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Fuzzy Sets and Systems - Fuzzy intervals
Interval eigenvalue analysis for structures with interval parameters
Finite Elements in Analysis and Design
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Computer experiments and global optimization
Computer experiments and global optimization
Algorithm 847: Spinterp: piecewise multilinear hierarchical sparse grid interpolation in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Interval and fuzzy dynamic analysis of finite element models with superelements
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Fuzzy Sets and Systems
A new uncertainty analysis for the transformation method
Fuzzy Sets and Systems
An interdependency index for the outputs of uncertain systems
Fuzzy Sets and Systems
Systems of fuzzy equations in structural mechanics
Journal of Computational and Applied Mathematics
Computing expensive multivariate functions of fuzzy numbers using sparse grids
Fuzzy Sets and Systems
Applied Fuzzy Arithmetic: An Introduction with Engineering Applications
Applied Fuzzy Arithmetic: An Introduction with Engineering Applications
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Computers and Structures
Interval analysis of acoustic field with uncertain-but-bounded parameters
Computers and Structures
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The objective of this paper is to give a general overview of recent research activities on non-probabilistic finite element analysis and its application for the representation of parametric uncertainty in applied mechanics. The overview focuses on interval as well as fuzzy uncertainty treatment in finite element analysis. Since the interval finite element problem forms the core of a fuzzy analysis, the paper first discusses the problem of finding output ranges of classical deterministic finite element problems where uncertain physical parameters are described by interval quantities. Different finite element analysis types will be considered. The paper gives an overview of the current state-of-the-art of interval techniques available from literature, focussing on methodological as well as practical aspects of the presented methods when their application in an industrial context is envisaged. Their possible value in the framework of applied mechanics is discussed as well. The paper then gives an overview of recent developments in the extension of the interval methods towards fuzzy finite element analysis. Recent developments in the framework of the transformation method as well as optimisation-based procedures are discussed. Finally, the paper concentrates specifically on implementation strategies for the application of the interval and fuzzy finite element method to large FE problems.