  The use of nonlinear projection matrix in co-rotational (CR) analysis was
pioneered by Rankin and Nour-Omid in 1990s (Computers & Structures, 30 (1988)
257-267; Comput. Methods Appl. Mech. Engrg., 93 (1991) 353-384), and has almost
became a standard manner for CR formulations deduction over the past thirty
years. This matrix however relies heavily on a hysterical and sophisticated
derivation of the variation of the local displacements to the global ones,
leading to complicated expressions for the internal force vector and the
tangent stiffness matrix, which may devalue the simplicity and convenience for
the original intention of using CR approach. This paper begins by making a
discussion on existing element independent CR formulation and the objective is
to develop a new and simple framework for general CR analysis that avoids using
conventional nonlinear projection matrix. Multiple numerical examples involving
various kinds of elements and different choices of element local CR frame are
presented to demonstrate the performance of the proposed framework. The
outcomes show that for all the examples the accuracy of the results are
comparable with those obtained in conjunction with conventional nonlinear
projection matrix.
