Interval Finite Element Analysis- Concepts and Recent Advances

Recently, criticism has arisen regarding the general application of the probabilistic concept when available information is limited. Because subjective probabilistic results have little value in compare to their computational cost. Consequently, alternative Non- Probabilistic approaches have been introduced for Non-deterministic numerical modeling. They enable realistic reliability assessment that considers the uncertain aspects of the analysis and design. In this context, Interval and Fuzzy and more recently Probability Bounds Analysis (PBA) are becoming increasingly popular for the analysis of numerical models. In the Interval approach, uncertainties are considered to be within a predefined range. The Fuzzy approach extends this methodology by introducing a level of membership that represents to what extent a certain value is member of the range of possible input values. This concept provides a tool to express a degree of possibility for a certain value. Based on α sublevel technique, the Fuzzy analysis requires the consecutive solution of a number of related interval problems. PBA incorporate the traditional probability methods with the concept of Interval. A PBA can be broken down to a series of Interval analysis. Thus, current research activities on this subject mainly concentrate on the actual solution and implementation of Interval analysis. In recent literature, the application of the interval concept for classical FEA has been studied extensively. While the solution of a set of Interval equations is easily formulated, the actual solution of this problem is extremely problematic. Nevertheless, some solution schemes with different nature have been developed. The aim of this paper is to give an overview of the recent activities in numerical implementations of the Interval and PBA by FEM in applied mechanics.