Nonlinear stochastic behavior of soft-core sandwich panels

The nonlinear stochastic behavior of soft-core sandwich panels and the evolution of uncertainty along the nonlinear path are investigated. The paper focuses on the way the geometrically nonlinear and unstable behavior is affected by uncertainty and considers, for the first time, the evolution of uncertainty along the unstable structural response. The structural modeling relies on the EHSAPT and its integration into the geometrically nonlinear stochastic regime. A tailored nonlinear FE model that is based on a variational formulation and an arc-length solution scheme are developed. The stochastic analysis adopts the Perturbation-based SFEM and its generalization for the evolution of uncertainty along the process axis. A numerical study demonstrates the stochastic methodology and explores the impact of uncertainty on the nonlinear structural behavior. The evolution of the stochastic stress resultants at the displaced end is studied along the two axes of evolution. The differences between the two representations and their physical and engineering significance are highlighted revealing significant changes to the uncertainty evolution pattern with the shift from global buckling to localized wrinkling instabilities. The representation of the stochastic results along the process axis also quantifies the level of uncertainty near critical and singular points where conventional analyses diverge.