Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming

Abstract

Recently, Krabbenhoft 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. Copyright © 2007 John Wiley & Sons, Ltd.