Title: Interval approach for nondeterministic linear static finite element method in continuum mechanics problems

Authors: Hao Zhang, Rafi L. Muhanna

Addresses: School of Civil Engineering, The University of Sydney, NSW 2006, Australia. ' School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

Abstract: This paper presents a non-traditional treatment for uncertainties in linear static Finite Element Method (FEM). Uncertainties are introduced as bounded possible values (intervals). FEM with interval parameters estimates the range of the system response based on the bounds of the system parameters. The obtained results should be accurate and efficiently computed. Toward this end, a rigorous interval FEM has been developed and applied to the continuum mechanics problems. The paper compares the different scenarios how the uncertain field (e.g. the interval modulus of elasticity of a plate) is discretised.

Keywords: interval analysis; finite element method; uncertainties; nondeterministic linear static FEM; continuum mechanics; interval arithmetic; Monte Carlo sampling; modulus of elasticity.

DOI: 10.1504/IJRS.2009.026841

International Journal of Reliability and Safety, 2009 Vol.3 No.1/2/3, pp.201 - 217

Available online: 27 Jun 2009 *

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