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This paper proposes a low order geometrically exact flexible beam formulationbased on the utilisation of generic beam shape functions to approximatedistributed kinematic properties of the deformed structure. The proposednonlinear beam shapes approach is in contrast to the majority of geometricallynonlinear treatments in the literature in which element based --- and hencehigh order --- discretisations are adopted. The kinematic quantitiesapproximated specifically pertain to shear and extensional gradients as well aslocal orientation parameters based on an arbitrary set of globally referencedattitude parameters. In developing the dynamic equations of motion, an Eulerangle parameterisation is selected as it is found to yield fast computationalperformance. The resulting dynamic formulation is closed using an example shapefunction set satisfying the single generic kinematic constraint. Theformulation is demonstrated via its application to the modelling of a series ofstatic and dynamic test cases of both simple and non-prismatic structures; thesimulated results are verified using MSC Nastran and an element-based intrinsicbeam formulation. Through these examples it is shown that the nonlinear beamshapes approach is able to accurately capture the beam behaviour with a veryminimal number of system states.

On the Geometrically Exact Low Order Modelling of a Flexible Beam: Formulation and Numerical Tests