B-spline based interval field decomposition method

Abstract

In this paper, we contribute a new B-spline based interval field decomposition method as a non-probabilistic approach that takes into account local effects in interval field modelling. With B-spline basis functions, the interval field formulation is highly intuitive and easy to construct. The computational efficiency outperforms the traditional local interval field decomposition method. The explicit expression of the proposed method facilitates the use of optimisation methods in determining field bounds where deterministic local values are available. The proposed method can incorporate the use of truncated hierarchical B-spline basis functions and multi-patch stitching method that facilitate modelling of inhomogeneous interval fields, which effectively address the spatial variability of the parameters describing the interval field. A numerical case of a simply supported beam with non-deterministic material parameters subjected to external loads is performed to illustrate the applicability of the proposed method.