基于响应面函数的摄动随机有限元方法研究

Study on Perturbation Stochastic Finite Element Method Based on Response Surface Function

针对随机结构问题,根据现有方法的优缺点,将响应面法和摄动随机有限元相结合。考虑结构载荷参数、材料参数和几何参数,结构的响应面近似函数采用步进回归分析技术被确定了,其中抽样方法为中心指数法,并利用摄动法推导出结构随机响应的中心矩表达式。以燃气涡轮叶片为例,计算出叶片的随机响应变量中心矩,及响应变量相对于输入变量的灵敏度,并分别与直接响应面法、直接Monte-Carlo模拟方法的计算结果对比。结果表明,该方法适用于结构相对复杂的模型,计算结果精度较高,计算速度较快。

Aiming at problem of the stochastic structure, according to the merits and demerits of the existing methods, the response surface method and perturbation-based stochastic finite element method are combined. Considering structure load parameters, material parameters and geometrical parameters, the approximate function of response surface structure is determined by using step regression analysis techniques, the sample of which is taken by the center index design method. And the central moment expression of the structure random response is derived by using perturbation method. Taking the gas turbine blade as an example, the central moment of the random response variables and the sensitivity of response variable corresponding to the input variables for the blade are calculated. And it is contrasted with the calculation results of direct response surface method and direct Monte-Carlo simulation method respectively. The results show that the method is suitable for a relatively complex structure model. The precision of computing result is higher, and the calculation speed is faster.