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.