@incollection{TranTranMatthiesetal.2017,
  author    = {Tran, N. T. and Tran, Thanh Ngoc and Matthies, M. G. and Stavroulakis, G. E. and Staat, Manfred},
  title     = {Shakedown Analysis Under Stochastic Uncertainty by Chance Constrained Programming},
  series = {Advances in Direct Methods for Materials and Structures},
  booktitle = {Advances in Direct Methods for Materials and Structures},
  publisher = {Springer},
  address   = {Cham},
  isbn      = {978-3-319-59810-9},
  doi       = {10.1007/978-3-319-59810-9_6},
  pages     = {85 -- 103},
  year      = {2017},
  abstract  = {In this paper we propose a stochastic programming method to analyse limit and shakedown of structures under uncertainty condition of strength. Based on the duality theory, the shakedown load multiplier formulated by the kinematic theorem is proved actually to be the dual form of the shakedown load multiplier formulated by static theorem. In this investigation a dual chance constrained programming algorithm is developed to calculate simultaneously both the upper and lower bounds of the plastic collapse limit and the shakedown limit. The edge-based smoothed finite element method (ES-FEM) with three-node linear triangular elements is used for structural analysis.},
  language  = {en}
}