@article{TranTrinhDaoetal.2022,
  author    = {Tran, Ngoc Trinh and Trinh, Tu Luc and Dao, Ngoc Tien and Giap, Van Tan and Truong, Manh Khuyen and Dinh, Thuy Ha and Staat, Manfred},
  title     = {FEM shakedown analysis of structures under random strength with chance constrained programming},
  series = {Vietnam Journal of Mechanics},
  volume    = {44},
  journal   = {Vietnam Journal of Mechanics},
  number    = {4},
  publisher = {Vietnam Academy of Science and Technology (VAST)},
  issn      = {0866-7136},
  doi       = {10.15625/0866-7136/17943},
  pages     = {459 -- 473},
  year      = {2022},
  abstract  = {Direct methods, comprising limit and shakedown analysis, are a branch of computational mechanics. They play a significant role in mechanical and civil engineering design. The concept of direct methods aims to determine the ultimate load carrying capacity of structures beyond the elastic range. In practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and constraints. If strength and loading are random quantities, the shakedown analysis can be formulated as stochastic programming problem. In this paper, a method called chance constrained programming is presented, which is an effective method of stochastic programming to solve shakedown analysis problems under random conditions of strength. In this study, the loading is deterministic, and the strength is a normally or lognormally distributed variable.},
  language  = {en}
}