Three‐dimensional Mohr–Coulomb limit analysis using semidefinite programming

Recently, Krabbenhøft et al . ( Int. J. Solids Struct . 2007; 44 :1533–1549) have presented a formulation of the three‐dimensional Mohr–Coulomb criterion in terms of positive‐definite cones. The capabilities of this formulation when applied to large‐scale three‐dimensional problems of limit analysis are investigated. Following a brief discussion on a number of theoretical and algorithmic issues, three common, but traditionally difficult, geomechanics problems are solved and the performance of a common primal–dual interior‐point algorithm (SeDuMi ( Appl. Numer. Math . 1999; 29 :301–315)) is documented in detail. Although generally encouraging, the results also reveal several difficulties which support the idea of constructing a conic programming algorithm specifically dedicated to plasticity problems.