尺寸和节点坐标进行了变量统一;运用均值点法对功能函数进行泰勒线性近似求解得到相应的非概率可靠性指标,并采用序列二次规划算法对优化模型进行求解。三个算例分析结果表明,算例均能快速稳定地收敛到最优解,结果符合工程结构设计经验,验证了本文所提方法的准确性和有效性。

A non-probabilistic reliability-based shape optimization design method of truss structure is proposed by representing uncertain parameters as interval variables.A non-probabilistic reliability-based shape optimization model is constructed,in which cross-sectional area and node coordinate,structural weight and non-probabilistic reliability indexes determined by homologous performance functions are used as design variables,objective function and constraints,respectively.To overcome the convergence deterioration caused by the coupling of two kinds of design variables,the strategy of dimensional normalization is introduced.An analytical solution of the non-probabilistic reliability index is given,in which the midpoint is selected as the linearization point of the limit-state function,and then the optimization model is solved by the sequential quadratic programming algorithm.The results of three numerical examples indicate that the solutions according with the design experiences for engineering structures can be obtained efficiently and stably,which demonstrates the accuracy and effectiveness of the proposed method.