Bazoune, A., Khulief, Y.A. and Stephen, N.G.,
Shape functions of three-dimensional Timoshenko beam element
Journal of Sound and Vibration, 259, (2), . (doi:10.1006/jsvi.2002.5122).
Beams represent fundamental structural components in many engineering applications, and shape functions are essential for the finite element discretization of such structures. Premeniecki (1) derived explicit expressions for the shape functions of two-dimensional Timoshenko and three-dimensional Euler-Bernoulli (EB) beam elements. Note that for the three-dimensional EB element presented in reference (1), a change of sign is required in those entries of the third column of the shape function matrix which correspond to the twist temrs. Since that pioneering work, there does not appear to have been any attempt to extend these results to a three-dimensional Timoshenko beam element, and it is the purpose of this note to fill this gap in the literature.
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