This paper presents theory for the Lagrange co-rotational (CR) formulation of finite elements in the geometrically nonlinear analysis of 3D structures. In this paper strains are assumed to be small while the magnitude of rotations from the reference configuration is not restricted. A new best fit rotator and consistent spin filter are derived. Lagrange CR formulation is applied with Hybrid Trefftz Stress elements, although presented methodology can be applied to arbitrary problem formulation and discretization technique, f.e. finite volume methods and lattice models, discreet element methods. Efficiency of CR formulation can be utilized in post-buckling stability analysis, damage and fracture mechanics, modelling of dynamic fragmentation of bodies made from quasi-brittle materials, solid fluid interactions and analysis of post-stressed structures, discreet body dynamics.
@article{arxiv.1110.5321,
title = {Corotational formulation for 3d solids. An analysis of geometrically nonlinear foam deformation},
author = {Łukasz Kaczmarczyk and Tomasz Koziara and Chris J. Pearce},
journal= {arXiv preprint arXiv:1110.5321},
year = {2013}
}