Reducing the Computational Effort for Performing Linear Optimization in the Lower-Bound Finite Elements Limit Analysis

Abstract

This study describes a technique for reducing the computational effort for performing linear optimization while solving any geotechnical stability problem with the use of the lower bound finite-element limit analysis. In the proposed method, a lower order polygon is initially used to model the Mohr-Coulomb yield function; the order of the polygon refers to its total number of sides. The initial solution is used to identify the governing side of the yield polygon that lies nearest to the point defining the existing stress state. Subsequently, this governing side of the linearized yield polygon is replaced with a number of the relevant sides of the higher order polygon. Because all the sides of the higher order polygon for imposing the linearized yield constraints do not enter the formulation, the associated computational effort becomes much smaller. With the proposed algorithm, the collapse loads were determined for smooth and rough strip footing, and the computational results were found to be quite convincing.