结构静力分析的区间摄动有限元法

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。

INTERVAL PERTURBATION FINITE ELEMENT METHOD FOR STRUCTURAL STATIC ANALYSIS

Based on a new method for evaluation the bounds of system responses with interval parameters, the high-order solution methods of interval perturbation finite element method based on Taylor expansion and interval parameter perturbation finite element method are presented. A new interval perturbation method is introduced, in which the inverse matrix of an uncertain stiffness matrix is expressed as a series of Neumann expansion series, and the upper and lower bounds of the perturbation of structural responses were obtained. The presented method is used for the direct robustness evaluation of the uncertain structural responses, and hence it is named as interval robust perturbation finite element method. The precision and efficiency are compared among these three methods. The results of numerical examples show that the new interval perturbation finite element method has good accuracy and can be applied in the uncertain analysis and optimization for large-scale aerospace structure.