Nonlinear stochastic evolution of spatial uncertainty along the process axis

Abstract

This paper builds upon the existing concept of process axis analysis in strongly nonlinear structural problems by introducing a novel approach for assessing the evolution of spatial uncertainty. Specifically, it adapts the stochastic perturbation method to enable Random Field representation of uncertainty and analyze its effect along the process axis. As an example, the delamination process of a composite beam bonded to a substrate using an adhesive layer is looked at. The strongly nonlinear physical behavior and the uncertainty that accompanies such behavior are investigated along the axis of the nonlinear delamination process. This approach is innovatively developed to allow a random field representation of uncertainty by the adaptation of the stochastic perturbation method to the process axis analysis. Numerical results are compared with reference ones obtained by quadrature-rule numerical integration and Monte Carlo simulation. The ability to handle strongly nonlinear problems while avoiding the singularity and divergence of the stochastic analysis near snap-through and snap-back folds, achieved by means of the projection of the stochastic perturbation method to the process axis, and the representation of the parametric and spatial uncertainties of the structural properties by Random Fields are among the innovative and original contributions of the present work.