A SGBEM approach for static shakedown analysis as CQO problem

In this paper the shakedown static approach was rephrased by using the Symmetric Galerkin Boundary Element Method (SGBEM) for multidomain type problems. The present formulation utilizes the self-equilibrium stress equation, connecting the stresses at the Gauss points of each substructure (bem-e) to plastic strains, through a stiffness matrix (self-stress matrix), involving all the bem-elements of the discretized system. The optimization problem was solved by Conic Quadratic Optimization (CQO) and implemented using the Karnak.sGbem code coupled with MatLab. In order to prove the efficency of the proposed strategy, some numerical tests, in which the shakedown multiplier was checked by SGBEM elastoplastic analysis considering load paths inside the amplified domain, were performed. The applications show the very important computational advantage of confining the domain discretization only in the potentially plastic zones and leaving the rest of the structure subdivided into elastic macroelements, the latter therefore being governed by few boundary variables.