﻿ 高温结构可靠性分析的时变响应面法
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1. 北京航空航天大学 可靠性与系统工程学院, 北京 100191;
2. 北京航空航天大学 可靠性与环境工程技术国防科技重点实验室, 北京 100191

Time-varying response surface method for high-temperature structural reliability analysis
MA Xiaobing1,2 , REN Hongdao1, CAI Yikun1
1. School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
2. Key Laboratory of National Defense Technology for Reliability & Environment Engineering Technology, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:The constitutive equation and carrying capacity of structure will change over time under high temperature conditions. The traditional structural reliability models are inefficient to solve these time-varying structural reliability problems. A time-varying response surface method with thermal response and response threshold value changing over time was proposed. The method can be used for high-temperature structural reliability analysis. Combined with Box-Behnken experimental design, a cross quadratic function of structure's basic variables and time was introduced for establishing a time-varying model of the thermal structural response. The function of structural response threshold value and time was established by using temperature as intermediate variable. The time-varying structural reliability calculation method was proposed when basic variables are normally distributed. A study case was given to demonstrate the applicability of this method and its greatly enhanced effectiveness besides accuracy.
Key words: high-temperature structure     experimental design     time-varying response surface method     time-varying limit state function     structure reliability

1 时变极限状态函数的建立方法 1.1 时变响应面法

1.2 结构响应量阈值的时变特征

1.3 结构时变可靠度的计算

f(xi,t)不是线性函数时,σy的求解比较困难,可以采用Monte Carlo抽样的方法求得近似解.一般情况下令f(xi,t)=α′ ixit即可以得到较好的拟合精度.时变响应量y的方差可表示为

2 案例分析

2.1 有限元建模及仿真计算

 图 1 结构前缘点应力时间历程Fig. 1 Stress-time relation of the leading edge structure
2.2 结构可靠性分析 2.2.1 试验设计

 图 2 各组样本仿真计算的应力时间历程Fig. 2 Stress-time relation of each simulation test
2.2.2 建立热应力的时变响应模型

2.2.3 材料强度的时变特征分析

 图 3 结构前缘点温度时间历程Fig. 3 Temperature-time relation of the leading edge structure

 图 4 材料强度时变数据Fig. 4 Time-varying strength data of the material
2.2.4 可靠度计算结果

 图 5 热结构可靠度R与时间的关系Fig. 5 Time-varying structural reliability of the high-temperature structure
2.3 结果对比

3 结 论

1) 对结构的热响应建立时变响应面模型并通过逐步回归确定得到待定参数的方法具有较高的精度.本文案例中,采用时变响应面模型对热应力进行拟合的相对误差小于0.1%.

2) 考虑材料强度退化效应的高温结构时变响应面法可高效地计算出高温结构可靠度与时间的关系,其在特定任务时间下的计算结果与传统计算方法所得结果一致.由于本文方法不需要针对特定时刻重复建立响应面模型,因此在保证计算精度的同时可大幅提高计算效率.

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#### 文章信息

MA Xiaobing, REN Hongdao, CAI Yikun

Time-varying response surface method for high-temperature structural reliability analysis

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(2): 198-202.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0142