Uncertainty analysis of large structures using universal grey number theory

Abstract

In this paper, a new uncertainty-based approach, termed the universal grey number-based Gaussian elimination method, is presented for the analysis of large structures that require the solution of systems of linear interval algebraic equations. Although exact ranges of the solution can be found using the enumeration method, it is known to be computationally expensive as it requires a large number of analyses. Although interval analysis has been used by some researchers, it is found to lead to wider ranges of the response quantities due to the dependency problem. Hence, modified procedures such as the truncation-based interval analysis have been suggested in the literature to overcome the dependency problem. In fact, no interval analysis-based method is available in the literature for solving large number of interval linear equations accurately. The present method is expected to overcome the limitations associated with the available methods in terms of accuracy and computational effort. To demonstrate the accuracy of the proposed method, the stress analysis of several truss structures under specified interval values of input parameters is considered. It is shown that the proposed method yields accurate results more efficiently with less computational effort compared to the truncation-based interval analysis and enumeration method.