This question is about beam element using Absolute Nodal Coordinate Formulation! The element uses nodal slope vector (which is not necessarily to be a vector of unit norm) to characterize the rotation of the cross section. Here as in sequel, e3 and e4 denote the two components of the slope vector at a node. Suppose in the analysis the cross section of the beam rotates according to a function of t (denoting time), say f(t). Then the rotational part of the boundary condition at this node should be e3/sqrt(e3^2+e4^2)=cos(f(t)) , e3/sqrt(e3^2+e4^2)=sin(f(t)) (which could be seen as two constraint equations). The above boundary condition is not as straightforward as conventional beam element with an explicit freedom (theta) to characterize section rotation. The paper listed below proposed a method to accommodate such a explicit characterization of rotation, but the authors didn't give expressions of internal force and tangent stiffness matrix. Is there any other literature dealing with this issue? The aforementioned example is just about one node. In a problem concerning the relative rotation of two node at a joint, the above approach's constraint equation will be much more complex and that motivate me to find a more ingenious solution.
http://www.tandfonline.com/doi/abs/10.1080/03052150802317457
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