This paper examines the variability of predicted responses when multiple stress–strain curves (reflecting variability from replicate material tests) are propagated through a finite element model of a ductile steel can being slowly crushed. Over 140 response quantities of interest (QOIs) (including displacements, stresses, strains, and calculated measures of material damage) are tracked in the simulations. Each response quantity's behavior varies according to the particular stress–strain curves used for the materials in the model. We desire to estimate or bound response variation when only a few stress–strain curve samples are available from material testing. Propagation of just a few samples will usually result in significantly underestimated response uncertainty relative to propagation of a much larger population that adequately samples the presiding random-function source. A simple classical statistical method, tolerance intervals (TIs), is tested for effectively treating sparse stress–strain curve data. The method is found to perform well on the highly nonlinear input-to-output response mappings and non-normal response distributions in the can crush problem. The results and discussion in this paper support a proposition that the method will apply similarly well for other sparsely sampled random variable or function data, whether from experiments or models. The simple TI method is also demonstrated to be very economical.
Simple Effective Conservative Treatment of Uncertainty From Sparse Samples of Random Variables and Functions
Manuscript received June 16, 2017; final manuscript received February 24, 2018; published online April 30, 2018. Assoc. Editor: Siu-Kui Au.
This paper has been authored by Sandia Corporation under Contract No. DE-NA0003525 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the paper for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this paper, or allow others to do so, for United States Government purposes.
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Romero, V. J., Schroeder, B. B., Dempsey, J. F., Breivik, N. L., Orient, G. E., Antoun, B. R., Lewis, J. R., and Winokur, J. G. (April 30, 2018). "Simple Effective Conservative Treatment of Uncertainty From Sparse Samples of Random Variables and Functions." ASME. ASME J. Risk Uncertainty Part B. December 2018; 4(4): 041006. https://doi.org/10.1115/1.4039558
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