Implicit dynamic buckling analysis of thin‐shell isogeometric structures considering geometric imperfections

Abstract

In continuation of our previous work on nonlinear stability analysis of trimmed isogeometric thin shells, this contribution is an extension to dynamic buckling analyses for predicting reliably complex snap‐through and mode‐jumping behavior. Specifically, a modified generalized‐α$$ \alpha $$ time integration scheme is used and combined with a nonlinear isogeometric Kirchhoff–Love shell element to provide second‐order accuracy while introducing controllable high‐frequency dissipation. In addition, a weak enforcement of essential boundary conditions based on a penalty approach is considered with a particular focus on the inhomogeneous case of imposed prescribed displacements. Moreover, we propose a least‐squares B‐spline surface fitting approach and corresponding error measures to model both eigenmode based and measured geometric imperfections. The imperfect geometries thus obtained can be naturally integrated into the framework of isogeometric nonlinear dynamic shell analysis. Based on this idea, the different modeling methods and the influence of the appropriately considered geometric imperfections on the dynamic buckling behavior can be investigated systematically. Both perfect and geometrically imperfect shell models are considered to assess the performance of the proposed method. We compare our method with established developments in this field and demonstrate superior achievements with regard to solution quality and robustness.