Abstract

EVANGELISTA JR, Francisco  and  AFANADOR-GARCIA, Nelson. A polynomial chaos expansion approach to the analysis of uncertainty in viscoelastic structural elements. Dyna rev.fac.nac.minas [online]. 2016, vol.83, n.199, pp.172-182. ISSN 0012-7353.  https://doi.org/10.15446/dyna.v83n199.53834.

The uncertainty propagation in mechanical systems through model calculations was analyzed in this article by stochastic polynomial series of standardized random variables called Polynomial Chaos Expansion. This paper aimed to simulate the propagation of uncertainty in more complex mechanical models such viscoelastic structures which involves time dependent parameters characterization of materials, interconversion of mathematical functions through Laplace transform, and resolution of the constitutive equation through convolution integrals. The application of multi-dimensional Hermite polynomials series allowed the prediction of the randomness of the output vector. In this work it was demonstrated that a polynomial chaos expansion accurately estimated the spread of uncertainty of the random variables. The results showed that the material parameters not only affects the coefficient of variation of the displacements, but also dictates the type and spread of the tails of the probability density function for the structural output.

Keywords : Stochastic analysis; Polynomial chaos expansions; Viscoelasticity; relaxation modulus.

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