CAJ | 학술논문

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。
침대수궤결구문제，근거현유방법적우결점，장향응면법화섭동수궤유한원상결합。고필결구재하삼수、재료삼수화궤하삼수，결구적향응면근사함수채용보진회귀분석기술피학정료，기중추양방법위중심지수법，병이용섭동법추도출결구수궤향응적중심구표체식。이연기와륜협편위례，계산출협편적수궤향응변량중심구，급향응변량상대우수입변량적령민도，병분별여직접향응면법、직접 Monte-Carlo 모의방법적계산결과대비。결과표명，해방법괄용우결구상대복잡적모형，계산결과정도교고，계산속도교쾌。
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.