Publicado

2016-10-01

Un enfoque de polinomio de expansión de caos al análisis de la incerteza en elementos estructurales visco elásticos

A polynomial chaos expansion approach to the analysis of uncertainty in viscoelastic structural elements

DOI:

https://doi.org/10.15446/dyna.v83n199.53834

Palabras clave:

Análisis estocástico, Polinomios de expansión de caos, Viscoelasticidad, módulo de relajación. (es)
Stochastic analysis, Polynomial chaos expansions, Viscoelasticity, relaxation modulus. (en)

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La propagación de la incerteza en sistemas mecánicos a través de modelos de cálculo fue analizado en este artículo por series de polinomios estocásticos de variables aleatorias estandarizadas llamados Polinomios de expansión de caos. Este artículo tuvo como objetivo simular la propagación de la incerteza en modelos mecánicos más complejos tales como estructuras visco elásticas el cual implica caracterización de parámetros dependientes del tiempo de materiales, interconversión de funciones matemáticas a través de transformada de Laplace, y resolución de la ecuación constitutiva mediante integrales de convolución. La aplicación de series de polinomios Hermite multidimensionales permitió la predicción de la aleatoriedad del vector de salida. En este trabajo se demostró que un polinomio de expansión de caos estima adecuadamente la propagación de la incerteza de las variables aleatorias. Los resultados mostraron que el parámetro material no solo afecta los coeficientes de variación del desplazamiento, sino también dicta el tipo y propagación de las colas de la función de densidad de probabilidad para la respuesta estructural.
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.

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[1]
“Un enfoque de polinomio de expansión de caos al análisis de la incerteza en elementos estructurales visco elásticos”, DYNA, vol. 83, no. 199, pp. 172–182, Oct. 2016, doi: 10.15446/dyna.v83n199.53834.

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