A unified formulation of small-strain corotational finite elements: I. Theory

This paper presents a unified theoretical framework for the corotational (CR) formulation of finite elements in geometrically nonlinear structural analysis. The key assumptions behind CR are: (i) strains from a corotated configuration are small while (ii) the magnitude of rotations from a base configuration is not restricted. Following a historical outline the basic steps of the element independent CR formulation are presented. The element internal force and consistent tangent stiffness matrix are derived by taking variations of the internal energy with respect to nodal freedoms. It is shown that this framework permits the derivation of a set of CR variants through selective simplifications. This set includes some previously used by other investigators. The different variants are compared with respect to a set of desirable qualities, including self-equilibrium in the deformed configuration, tangent stiffness consistency, invariance, symmetrizability, and element independence. We discuss the main benefits of the CR formulation as well as its modeling limitations.