A numerical shakedown analysis method for strength evaluation coupling with kinematical hardening based on two surface model

Abstract

The current research utilizes an efficient shakedown computation technique to determine the load-bearing capacity of a structure. It can predict the strengths of a structure under arbitrary varying loads where failure form of alternate plasticity and incremental collapse will be avoided. To achieve a realistic result, a kinematical hardening material model is formulated into the shakedown analysis based on Melan's static theorem using a two-surface model so that both incremental collapse and alternating plasticity can be captured. Thus it leads to a nonlinear convex optimization problem which later reformulated to an efficient form for numerical computation. In contrast to the results of benchmark examples for a steel hollow section bar and a plate with hole, the present method is well suited to determine the limit and shakedown states of these two problems especially for a large scale case. Specifically, the present approach does not require full loading history. In order to better illustrate the computing power potential of this algorithm, the proposed technique is also utilized to determine the load-bearing capacity of a cast aluminum beam to be used in a high-speed train. In addition to constructing the plastic and shakedown domain, the proposed approach is also employed to study how kinematical hardening material model influences the feasible load domains.