Lower bound limit analysis using non‐linear programming

This paper describes a new formulation, based on linear finite elements and non‐linear programming, for computing rigorous lower bounds in 1, 2 and 3 dimensions. The resulting optimization problem is typically very large and highly sparse and is solved using a fast quasi‐Newton method whose iteration count is largely independent of the mesh refinement. For two‐dimensional applications, the new formulation is shown to be vastly superior to an equivalent formulation that is based on a linearized yield surface and linear programming. Although it has been developed primarily for geotechnical applications, the method can be used for a wide range of plasticity problems including those with inhomogeneous materials, complex loading, and complicated geometry. Copyright © 2002 John Wiley & Sons, Ltd.

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