Modified unified co-rotational framework with beam, shell and brick elements for geometrically nonlinear analysis

The co-rotational finite element formulation is an attractive technique extending the capabilities of an existing high performing linear element to geometrically nonlinear analysis. This paper presents a modified co-rotational framework, unified for beam, shell, and brick elements. A unified zero-spin criterion is proposed to specify the local element frame, whose origin is always located at the centroid. Utilizing this criterion, a spin matrix is introduced, and the local frame is invariant to the element nodal ordering. Additionally, the projector matrix is redefined in a more intuitive way, which is the derivative of local co-rotational element frame with respect to the global one. Furthermore, the nodal rotation is obtained with pseudo vector and instantaneous rotation, under a high-order accurate transformation. The resulting formulations are achieved in unified expression and thus a series of linear elements can be embedded into the framework. Several examples are presented to demonstrate the efficiency and accuracy of the proposed framework for large displacement analysis.