generalized warping in flexural-torsional buckling analysis of composite beams

the finite element method is employed for the flexural-torsional linear buckling analysis of beams of arbitrarily shaped composite cross-section taking into account generalized warping (shear lag effects due to both flexure and torsion). the contacting materials, that constitute the composite cross section, may include a finite number of holes. a compressive axial load is applied to the beam. the influence of nonuniform warping is considered by the usage of one independent warping parameter for each warping type, i.e. shear warping in each direction and primary as well as secondary torsional warping, multiplied by the respective warping function. the calculation of the four aforementioned warping functions is implemented by the solution of a corresponding boundary value problem (longitudinal local equilibrium equation). the resulting stress field is corrected through a shear stress correction. the equations are formulated with reference to the independent warping parameters additionally to the displacement and rotation components.