Abstract
A Timoshenko beam finite element is constructed with an arbitrary number of degrees of freedom. These are the displacement and cross-section rotation at each of two end nodes, together with coefficients of polynomial expansions of the transverse displacement and the shear deformation. Each of these series can be truncated after an arbitrary number of terms, which enables the element to be formulated to achieve any required degree of accuracy. Most of the existing complex beam elements are shown to be special cases of the new formulation. Because only very simple nodal variables are used, the element can be readily incorporated in user-orientated computer programs.
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