Static stochastic analysis in cylindrical panels’ geometry

Resumo

Cylindrical panels under uncertainties, described by a uniform probability density function, on
parameters such as thickness and radius, are investigated when static loading is submitted. Firstly, an analytical
approach - based on the equilibrium equations governed by Donnell’s nonlinear shallow shell theory, Airy’s stress
function and standard Galerkin method - is taken to evaluate the effects of parameters uncertainties on the buckling
load and post critical nonlinear equilibrium. Then, an approach based on the finite element method is considered
to model the same geometry where the mesh is composed by shell elements and its convergence is conducted in
terms of buckling load. The nonlinear equilibrium path is obtained through the modified Riks method and a
perturbation parameter. In both methodologies, a set of deterministic samples simulates the stochastic system,
which are evaluated from Chi-Squared hypothesis test. The uncertainty in the thickness results in a stochastic
system where the nonlinear equilibrium path can be described as a uniform probability distribution. On the other
hand, the radius shows a stretching along the curve where a two-component Gaussian mixture fits better the
obtained response where the mean of axial load as respect to a certain displacement cannot be represented by the
mean of its lower and upper boundaries.