Finite element technique for thin-walled girders

The numerical model for analyzing thin-walled girders is developed. The theory is based on the conventional idea of Vlasov developed originally for torsional problems of thin-walled girders with closed cross-sections. This idea is combined with the finite element method. Economical aspects often support developing these kinds of coalitions, taking into account the special nature and properties of structures considered, to reduce the size of the computational model required. The displacement approximation is spanned at certain cross-sectional planes between which the interpolation is performed. This procedure permits the application of the method in which the lateral displacement state is chosen, in advance. Attention is paid to an algorithm to create a basis system for the displacement state of a general, arbitrary shaped cross-section, consisting of piecewise rectilinear cross-sections of separate shells. The effects of torsion, distortion, torsional and distortional warping as well as shear deformations can be included in the analysis through the creation of the displacement state. The expressions for strains are derived in a local orthogonal coordinate system to avoid too complicated formulae due to curvilinear coordinates. In numerical examples the cross-sections of the girders analyzed have been of varying shape or wall thickness, the girders have been straight or curved having perpendicular or skew support lines. The cross-sections have also been of open or closed composition. The numerical comparisons performed reveal throughout a good agreement between the results of the present method and experimental and numerical data found in the literature. Especially, a very good conformity with numerical thin shell solutions can be observed.