Abstract A new upper bound formulation of limit analysis two‐ and three‐dimensional solids is presented. In contrast to most discrete methods the present one formulated in terms stresses rather than velocities plastic multipliers. However, by means duality theory it shown that does indeed result rigorous solutions. Also, kinematically admissible discontinuities, which have previously been be very efficient, are given an interpretation stresses. This allows for a much simpler implementation...

Abstract The non‐linear programming problem associated with the discrete lower bound limit analysis is treated by means of an algorithm where need to linearize yield criteria avoided. interior point method and completely general in sense that no particular finite element discretization or criterion required. As methods for linear number iterations affected only little size. Some practical implementation issues are discussed reference special structure common load optimization problem,...

Abstract 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 positive‐definite cones. The capabilities this when applied to large‐scale problems limit analysis are investigated. Following brief discussion on number theoretical and algorithmic issues, three common, but traditionally difficult, geomechanics solved performance common primal–dual interior‐point algorithm (SeDuMi Appl....

Abstract The problem of small‐deformation, rate‐independent elastoplasticity is treated using convex programming theory and algorithms. A finite‐step variational formulation first derived after which the relevant potential discretized in space subsequently viewed as Lagrangian associated with a mathematical program. Next, an algorithm, based on classical primal–dual interior point method, developed. Several key modifications to conventional implementation this algorithm are made fully...

The objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application soil mechanics. Unlike conventional finite element meshes, a grid incorporates statically admissible stress discontinuities between adjacent elements. These permit large jumps over infinitesimal distance and reduce the number elements needed predict collapse load accurately. In general, role crucial as their arrangement distribution has dramatic influence on accuracy...

SUMMARY A new methodology for computational plasticity of nonassociated frictional materials is presented. The approach inspired by the micromechanical origins friction and results in a set governing equations similar to those standard associated plasticity. As such, procedures previously developed are applicable with minor modification. This illustrated adaptation implicit scheme. Moreover, can be cast terms variational principle, which after discretization solved means newly second‐order...

Summary A total stress model applicable to clays under undrained conditions is presented. The involves three strength parameters: the shear strengths in triaxial compression, extension, and simple shear. amount of physical anisotropy implied by a function relative magnitude these assuming Mises‐type plastic potential. Elastoplastic deformation characteristics below failure are accounted for hardening law requiring two additional parameters that can be related axial strains halfway...

Abstract Modelling of landslides in sensitive clays has long been recognised as a challenge. The strength reduction when undergoing plastic deformation makes the failure proceed progressive manner such that small slope may lead to series retrogressive failures and thus an unexpected catastrophic landslide. clay entire process mimic both solid-like (when it is intact) fluid-like fully remoulded, especially for quick clays) behaviours. Thereby, successful numerical prediction requires not only...

Lower-bound calculations based on the FEM are used to determine bearing capacity of a strip foundation subjected an inclined, eccentric load cohesionless soil with varying surcharges and friction angles 25, 30, 35°. The is assumed be perfectly plastic following Mohr-Coulomb failure criterion. results reported as graphs showing function angle, eccentricity, inclination, surcharge. These have been compared, for smaller eccentricities, except in case no surcharge, lower-bound values greater,...

A procedure for strength reduction analysis using finite-element limit is presented. The scheme completely general and does not require decision making regarding the loads needed to drive system failure. Rather, based on ability of modern interior-point methods detect infeasibility in a controlled reliable manner. new illustrated by an example involving strip footing top slope.