Analysis of Uncertain Structural Systems Using Interval Analysis

Abstract

The imprecision or uncertainty present in many engineering analysis/design problems can be modeled using probabilistic, fuzzy, or interval methods. This work considers the modeling of uncertain structural systems using interval analysis. By representing each uncertain input parameter as an interval number, a static structural analysis problem can be expressed in the form of a system of linear interval equations. In addition to the direct and Gaussian elimination-based solution approaches, a combinatorial approach (based on an exhaustive combination of the extreme values of the interval numbers) and an inequality-hased method are presented for finding the solution of interval equations. The range or interval of the solution vector (response parameters) is found to increase with increasing size of the problem in all of the methods. An interval-truncation approach is proposed to limit the growth of intervals of response parameters so that realistic and accurate solutions can be obtained in the presence of large amounts of uncertainty. Numerical examples are presented to illustrate the computational aspects of the methods and also to indicate the importance of the truncation approach in practical problems. The utility of interval methods in predicting the extreme values of the response parameters of structures is discussed.