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

The well-known yield-line analysis procedure for slabs has recently been systematically automated, enabling the critical yield-line pattern to be identified quickly and easily, whatever the slab geometry. This has been achieved by using the discontinuity layout optimization (DLO) procedure, which involves using optimization to identify the critical layout of yield-line discontinuities interconnecting regularly spaced nodes distributed across a slab. However, whilst highly accurate solutions can be obtained, the corresponding yield-line patterns are often quite complex in form, especially when relatively dense nodal grids are employed. Here a method of rationalizing the DLO-derived yield-line patterns via a geometry optimization post-processing step is described. Geometry optimization involves adjusting the positions of the nodes, thereby simultaneously simplifying and improving the accuracy of the solution. The mathematical expressions involved are derived analytically, and various practical issues are highlighted and addressed. Finally, an interior point optimizer is used to obtain rationalized solutions for a variety of sample slab analysis problems, clearly demonstrating the efficacy of the proposed rationalization technique.