A selective strategy for shakedown analysis of engineering structures

Abstract

SUMMARYDetermining the load‐bearing capacity of engineering structures is essential for their design. In the case of varying thermo‐mechanical loading beyond the elastic limit, the statical shakedown analysis constitutes a particularly suitable tool for this. The application of the statical shakedown theorem, however, leads to a nonlinear convex optimization problem, which is typically characterized by large numbers of variables and constraints. In the present work, this optimization problem is solved by a primal–dual interior‐point algorithm, which shows a remarkable performance due to its problem‐tailored formulation. Nevertheless, the solution procedure remains still a demanding task from computational point of view. Thus, the aim of this paper is to tackle the task of solving large‐scale problems by use of a new so‐called selective algorithm. This algorithm detects automatically the plastically most affected zones within the structure, which have the highest influence on the solution. The entire system is then reduced to a substructure consisting of these zones, based upon which a new optimization problem can be set up, which is solved with significantly less effort. Consequently, the running time decreases drastically, as is shown by application to numerical examples from the field of power plant engineering. Copyright © 2013 John Wiley & Sons, Ltd.

Effective treatment of complex statical and dynamical load combinations within shakedown analysis of 3D frames

“…(8) and (9) allow the evaluation of the set of generalized yield stress t yk 2 @E½s associated to the mechanism _ e k , simply by assuming uniaxial stress fields reaching their maximum strength capacity in each region, either in tension or in compression.…”

“…The interest in direct methods has also been encouraged by the availability of new and efficient optimization algorithms [6,7], such as the Interior Point Method (IPM) which is employed for solving very large non-linear problems [8][9][10][11], like those obtained in the Finite Element (FE) discretization of real-scale engineering structures. The availability of high optimized IPM solvers, such as MOSEK [12], makes this approach interesting.…”

Structural Shakedown: A New Methodology for Estimating the Residual Displacements

“…. In this paper, the equilibrium finite element method based on internal force approximation is applied for the discretization of structures (taking in to account an assumption of small displacements) (Alawdin 2005;Belytschko 1972;Kalanta et al 2009;Kaliszky, Lógó 2002;McGuire et al 2000;Ngo, Tin-Loi 2007;Simon et al 2013;Venskus et al 2010). Optimization problems of elastic-plastic steel structures subjected to VRL are nonconvex mathematical programming problems (Atkočiūnas 2012;Rozvany 2011).…”

Limit state numerical procedures for cyclically loaded elastoplastic structures

“…Based on the interior point method a variety of powerful algorithms or related techniques have been developed by many authors either for limit or shakedown analysis e.g. Pastor and Loute, 2005;Akoa et al, 2007;Krabbenhøft et al, 2007c;Hachemi et al, 2009;Tran et al, 2010;Simon and Weichert, 2011;Garcea and Leonetti, 2011;Simon and Weichert, 2012;Simon et al, 2013;).…”