Lower bound limit analysis with adaptive remeshing

Abstract

SUMMARYThe objective of this work is to present an adaptive remeshing procedure for lower bound limit analysis with application to soil mechanics. Unlike conventional finite element meshes, a lower bound grid incorporates statically admissible stress discontinuities between adjacent elements. These discontinuities permit large stress jumps over an infinitesimal distance and reduce the number of elements needed to predict the collapse load accurately. In general, the role of the discontinuities is crucial as their arrangement and distribution has a dramatic influence on the accuracy of the lower bound solution (Limit Analysis and Soil Plasticity, 1975). To ensure that the discontinuities are positioned in an optimal manner requires an error estimator and mesh adaptation strategy which accounts for the presence of stress singularities in the computed stress field.Recently, Borges et al. (Int. J. Solids Struct. 2001; 38:1707-1720) presented an anisotropic mesh adaptation strategy for a mixed limit analysis formulation which used a directional error estimator. In the present work, this strategy has been tailored to suit a discontinuous lower bound formulation which employs the stresses and body forces as primary unknowns. The adapted mesh has a maximum density of discontinuities in the direction of the maximum rate of change in the stress field. For problems involving strong stress singularities in the boundary conditions (e.g. a strip footing), the automatic generation of discontinuity fans, centred on the singular points, has been implemented.The efficiency of the proposed technique is demonstrated by analysis of two classical soil mechanics problems; namely the bearing capacity of a rigid strip footing and the collapse of a vertical cut.

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“…The reader is referred to [13,14] for a justification of those spaces. When resorting to them, the saddle point problem is consequently modified, as illustrated in Figures 1b-c.…”

Adaptive mesh-free lower bound limit analysis using non-linear programming

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AAR-based decomposition method for lower bound limit analysis

“…Different discretisations of the optimisation problem in (1) yield different static and kinematic formulations that give respectively lower [LS02,LSKH05] or upper bounds [KLS07] of the exact optimal load factor λ opt , and the two type of solutions may be in turn combined for designing remeshing strategies [MBHP09]. The method has been well studied and applied for instance in the analysis of anchors [MS10,MLH13], masonry structures [GSP10] or inhomogeneous materials [Bd14].…”