Keywords: co-rotational formulation, finite element method, solid finite elements, geometrically nonlinear analysis, consistent tangent stiffness matrix, polar decomposition, spin-fitter matrix.

The co-rotational formulation offers a fast and numerically stable pseudo-linear ap- proach for solving structural problems involving large displacements and small strains. In this study, two well-established co-rotational formulations, Crisfi eld’s and Felippa’s, are rewritten using a unifi ed notation to enable a direct comparison for 3D solid fi nite elements. Felippa’s consistent formulation targets beams and shells, while Crisfi eld’s approach includes 3D solids but is not fully consistent. Despite different initial appear- ances, the deformational displacement vectors and internal force vectors are shown to be mathematically identical, guaranteeing the same displacement response. However, the tangent stiffness matrices differ: Crisfi eld’s omits complex terms, resulting in slower convergence, whereas Felippa’s consistent version is expected to require fewer Newton–Raphson (NR) iterations. Additionally, this study presents easy-to-implement matrix forms of Crisfi eld’s matrix A and Felippa’s spin-fi tter matrix G, for 3D solid elements with a rotation matrix obtained via polar decomposition. This work lays the foundation for a forthcoming paper on a new consistent co-rotational formulation for 3D solid elements in a simple matrix form for effi cient nonlinear analysis.

download the full-text of this paper (PDF, 15 pages, 419 Kb)

go to the previous paper
go to the next paper
return to the table of contents
return to the volume description