A combined approach of SGBEM and conic quadratic optimization for limit analysis

The static approach to evaluate the limit multiplier directly was rephrased using the Symmetric Galerkin Boundary Element Method (SGBEM) for multidomain type problems [1,2]. The present formulation couples SGBEM multidomain procedure with nonlinear optimization techniques, making use of the self-equilibrium stress equation [3-5]. This equation connects the stresses at the Gauss points of each substructure (bem-e) to plastic strains through a self-stress matrix computed in all the bem-elements of the discretized system. The analysis was performed by means of a conic quadratic optimization problem, in terms of discrete variables, and implemented using Karnak.sGbem code [6] coupled with MathLab. Finally, some numerical tests are shown and the limit multiplier values are compared with those available in the literature [4,8]. The applications show a very important computational advantage of this strategy which allows one to introduce a domain discretization only in the zones involved in plastic strain action and to leave the rest of the structure as elastic macroelements, therefore governed by few boundary variables.