A cycle-oriented incremental analysis of shakedown problems

An effective method for determination of a quasi‐static shakedown loading and of a steady‐state response is proposed. The classical optimization problem based on Melan's theorem is suitably reformulated to meet the requirements of incremental analysis. The main attention is focused on the reduction of a computational time required for a completion of a transient elastic–plastic phase of deformation. The method differs significantly from classical incremental analyses. Here, a load cycle is approximated by the finite number of loading systems covering the cycle. Each system is then combined with a separate domain of the structure in which the load system can be treated as a dominant one. In this manner, the structure consists of parts, each of them undergoing suitably chosen one‐parameter loading only. Such a modification allows us to build a set of non‐linear equations for all loading systems covering the whole load cycle. As a consequence the structure can be treated as the one in which the transient plastic phase of deformation is analysed load cycle by load cycle without making load increments inside the considered cycle. Due to this innovation a significant reduction of the computational time required for the solution of the steady‐state response of the structure is obtained what is illustrated on 3‐D frames. © 1997 John Wiley & Sons, Ltd.