FINITE ROTATION ANALYSIS AND CONSISTENT LINEARIZATION USING PROJECTORS

A systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accommodate finite rotation analysis. This procedure is a generalization of the work presented in Computers and Structures, Volume 30, pp. 257-267. The basis of our approach is the element-independent co-rotational algorithm, where the element rigid body motion (translations and rotations) is separated from the deformational part of its total motion. The variation of this co-rotational relation results in a projector matrix, with the property that a consistent internal force vector is invariant under its action. The consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector. This results in an unsymmetric tangent matrix whose anti-symmetric part depends on the out-of-balance force vector. In this paper we prove that using the symmetric part of the tangent matrix, the Newton iteration retains its quadratic rate of convergence. This approach has been used to solve a number of large rotation test example problems. The results demonstrate that it is possible to analyze structures undergoing large rotations within a general co-rotational framework, using simple and economical finite elements. The resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre- and post-processors to the element routines.