Koiter postbuckling FEM analysis of plate assemblages using a corotational formulation

A general strategy to recover objective nonlinear structural FE models based on corotational description and aimed to Koiter asymptotic approach has been discussed in recent papers. The corotational description has been used as a general tool to satisfy the objectivity requirement by referring each element to a local frame which moves (rotates) with the element, so filtering its rigid motion. In this description, the nonlinearity of the problem derives essentially from the change of reference, from the global fixed frame to the local one, the strain energy being governed by their relative rotations. The great advantage of the method consists in the discretization phase of the process. The construction of the FE model, for the smallness of the displacements and rotations in the corotational frame, is the same of the linear elastic case, with great advantage in term of simplicity and of reuse of standard FE library. The main difficulty is in the determination of the relationship between finite element parameters in the corotational frame and the corresponding quantities in the fixed global frame. In particular, in finite kinematics the presence of finite rotations noticeably complicates the algebra for obtaining kinematics expressions. The above strategy is here developed with reference to plate assemblages based on the Reissner-Mindlin model. The starting point is an high-performance plate finite element, based on a mixed stress formulation and with a good behavior in the linear/elastic case. Here, a quadrilateral 4-node finite element involving compatible displacements (6 displacement dofs per node) is used. In particular, a displacement scheme à la Allman, involving drilling rotations, is used for the in-plane behavior, and 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. Assuming a corotational frame, so that the average of local relative rotations is zero, basic expressions for the first four corotational derivatives of the strain energy are provided, allowing the set up of a fourth–order accurate asymptotic analysis, starting from standard, locally linear finite elements. 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 coupled multimodal buckling is shown by comparison with the commercial code ABAQUS and the asymptotic code KASP.