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H. Nguyen-Xuan, T. Rabczuk, T. Nguyen-Thoi, N. T. Tran, N. Nguyen-Thanh, Computation of limit and shakedown loads using a node-based smoothed finite element method, International Journal for Numerical Methods in Engineering, in press, doi: 10.1002/nme.3317, 2011.

This paper presents a novel numerical procedure for computing limit and shakedown loads of structures using a node-based smoothed FEM in combination with a primal–dual algorithm. An associated primal–dual form based on the von Mises yield criterion is adopted. The primal-dual algorithm together with a Newton-like iteration are then used to solve this associated primal–dual form to determine simultaneously both approximate upper and quasi-lower bounds of the plastic collapse limit and the shakedown limit. The present formulation uses only linear approximations and its implementation into finite element programs is quite simple. Several numerical examples are given to show the reliability, accuracy, and generality of the present formulation compared with other available methods.

finite element method;
limit analysis;
node-based smoothed finite element method (NS-FEM);
primal–dual algorithm;
shakedown analysis;
strain smoothing