Performance of the MLPG method for static shakedown analysis for bounded kinematic hardening structures

Shakedown analysis is an extension of plastic limit analysis to the case of variable repeated loads and plays a significant role in safety assessment and structural design. This paper presents a solution procedure based on the meshless local Petrov–Galerkin (MLPG) method for lower-bound shakedown analysis of bounded kinematic hardening structures. The numerical implementation is very simple and convenient because it is only necessary to construct an array of nodes in the targeted domain. Moreover, the natural neighbour interpolation (NNI) is employed to construct trial functions for simplifying the imposition of essential boundary conditions. The kinematic hardening behaviour is simulated by an overlay model and the numerical difficulties caused by the time parameter are overcome by introducing the conception of load corner. The reduced-basis technique is applied to solve the mathematical programming iteratively through a sequence of reduced residual stress subspaces with very low dimensions and the resulting non-linear programming sub-problems are solved via the Complex method. Numerical examples demonstrate that the proposed solution procedure is feasible and effective to determine the shakedown loads of bounded kinematic hardening structures as well as unbounded kinematic hardening structures.