Uncertainty in Boundary Conditions - An Interval Finite Element Approach.

In this work, we introduce an interval formulation that accounts for uncertainty in supporting conditions of structural systems. Uncertainty in structural systems has been the focus of a wide range of research. Different models of uncertain parameters have been used. Conventional treatment of uncertainty involves probability theory, in which uncertain parameters are modeled as random variables. Due to specific limitation of probabilistic approaches, such as the need of a prior knowledge on the distributions, lack of complete information, and in addition to their intensive computational cost, the rationale behind their results is under debate. Alternative approaches such as fuzzy sets, evidence theory, and intervals have been developed. In this work, it is assumed that only bounds on uncertain parameters are available and intervals are used to model uncertainty. Here, we present a new approach to treat uncertainty in supporting conditions. Within the context of Interval Finite Element Method (IFEM), all uncertain parameters are modeled as intervals. However, supporting conditions are considered in idealized types and described by deterministic values without accounting for any form of uncertainty. In the current developed approach, uncertainty in supporting conditions is modeled as bounded range of values, i.e., interval value that capture any possible variation in supporting condition within a given interval. Extreme interval bounds can be obtained by analyzing the considered system under the conditions of the presence and absence of the specific supporting condition. A set of numerical examples is presented to illustrate and verify the accuracy of the proposed approach.