多随机变量的桁架结构系统的可靠性分析及优化设计

针对桁架结构系统，采用随机有限元法（SFEM）计算结构系统的响应量，考虑内力重新分配，建立失效模式的安全余量方程，用验算点法计算失效模式安全余量的可靠性指标，用改进的分枝限界法，寻找主要失效模式，通过对主要失效模式方程线性化研究，计算失效模式安全余量之间的相关系数，寻找主要失效模式，通过对主要失效模式方程线性化研究，计算失效模式安全余量之间的相关系数，最后用PNET法计算出结构系统的失效概率，同时给出多随机变量的结构系统可靠度的敏度表达式，采用最佳矢量法，求解了大型桁架结构系统基于可靠性指标约束下的最小重量的优化设计问题，最后，给出了实际算例，计算结果表明；采用随机有限元法能更好地考虑结构系统的多个随机变量对系统可靠性产生的影响；所采用的可靠性分析方法和优化方法是有效的。

Reliability Analysis and Optimization Design for Truss Structural Systems with Multiple Random Variables

The static response of truss structural system is analyzed by using the Stochastic Finite Element Method.Taking redistribution of internal forces into account,safety margin functions of failure modes are established.Using the advanced branch and bound method,the significant failure modes are identified.By linearization research of safelty margin functions of the significant failure modes,calculating the correlation coeffictients of failure modes safety margins,the reliability of structural system is evaluated by PNET method.At the same time,the expression of sensitivity analysis for the reliability of structrual system with multiple random variables is derived.Using the optimum vector algorithm,the problem of minimum weight design with the constraint of structural system reliability is solved.Finally,the exaple is given,and the evaluated results demonstrate that the method presented is effective and feasible.