Title: A new interval finite element formulation with the same accuracy in primary and derived variables

Authors: M.V. Rama Rao, Robert L. Mullen, Rafi L. Muhanna

Addresses: Department of Civil Engineering, Vasavi College of Engineering, Hyderabad 500 031, India. ' Department of Civil and Environmental Engineering, College of Engineering and Computing, University of South Carolina, Columbia, SC 29208, USA. ' Georgia Institute of Technology, Atlanta, GA 31407, USA

Abstract: This paper addresses the main challenge in interval computations, which is to minimise the overestimation in the target quantities. When sharp enclosures for the primary variables are achievable in a given formulation, such as the displacements in interval finite elements, the calculated enclosures for secondary or derived quantities, such as stresses and strains, are usually obtained with significantly increased overestimation. One should follow special treatment in order to decrease the overestimation in the derived quantities. In this work, we introduce a new formulation for Interval Finite Element Methods (IFEM) where both primary and derived quantities of interest are included in the original uncertain system as primary variables. The formulation is based on the variational approach and the Lagrange multiplier method by imposing certain constraints that allows the Lagrange multipliers themselves to be the derived quantities. Numerical results of this new formulation are illustrated in a number of example problems.

Keywords: interval FEM; IFEM; uncertainty; dependent variables; finite element method; FEM; overestimation; Lagrange multiplier.

DOI: 10.1504/IJRS.2011.041184

International Journal of Reliability and Safety, 2011 Vol.5 No.3/4, pp.336 - 357

Received: 29 Jul 2010
Accepted: 08 Nov 2010
Published online: 31 Mar 2015 *

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