Analysis of uncertain structural systems using interval analysis

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 parameter as an interval number, a static structural analysis problem can be expressed in the form of a system of linear interval equations. The direct method (equivalent to Gaussian elimination), an inequality-based method (that identifies the solution domain of the system), and a combinatorial approach (based on exhaustive combination of the extreme values of the interval numbers) are investigated for finding the solution of interval equations. By comparing the extreme values of stresses given by the various methods, the relative performance of the methods is studied. An interval-truncation approach is outlined to limit the growth of intervals of response parameters so that realistic solutions can be obtained in the presence of large amounts of uncertainty. The practical utility of interval methods in the analysis/design of uncertain engineering systems is discussed.