Elastoplastic analysis of frames composed of softening materials by restricted basis linear programming

Structural Optimization by Spherical Interpolation of Objective Function and Constraints

“…Next, using Eqs. (9) and (10), the tangential vector, w, related to the 2 successive reference points for the objective function and the 2 constraints have been obtained. Then, using Eqs.…”

“…In methods such as the sequential linear programming [2,10] and the sequential quadratic programming [6,[11][12][13], Taylor expansion is used for interpolation of the functions, while in the method presented here, the functions are approximated by spheres in the n-dimensional space for n-dimensional problems. Hence, the method uses the radii of curvature, which are the radii of the spheres which are tangent to the given n-dimensional functions of constraints and objective function.…”

Elastoplastic analysis of plane stress/strain structures via restricted basis linear programming

“…It is worth noting that what is given in Eq. (37) is the initial MP which has to be updated after each plasticity event as described in [18]. In such a way, all problem parameters (including load and plastic multipliers) are decomposed into what has been obtained for the variables up to the current stage of loading (hatted parameters) and an increment which is expected for the next loading step (dotted variables).…”

“…Also some researchers dealt with piecewise-linearization of yield surfaces, so as to be uti-lized in optimization approaches as linear constraints [14][15][16]. Recently a modified version of RBLP has been proposed in the spirit of framed structures, which automatically captures and handles any local unloading and removes any need for sub-problem solution in the cases of reaching yield surface corners [17,18]. This approach has been successfully used in elastoplastic analysis of softening frames and the proposed maximization criterion has shown an excellent capability in capturing the exact response of structures.…”

“…In this paper, the RBLP is extended to 2D-Stress/Strain problems following a similar approach discussed in [17,18].To this end, theoretical aspects of problem including: field approximation, piecewise-linearization of von Mises yield model in 2D-stress/strain, and development of linear mixed hardening constitutive laws are presented in Section 2. Formulation of the problem and its implementation in the MP problem are explained in Section 3.…”