Effective Stiffness of Thin-Walled Beams with Local Imperfections

Abstract

Thin-walled beams are increasingly used in light engineering structures. They are economical, easy to manufacture and to install, and their load capacity-to-weight ratio is very favorable. However, their walls are prone to local buckling, which leads to a reduction of compressive, as well as flexural and torsional, stiffness. Such imperfections can be included in such components in various ways, e.g., by reducing the cross-sectional area. This article presents a method based on the numerical homogenization of a thin-walled beam model that includes geometric imperfections. The homogenization procedure uses a numerical 3D model of a selected piece of a thin-walled beam section, the so-called representative volume element (RVE). Although the model is based on the finite element method (FEM), no formal analysis is performed. The FE model is only used to build the full stiffness matrix of the model with geometric imperfections. The stiffness matrix is then condensed to the outer nodes of the RVE, and the effective stiffness of the cross-section is calculated by using the principle of the elastic equilibrium of the strain energy. It is clear from the conducted analyses that the introduced imperfections cause the decreases in the calculated stiffnesses in comparison to the model without imperfections.

Optimal Design of Bubble Deck Concrete Slabs: Sensitivity Analysis and Numerical Homogenization

“…Although the procedure presented in this work has not been experimentally verified, the homogenization method itself, used in the presented procedure, has already been verified on various engineering examples in our previous works [ 35 , 36 , 39 , 40 , 41 ]. The proposed algorithm can of course be implemented in a completely different computing environment; however, the procedure should be consistent with the diagram presented in Figure 4 and the general design guidelines presented in the previous paragraph.…”

“…Homogenization based on strain energy equivalence is a universal method that can be used not only for cardboard homogenization. It was used, e.g., for the homogenization of the cross-section of prefabricated Filigran slabs [ 35 ] and the analysis of thin-walled beams [ 36 ].…”

Time history comparative analyses of a thin-walled cold-formed steel structure considering P-D effect

“…Cold-formed steel profiles have a number of advantages over hot-rolled profiles, including better dimensional accuracy, lower material cost, and improved consistency of properties [25,26]. However, there are also some limitations to cold-formed steel, including a reduced capacity to resist lateral torsional buckling and lower ductility at low temperatures.…”