Lower bound limit analysis using non-linear programming

TLDR: 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, and is shown to be vastly superior to an equivalent formulation that is based on a linearized yield surface and linear programming.

Abstract: 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.