Discontinuity Layout Optimization (DLO) allows the systematic automation of the well-known yield line method for reinforced concrete slab analysis  allowing the ultimate load capacity and critical failure mechanism to be calculated, typically in seconds. 

Key Publications

Automatic yield-line analysis of slabs using discontinuity layout optimization
Gilbert, M., He, L., Smith, C. C., & Le, C.
Proceedings of the Royal Society A, 470(2168).
https://doi.org/10.1098/rspa.2014.0071

Automatic yield-line analysis of practical slab configurations via discontinuity layout optimization
He, L., Gilbert, M., & Shepherd, M.
Journal of Structural Engineering, 143(7).
https://doi.org/10.1061/(ASCE)ST.1943-541X.0001700

Automatic rationalization of yield-line patterns identified using discontinuity layout optimization
He, L., & Gilbert, M.
International Journal of Solids and Structures.
https://doi.org/10.1016/j.ijsolstr.2015.12.014

Limit Analysis of Masonry analysis is typically undertaken using a rigid block approach.  However for large problems  Layout Optimization techniques can become attractive to map patterns of deformation using homogeneization principles, and allowing direct coupling with geotechnical slip-line analyses.  Two distinct approaches to this are being investigated. 

Key Publications

Limit analysis of masonry walls using discontinuity layout optimization and homogenization
Valentino, J., Gilbert, M., Gueguin, M., & Smith, C. C.
International Journal for Numerical Methods in Engineering.
https://doi.org/10.1002/nme.7124