Keywords: stiffness matrix, non-uniform warping, composite, beam, flexure, torsion, shear deformation, boundary element method.

In this paper, the most recent developments concerning formulation, numerical implementation, and applications of an advanced stiffness matrix (20x20) and the corresponding nodal load vector of a member of arbitrary composite cross section taking into account generalized warping effects (shear lag as a result of both flexure and torsion), subjected to arbitrary external loading including warping moments, are reviewed. Non-uniform warping distributions, which are responsible for shear lag effects are taken into account by employing four independent warping parameters, multiplying a shear warping function in each direction and two torsional warping functions, which are obtained by solving corresponding boundary value problems. Ten boundary value problems, with respect to kinematical components, are formulated and solved using the analog equation method, a boundary element based technique. Warping functions and geometric constants, including the additional ones arising from warping, are evaluated employing a pure boundary element method approach. The aforementioned problems are formulated employing an improved stress field arising from the correction of shear stress components. The use of stress field stemming right from the kinematical assumptions is avoided, since it is proved to exhibit discrepancies in the computation of stress values, especially near supports and concentrated forces. Applications are presented to illustrate the accuracy of the advanced beam element, while the discrepancies arising from the use of the classical "12x12" or "14x14" stiffness matrices, employed in commercial software packages, are also demonstrated.

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