Automatic yield-line analysis of slabs using discontinuity layout optimization

Abstract

The yield-line method of analysis is a long established and extremely effective means of estimating the maximum load sustainable by a slab or plate. However, although numerous attempts to automate the process of directly identifying the critical pattern of yield-lines have been made over the past few decades, to date none has proved capable of reliably analysing slabs of arbitrary geometry. Here, it is demonstrated that the discontinuity layout optimization (DLO) procedure can successfully be applied to such problems. The procedure involves discretization of the problem using nodes inter-connected by potential yield-line discontinuities, with the critical layout of these then identified using linear programming. The procedure is applied to various benchmark problems, demonstrating that highly accurate solutions can be obtained, and showing that DLO provides a truly systematic means of directly and reliably automatically identifying yield-line patterns. Finally, since the critical yield-line patterns for many problems are found to be quite complex in form, a means of automatically simplifying these is presented.

Automatic rationalization of yield-line patterns identified using discontinuity layout optimization

“…1. Improved solutions can be obtained by using an increased number of nodes; the resulting greatly increased number of potential yield-lines can be handled efficiently using the adaptive solution scheme proposed for truss layout optimization by Gilbert and Tyas 2003, and used for this application in Gilbert et al 2014. However, whilst highly accurate solutions can be obtained using the DLO procedure, the corresponding yield-line patterns are often quite complex in form, especially when relatively dense nodal grids are employed.…”

“…Recently, this goal was achieved by Gilbert et al (2014), who used discontinuity layout optimization (DLO) to automate the process of identifying the most critical yieldline pattern. Instead of discretizing the problem using elements arranged in a finite element mesh, when using DLO the slab area is populated by nodes, and these are then interconnected with a large set of potential yield-lines, which are free to cross-over one another.…”

“…However, whilst highly accurate solutions can be obtained using the DLO procedure, the corresponding yield-line patterns are often quite complex in form, especially when relatively dense nodal grids are employed. In an attempt to address this, a modified formulation was also proposed by Gilbert et al (2014). The modified formulation involved penalizing short yield-lines, leading to solutions that were generally simpler in form than the original.…”

“…The kinematic DLO limit analysis formulation for a weightless slab can be written as an optimization problem as follows (after Gilbert et al 2014):…”

Modelling rotational failure in confined geometries using DLO

“…The application of DLO to three-dimensional problem and plane-strain problems involving purely translational failure mechanisms has been described by Hawksbee et al (2013) and Smith and Gilbert (2007), respectively, and to plane-strain rotational mechanisms in non-dilational materials by Smith and Gilbert (2013). Recently, a formulation suitable for the analysis of slabs has been also presented (Gilbert et al, 2014). A simple exemplar MATLAB code for plane-strain translational DLO can be found in Gilbert et al (2010).…”