Reliability Analysis of Interval Parameters Bar Structures with Affine Arithmetic
By representing the uncertain parameters as interval numbers, the reliability index equations of bars structures were obtained. A modified matrix affine arithmetic polynomial evaluation method plus recursive derivative information was proposed in this paper, which keeps all powers of noise symbols without approximation. Based on the nature that affine forms and intervals variables could transform each other, affine forms of bounded uncertain variables and modified affine arithmetic including derivative information for interval univariate polynomial evaluation were introduced into modeling and calculating non-probabilistic reliability index. An extended beam example and a ten-bar truss structure example were provided to illustrate the validity and feasibility of the presented procedures.
L.Y. Xie, M.N. James, Y.X. Zhao and W.X. Qian
G.L. Liu et al., "Reliability Analysis of Interval Parameters Bar Structures with Affine Arithmetic", Advanced Materials Research, Vols. 118-120, pp. 201-205, 2010