Uncertainty quantification for random fields estimated from effective moduli of elasticity

Pierce-Brown, Jack; Neves, Luis C.; Brown, Donald L.

Abstract

The stochastic finite element method is a useful tool to calculate the response of systems subject to uncertain parameters and has been applied extensively to analyse structures composed of randomly heterogeneous materials. The methodology to estimate the parameters of the random field underlying a stochastic finite element model often utilises the midpoint approximation wherein material properties that are measured over a sample volume are treated as point observations of the random field at the centroid of the sample volume. This paper investigates the error induced by this approximation for the case of effective moduli of elasticity resulting from tensile loading as well as 3 and 4-point bending. A computer experiment has been performed consisting of the generation of synthetic stiffness profiles from a lognormal stochastic process, the calculation of effective properties as weighted harmonic averages and the estimation of random field parameters through the method of moments. The uncertainty in the parameter estimates is quantified and a recommendation is made as to which bending test is superior for obtaining random field parameter estimates with reference to the statistics of the base process and the tensile loading condition.

Citation

Pierce-Brown, J., Neves, L. C., & Brown, D. L. (2018). Uncertainty quantification for random fields estimated from effective moduli of elasticity. In Proceedings of the 8th International Workshop on Reliable Computing "Computing with Confidence", 16-18 July 2018, University of Liverpool, Liverpool, UK (51-62)

• Conference Name: 8th International Workshop on Reliable Computing "Computing with Confidence"
• Conference Location: Liverpool, UK
• Start Date: Jul 16, 2018
• End Date: Jul 18, 2018
• Acceptance Date: Jun 3, 2018
• Online Publication Date: Jul 16, 2018
• Publication Date: Jul 16, 2018
• Deposit Date: Jul 4, 2018
• Publicly Available Date: Jul 16, 2018
• Peer Reviewed: Peer Reviewed
• Pages: 51-62
• Book Title: Proceedings of the 8th International Workshop on Reliable Computing "Computing with Confidence", 16-18 July 2018, University of Liverpool, Liverpool, UK
• Chapter Number: 6
• ISBN: N/a
• Keywords: Uncertainty Quantification, Effective Elastic Modulus, Midpoint Approximation, Random Field Theory, Stochastic Finite Element Method
• Public URL: https://nottingham-repository.worktribe.com/output/947022
• Publisher URL: http://rec2018.uk/papers/proceedings/proceedings.pdf