A selective strategy for shakedown analysis of engineering structures

TLDR

Determining load‑bearing capacity is essential, and statical shakedown analysis is a suitable tool for thermo‑mechanical loading beyond the elastic limit, but it leads to large nonlinear convex optimization problems. The paper aims to solve large‑scale shakedown problems using a new selective algorithm. The authors employ a primal–dual interior‑point algorithm and a selective approach that automatically identifies the most plastically affected zones, reduces the system to a substructure, and solves the resulting smaller optimization problem more efficiently. Running time decreases drastically, as shown by numerical examples from power plant engineering. © 2013 John Wiley & Sons, Ltd.

Abstract

SUMMARY Determining 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.