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.
