Uncertainty quantification in the collision of two discs

FERNANDO S. BUEZAS; MARTA B. ROSALES; RUBENS SAMPAIO

Buenos Aires

Congreso; IV Congreso de Matemática Aplicada, Computacional e Industrial; 2013

ASAMACI

The propagation of parameter uncertainties is analyzed in the impact problem of two discs. Focus is posed on the variables time of contact and the impact force involved during the collision. The probability density function (PDF) for each of the stochastic parameters are derived via the Principle of Maximum Entropy (PME). The problem is addressed first for small deformations, within the Hertz theory, using Monte Carlo simulations. When the discs undergo large deformations, the equations of Finite Elasticity are discretized by the finite element method (FEM) and combined with Monte Carlo simulations. In a first illustration, the modulus of elasticity is assumed stochastic with a gamma PDF. Further, the disc collision problem is analyzed when two parameters are stochastic: the modulus of elasticity and the Poisson´s ratio. It is shown that under certain dispersion ranges, the PDF of the interaction force function undergoes a qualitatively change exhibiting bimodality.