An efficient iterative model reduction method for stochastic systems having geometric nonlinearities

Abstract

The dynamic analysis of systems has several applications in the project or monitoring and controlling machines and equipments. In particular, the analysis of nonlinear systems has academic and industrial appeal for owning many particularities such as structural integrity, models updating, stability and real-time predictability. Those particularities complicate the study of these models. However, the development of more representative mathematical models requires normally costly computations. By considering the uncertainties associated with the fabrication process (geometrical dimensions, physical and material properties), as well as those related to the operational conditions (boundary conditions, external forces, etc.), it complicates further the analysis of those nonlinear systems. Thus, this paper proposes a methodology to analyze nonlinear systems subjected to uncertainties using the stochastic finite element method. In view of the high computational cost needed to construct the confidence region predicted with the stochastic nonlinear computational model, it is proposed herein a new model reduction method based on the construction of an adaptive iterative enriched basis to deal with the stochastic nonlinear system addressed herein composed by a thin rectangular plate used as an application. The results demonstrate clearly the efficiency and accuracy of the proposed method as an efficient tool to approximate the nonlinear responses of more complex nonlinear systems subjected to uncertainties. Also, it demonstrates the relevance of taking into account the uncertainties in the modeling of nonlinear systems to consider more realistic situations.