A Python script for discontinuity layout optimization

Abstract Discontinuity layout optimization (DLO) is a powerful numerical limit analysis technique that can be used to identify the collapse load and associated failure mechanism of solid or structure. The method successfully automates traditional ‘upper bound’ plasticity, with applications including metal extrusion problems, where die forces are sought, geotechnical engineering stability foundations retaining walls established. Notably basic DLO uses same underlying mathematical formulation as ‘ground structure’-based truss (or ‘topology’) demonstrated in this contribution via Python script capable solving plane strain problems. Extensions presented allow treatment larger-scale problems incorporating cohesive-frictional materials, self-weight treated new conceptually elegant way. Finally, various examples illustrate capabilities DLO, displacement vectors shown aid interpretation.