A Comparison of Conic Programming Software for Finite Element Limit Analysis

Abstract

Some common criteria for predicting the plastic failure of geomaterials, including the Mohr-Coulomb model, can be represented as conic constraints. Thus, by formulating finite element limit analysis (FELA) problems with such materials as second-order cone programs (SOCPs), solutions to small-and medium-scale problems are readily obtained using current state-of-the-art optimisation software that are based on polynomially-bounded interior-point methods (IPMs). Unfortunately, when progressing to large-scale 2D and 3D problems, these schemes often struggle with the increased computational burden of obtaining a search direction at each iteration of the IPM using conventional direct solvers that implement some form of Gaussian elimination. In this paper, current conic optimisation software is compared for some medium and large-sized FELA problems. Additionally, a scheme which avoids the factorisation of large linear systems, through the use of a Krylov subspace solver, is developed and compared to existing software.