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 thin-walled 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.
Keywords
geometrically exact beam and shell theories, corotational
description, postbuckling analysis