Introduction

Discontinuity Layout Optimization (DLO) uses Layout Optimization methods to determine the optimal layout of discontunuities (e.g. sliplines or yield line) that give the least energy collapse mechanim in a plastic analysis. It is able to model a wide range of failure criteria relevant to engineering problems  including Mohr-Coulomb and Tresca.

Formulations

Methodology

The underlying methodology of the DLO procedure is illustrated below.  Conceptually it is very similar to Layout Optimization, with the displacements in DLO being analagous to forces in LO and stresses in DLO being analagous to virtual displacements in LO. Python and MATLAB scripts implementing the core principles of the method are  available here and here.

Key Publications

Application of discontinuity layout optimization to plane plasticity problems
Smith, C., & Gilbert, M.
Proceedings Royal Society A, 463(2086), 2461-2484.
https://doi.org/10.1098/rspa.2006.1788

Identification of rotational failure mechanisms in cohesive media using discontinuity layout optimization
Smith, C. C., & Gilbert, M.
Geotechnique: International Journal of Soil Mechanics, 63(14), 1194-1208.
https://doi.org/10.1680/geot.12.P.082 

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

The stress function basis of the upper bound theorem of plasticity
Smith, C. C., & Gilbert, M.
International Journal of Solids and Structures, 244-245.
https://doi.org/10.1016/j.ijsolstr.2022.111565

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