We provide a robust finite element formulation for quantitative prediction of surface wrinkling of pressurized elastic shells on soft substrates. Our theory is build on three basic assumptions which involve thin shell kinematics, the approximation of the substrate response by a Winkler foundation and a model order reduction of the displacement field. Our element keeps all the nonlinear terms of the reduced model. The proposed formulation does not require any perturbations, either in the initial geometry or in the load, to incite the transition from fundamental to secondary equilibrium path for the considered set of shells, due to inherent asymmetric imperfections in the mesh. Numerical simulations using the derived element and an advanced path-following method on full spheres, hemispheres and spheroids show a very good quantitative agreement with theoretical predictions and experiments on the characteristic wavelength of the pattern as well as the qualitative depiction of the pattern evolution.
COBISS.SI-ID: 8813409
We propose an efficient computational model for predicting the surface wrinkling in axially compressed bi-layer cylindrical shell-substrate composites. To capture the transitions between the wrinkling modes in the far post-buckling regime, we use implicit dynamics. In this context we apply a generalized and an energy-decaying time stepping schemes that numerically dissipate in the high frequency range. The other components of the model are a geometrically exact, rotation-less, nonlinear shell finite element for the cylinder and an elastic foundation that represents the substrate. We show that the proposed computational model predicts the wrinkling pattern transition from axisymmetric to diamond-like mode, which is consistent with the numerical and laboratory experiments reported earlier. Furthermore, the results of our computational model show the existence of several diamond-like mode jumps in the post-buckling regime, a result that has not yet been reported for the axially compressed shell-substrate cylinders.
COBISS.SI-ID: 9108321