Asymptotic FEM analysis of folded structures using a corotational formulation

The general strategy for recovering objective nonlinear structural FE models based on corotational description and aimed to Koiter asymptotic approach [1] is here applied for the analysis of folded structures. The starting point is an high-performance shell finite element, based on a mixed stress-displacement formulation and whit a good behavior in the linear/elastic case. A quadrilateral 4-nodes finite element involving 6 dofs per node is used. The in–plane behavior is based on a displacement scheme `a la Allman [2], involving the drilling rotations and an enriched cubic shape function ruled by the rotations average and without penalty constraints. Whereas a linked displacement interpolation is used for the out-plane behavior. The stress resultants approximation is ruled by the minimum number of parameters, both for the in-plane and the out-plane part. The element is free from locking and spurious zero-energy modes. This guaranty good performance and reliability in nonlinear context. Several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach. In particular, the accuracy in reproducing the nonlinear equilibrium path in both cases of monomodal and intercative multimodal buckling is shown by comparison with the commercial program ABAQUS [4] and the asymptotic program KASP [5].