INVESTIGADORES
ROSALES Marta Beatriz
congresos y reuniones científicas
Título:
STOCHASTIC BIFURCATION ON THE IMPACT PROBLEM BETWEEN TWO ELASTIC BODIES
Autor/es:
FERNANDO S. BUEZAS; MARTA B. ROSALES; RUBENS SAMPAIO
Lugar:
Salta
Reunión:
Congreso; MECOM 2012; 2012
Resumen:
An uncertainty quantification study is carried out in the problem of frontal collision of two
elastic bodies. The time of contact and the resultant force function involved during the collision are
the quantities of interest. If the initial conditions and the mechanical and geometrical properties were
known, the response prediction would be deterministic. However, if the data contains any uncertainty,
a stochastic approach becomes appropriate. Based on the Principle of Maximum Entropy (PME), and
under certain restrictions on the parameter values, we derive the probability density function (PDF) for
each of the stochastic parameters to construct a probabilistic model. Two cases are dealt with: one of a
collision involving two spheres and another of the collision of two discs. In the first case, a parameter
involving geometry and material properties is assumed stochastic. Since an analytical model exists, the
propagation of the uncertainty of the time of contact can be done analytically. However, the interaction
force function can only be computed from the solution of a nonlinear ordinary differential equation,
hence not analytically. Given the PDF of the parameter, the problem of uncertainty propagation is tackled
using Monte Carlo simulations. The comparison of both approaches yields an excellent agreement. With
respect to the collision of two discs, first the small deformation problem, within the Hertz theory, is
addressed with a Monte Carlo method. When the discs undergo large deformations, the problem is
approximated using the equations of Finite Elasticity discretized by the finite element method (FEM)
and combined with a 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 Poissons ratio. It is shown that under certain dispersion
ranges, the PDF of the interaction force function undergoes a qualitatively change exhibiting bimodality.