Vol. 7, No. 6, 2012

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ISSN: 1559-3959
Nonlinear FEM analysis for beams and plate assemblages based on the implicit corotational method

Giovanni Garcea, Antonio Madeo and Raffaele Casciaro

Vol. 7 (2012), No. 6, 539–574
Abstract

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
Milestones
Received: 30 May 2012
Revised: 30 August 2012
Accepted: 14 September 2012
Published: 19 November 2012
Authors
Giovanni Garcea
Dipartimento di Modellistica per l’ingegneria
Università della Calabria
Via P. Bucci Cubo 39/C 87036 Rende (CS)
Italy
Antonio Madeo
Dipartimento di Modellistica per l’ingegneria
Università della Calabria
Via P. Bucci Cubo 39/C 87036 Rende (CS)
Italy
Raffaele Casciaro
Dipartimento di Modellistica per l’ingegneria
Università della Calabria
Via P. Bucci Cubo 39/C 87036 Rende (CS)
Italy