Solving algebraic problems with high accuracy
Proc. of the symposium on A new approach to scientific computation
Bounding the solution of interval linear equations
SIAM Journal on Numerical Analysis
Perturbation finite element method of structural analysis under fuzzy environments
Engineering Applications of Artificial Intelligence
Finite Elements in Analysis and Design
Fuzzy structural analysis based on fundamental reliability concepts
Computers and Structures
Interval analysis of acoustic field with uncertain-but-bounded parameters
Computers and Structures
Engineering Applications of Artificial Intelligence
Finite Elements in Analysis and Design
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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.