Strict upper and lower boundswith adaptive remeshing in limit state analysis
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By writing the limit state analysis as an optimisation problem, and after resorting to suitable discretisations of the stress and velocity field, we compute strict bounds of the load factor. The optimisation problem is posed as a Second Order Conic Program (SOCP), which can be solved very efficiently using specific algorithms for conic programming. Eventually, the optimum stress and velocity fields of the lower and upper bound problem are used to construct an error measure (elemental gap) employed in an adaptive remeshing strategy. This technique is combined with an additional adaptive nodal remeshing that is able to reproduce fan-type mesh patterns around points with discontinuous surface loads. We paticularise the resulting formulation for twodimensional problems in plane strain, with VonMises andMohr-Coulomb plasticity. We demonstrate the effetiveness of the method with a set of numerical examples extracted from the literature.