Rigid-plastic finite element analysis of steel plates, structural girders and connections

Abstract

The performance of three triangular plate elements for rigid-plastic finite element analysis of steel plates is evaluated. The element types considered are two variants of the constant stress triangle, the first one with no prescribed stress continuity at all and the second one with prescribed stress continuity in inter-element normal stresses. The third element type is an element with linearly varying stresses with complete inter-element stress continuity. The von Mise yield surface for steel plates is linearised, whereby the rigid-plastic analysis is formulated as a linearly constrained optimisation problem, which is solved by a very effective internal point method. Linear elements representing flanges and stiffeners in structural girders are introduced, as well as general joint elements for solving contact problems in for example endplate design. The basic singular performance of simple steel plates regarding application of point loads is first considered. It is shown how the bending strength of a flange distributes concentrated forces, the results of which turn out to be mesh independent for a mesh size, which can be determined by a simple analytical expression. Bearing capacities are compared to those obtained by well-established methods defined in various codes of standard. The ability to reproduce beam bending solutions is thereafter considered and the results are compared to well-known analytical solutions. The joint element is applied in studying bolted endplate connections. An analytical method is developed and compared to the numerical model. Finally, with the knowledge of the performance in basic problems, a truss with welded connections and a portal frame with bolted endplate connections are analysed. These examples show that the weak parts in large multi-component structural systems are properly identified and that the methods developed may become an important numerical tool in designing steel structures.