Title of article :
Lower bound limit analysis with adaptive remeshing
Author/Authors :
Andrei V. Lyamin، نويسنده , , Scott W. Sloan، نويسنده , , Kristian Krabbenhoft، نويسنده , , Mohammed Hjiaj، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2005
Abstract :
The 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
Keywords :
limit analysis , Adaptivity , Finite elements , Error estimation , Lower Bound
Journal title :
International Journal for Numerical Methods in Engineering
Journal title :
International Journal for Numerical Methods in Engineering