A Newton iteration‐based interval analysis method for nonlinear structural systems with uncertain‐but‐bounded parameters

Abstract

AbstractIn this article, the propagating effect of uncertainties in nonlinear structural systems is investigated. Via considering uncertain‐but‐bounded parameters as interval variables, a Newton iteration‐based interval analysis method (NI‐IAM) is proposed to quantify the uncertainty of the nonlinear structural response, namely predicting the upper and lower bounds of the response. In the proposed method, a nonlinear structural system with uncertain interval parameters is described as a series of interval nonlinear equations. With Taylor series expansion, an interval iteration scheme is established to successively approximate the upper and lower bounds of the response based on the Newton method. The structural response bounds in every iteration step are updated by solving linear interval increment determination equations via the Lagrangian multiplier method. Thereout, an uncertain nonlinear problem is simplified to a series of uncertain linear issues. The convergence of the proposed method is further discussed in this article. Numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method by contrast with several existing methods. Moreover, the compatibility between numerical results of the perturbation‐based probabilistic method and the proposed method is then studied and verified.