Interval and Subinterval Analysis Methods of the Structural Analysis and Their Error Estimations

In this paper, the interval analysis method is introduced to calculate the bounds of the structural displacement responses with small uncertain levels' parameters. This method is based on the first-order Taylor expansion and finite element method. The uncertain parameters are treated as the intervals, not necessary to know their probabilistic distributions. Through dividing the intervals of the uncertain parameters into several subintervals and applying the interval analysis to each subinterval combination, a subinterval analysis method is then suggested to deal with the structures with large uncertain levels' parameters. However, the second-order truncation error of the Taylor expansion and the linear approximation of the second derivatives with respect to the uncertain parameters, two error estimation methods are given to calculate the maximum errors of the interval analysis and subinterval analysis methods, respectively. A plane truss structure is investigated to demonstrate the efficiency of the presented method.