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A new three-dimensional limit analysis formulation that uses the recently developed discontinuity layout optimization (DLO) procedure is described. With DLO, limit analysis problems are formulated purely in terms of discontinuities, which take the form of polygons when three-dimensional problems are involved. Efficient second-order cone programming techniques can be used to obtain solutions for problems involving Tresca and Mohr–Coulomb yield criteria. This allows traditional ‘upper bound’ translational collapse mechanisms to be identified automatically. A number of simple benchmark problems are considered, demonstrating that good results can be obtained even when coarse numerical discretizations are employed.

Application of discontinuity layout optimization to three-dimensional plasticity problems