Improving interval analysis in finite element calculations by means of affine arithmetic

Interval-based uncertainty models have proven to be well-suited for structural safety engineering with few data at hand. The practical use of interval analysis is hindered by the dependency problem, which leads to an overestimation of the uncertainty on the results. Affine arithmetic is a generalization of interval arithmetic that accounts for the relation between variables. By circumventing the dependency problem, it yields more accurate results. This paper presents a novel method to solve affine systems of linear equations, which allows for the application of affine arithmetic in finite element analysis. The proposed procedure is illustrated with three applications.