Limit analysis using discontinuity layout optimization: novel methods and applications

The discontinuity layout optimization (DLO) limit analysis procedure is a powerful numerical analysis procedure that has the potential to be applied to a wide range of challenging engineering problems. Here a new homogenized formulation for masonry structures is developed that obviates the need to model individual masonry units and joints; the formulation is initially applied to a range of walls subjected to in-plane loading. In the homogenized formulation developed, masonry joints are reduced to interfaces and blocks are assumed to be infinitely resistant. The model takes account of the interlock and aspect ratios of the blocks, and the cohesion and coefficient of friction of the joints. Using the homogenized failure surface derived, details of a numerical method developed to determine the collapse load of trapezoidal buttress wall subject to common loading scenarios are then also presented, with results compared to those from traditional numerical methods based on no-tension cracked stability methods.
A shell DLO formulation is then developed and demonstrated via application to a range of steel assemblies, using an isotropic material model. This shell model is then applied to masonry structures, adopting both discretized and homogenized modelling
approaches. In the discretized model planes coinciding with the physical locations of masonry joints are assigned reduced mechanical properties. In the homogenized
model, both coupled and uncoupled in-plane and out-of-plane criteria are developed based on Love-Kirchoff and Reissner-Mindlin plate theory. The resulting formulations are validated against both numerical benchmark problems and experimental results.