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.
Journal / conference name:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Chapter / Report / Application number:
One of the oldest and most fundamental problems in the field of engineering mechanics involves calculation of the amount of load that can be carried by a structure, and in identifying the associated failure mechanism (layout of failure planes, or ‘discontinuities’). Discontinuity layout optimization (DLO) is an engineering analysis procedure...