Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances

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. (C) 2010 Elsevier B.V. All rights reserved.