Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation

Abstract

The paper presents a complete experimental validation of an advanced computational methodology adapted to the nonlinear post-buckling analysis of geometrically nonlinear structures in presence of uncertainty. A mean nonlinear reduced-order computational model is first obtained using an adapted projection basis. The stochastic nonlinear computational model is then constructed as a function of a scalar dispersion parameter, which has to be identified with respect to the nonlinear static experimental response of a very thin cylindrical shell submitted to a static shear load. The identified stochastic computational model is finally used for predicting the nonlinear dynamical post-buckling behavior of the structure submitted to a stochastic ground motion.

Uncertainty Quantification for Nonlinear Reduced-Order Elasto-Dynamics Computational Models

“…This would imply that the linear mistuning would be considered by extracting the random linear part from random matrix [K], keeping the nonlinear quadratic and cubic terms as deterministic terms for the nonlinear calculations. Nevertheless, this case has been investigated in [7] in the context of the post-buckling nonlinear dynamical analysis of an uncertain cylindrical shell. With such method, a strong nonlinear level of uncertainty δ N L K = 0.45 yielded an equivalent linear uncertainty level δ L K = 0.025 for the linear part of the structure, yielding a subsequent scale effect, preventing to distinguish any differences between the linear and nonlinear uncertainty cases.…”

“…Solving the stochastic nonlinear equations in the time-domain with efficient algorithms based on the arc-length methods [7,8] All the details concerning the theoretical construction of such methodology and its application to a large finite element model of an industrial bladed-disk can be found in [8].…”

“…Choosing the projection basis as the linear eigenmodes of the tuned structure [10] 5. Direct construction of the mean nonlinear reduced-order model (MEAN-NL-ROM) by projection of the finite element operators on the chosen projection basis [6,7] 6. Implementing the mistuning through the nonparametric probabilistic framework [11] and controlling the mistuning level by dispersion parameter = (δ M , δ D , δ C , δ Kc , δ K ), each scalar controlling the dispersion of the random mass, damping, gyroscopic coupling, centrifugal stiffness, elastic stiffness matrices.…”

“…Uncertainties have then to be taken into account in the computational models by using probabilistic models as soon as the probability theory can be used. Recently, a computational methodology adapted to the uncertainty quantification of structures in presence of geometric nonlinearities has been proposed and validated in the context of structural dynamics [6,7,8]. The implementation of random uncertainties is carried out through the nonparametric probabilistic framework from a nonlinear reduced-order model.…”

Computational Vibroacoustics in Low- and Medium- Frequency Bands: Damping, ROM, and UQ Modeling

“…Several works have been published concerning experimental validation of the nonparametric probabilistic approach of both the computational model-parameter uncertainties and the model uncertainties induced by modeling errors (e.g., [96,[106][107][108][109][110][111]). …”