A Python script for discontinuity layout optimization

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