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基于新的区间参数系统响应界值的评估方法,推导了基于Taylor展开的区间摄动有限元法和区间参数摄动有限元法的高阶求解方法。并提出了一种新的区间摄动有限元法,该方法将刚度矩阵的逆矩阵用一系列Neumann展开级数来表示,最终得到结构响应摄动量的上下界限,是对结构响应鲁棒性的一种直接评估,因此称之为区间鲁棒摄动有限元法。比较了三种区间摄动有限元法的计算精度和计算效率。算例结果表明:区间鲁棒摄动有限元法具有较好的精度,能够适用于大型航空航天结构的不确定分析和优化。
Based on the new evaluation method of interval parameter system response bounds, the high-order solution method of interval perturbation finite element method and interval perturbation finite element method based on Taylor expansion is derived. A new method of interval perturbation finite element method is proposed. The inverse matrices of the stiffness matrix are expressed by a series of Neumann expansions. Finally, the upper and lower limits of the structural response perturbation are obtained, which are robust to structural response A direct evaluation, therefore, is called the interval robust perturbation finite element method. The computational accuracy and computational efficiency of three kinds of interval perturbation finite element method are compared. The results show that the robust finite perturbation method has good accuracy and can be applied to the uncertainty analysis and optimization of large aerospace structures.