MACRO-ZONES SGBEM APPROACH FOR STATIC SHAKEDOWN ANALYSIS AS CONVEX OPTIMIZATION

A new strategy utilizing the Multidomain SGBEM for rapidly performing shakedown analysis as a convex optimization problem has been shown in this paper. The present multidomain approach, called displacement method, makes it possible to consider step-wise physically and geometrically nonhomogeneous materials and to obtain a self-equilibrium stress equation regarding all the bem-elements of the structure. Since this equation includes influence coefficients, which characterize the input of the quadratic constraints, it provides a nonlinear optimization problem solved as a convex optimization problem. Furthermore, the strategy makes it possible to introduce a domain discretization exclusively of zones involved by plastic strain storage, leaving the rest of the structure as elastic macroelements, consequently governed by few boundary variables. It limits considerably the number of variables in the problem and makes the proposed strategy extremely advantageous. The implementation of the procedure by the Karnak.sGbem code, coupled with optimization toolbox Matlab 7.6.0, made it possible to perform some numerical tests showing the high performance of the algorithm due to solution accuracy and low computational cost.