An iteration method for predicting static response of nonlinear structural systems with non-deterministic parameters

Abstract

• Important source of the limitation of the point-based iteration method is pointed out. • Interval-based iteration method is proposed to predict confident bounds of nonlinear static response. • Difference between the interval-based iteration method and the point-based iteration method is discussed. Confident numerical method is a crucial issue in the field of structural health monitoring. This paper focuses on uncertainty propagation in nonlinear structural systems with non-deterministic parameters. An interval-based iteration method is proposed on the basis of interval analysis and Taylor series expansion. The proposed method aims to improve the bounds of static response calculated by the point-based iteration method. In the proposed method, the iterative interval of static response is updated by revising the lower and upper bounds, respectively, which is the essential difference in comparison with the previous point-based iteration method. In this paper, interval parameters are employed to quantify the non-deterministic parameters instead of random parameters in the case of insufficient sample data. Iterative scheme is established based on the first-order Taylor series expansion. For the implementation of interval-based iteration method, a general procedure is formulated. Moreover, the important source of the limitation of point-based iteration method is revealed profoundly, and the good performance of the proposed method is demonstrated by three numerical comparisons.