Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

In our previous paper the implicit corotational method (ICM) was presented as a general procedure for recovering objective nonlinear models fully reusing the information obtained by the corresponding linear theories.The present work deals with the implementation of the ICM as a numerical tool for the finite element analysis of nonlinear structures using either a path-following or an asymptotic approach.Different aspects of the FEM modeling are discussed in detail, including the numerical handling of finite rotations, interpolation strategies, and equation formats.Two mixed finite elements are presented, suitable for nonlinear analysis: a three-dimensional beam element, based on interpolation of both the kinematic and static fields, and a rotation-free thin-plate element, based on a biquadratic spline interpolation of the displacement and piece-wise constant interpolation of stress.Both are frame invariant and free from nonlinear locking.A numerical investigation has been performed, comparing beam and plate solutions in the case of thinwalled beams.The good agreement between the recovered results and the available theoretical solutions and/or numerical benchmarks clearly shows the correctness and robustness of the proposed approach as a general strategy for numerical implementations.This paper has been developed within the national joint research project "Performance-based modeling and analysis of nonlinear structures," supported by the Italian Ministry of University Scientific and Technology Research (MIUR).We would like to thank all the participants in the project for their comments and suggestions.Special thanks are addressed to Giuseppe Zagari, for his help in setting up the computer codes and performing the numerical tests.