@article{FinkMarshallShahetal.2000,
  author    = {Fink, G. R. and Marshall, J. C. and Shah, N. J. and Weiss, P.H. and Halligan, P. W. and Grosse-Ruyken, M. and Ziemons, Karl and Zilles, K. and Freund, H. J.},
  title     = {Line bisection judgments implicate right parietal cortex and cerebellum as assessed by fMRI},
  series = {Neurology},
  volume    = {54},
  journal   = {Neurology},
  number    = {6},
  isbn      = {1526-632X},
  pages     = {1324 -- 1331},
  year      = {2000},
  language  = {en}
}
@article{StaatVu2006,
  author    = {Staat, Manfred and Vu, Khoi Duc},
  title     = {Limit loads of circumferentially flawed pipes and cylindrical vessels under internal pressure},
  series = {International Journal of Pressure Vessels and Piping. 83 (2006), H. 3},
  journal   = {International Journal of Pressure Vessels and Piping. 83 (2006), H. 3},
  isbn      = {0308-0161},
  pages     = {188 -- 196},
  year      = {2006},
  language  = {en}
}
@inproceedings{StaatTranPham2008,
  author    = {Staat, Manfred and Tran, Thanh Ngoc and Pham, Phu Tinh},
  title     = {Limit and shakedown reliability analysis by nonlinear programming},
  year      = {2008},
  abstract  = {7th International Conference on Reliability of Materials and Structures (RELMAS 2008). June 17 - 20, 2008 ; Saint Petersburg, Russia. pp 354-358. Reprint with corrections in red Introduction Analysis of advanced structures working under extreme heavy loading such as nuclear power plants and piping system should take into account the randomness of loading, geometrical and material parameters. The existing reliability are restricted mostly to the elastic working regime, e.g. allowable local stresses. Development of the limit and shakedown reliability-based analysis and design methods, exploiting potential of the shakedown working regime, is highly needed. In this paper the application of a new algorithm of probabilistic limit and shakedown analysis for shell structures is presented, in which the loading and strength of the material as well as the thickness of the shell are considered as random variables. The reliability analysis problems may be efficiently solved by using a system combining the available FE codes, a deterministic limit and shakedown analysis, and the First and Second Order Reliability Methods (FORM/SORM). Non-linear sensitivity analyses are obtained directly from the solution of the deterministic problem without extra computational costs.},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}
@article{StaatHeitzer2002,
  author    = {Staat, Manfred and Heitzer, M.},
  title     = {Limit and Shakedown Analysis with Uncertain Data},
  series = {Stochastic optimization techniques : numerical methods and technical applications / Marti, K. [ed]},
  journal   = {Stochastic optimization techniques : numerical methods and technical applications / Marti, K. [ed]},
  publisher = {Springer},
  address   = {Heidelberg},
  isbn      = {3-540-42889-5},
  pages     = {241 -- 254},
  year      = {2002},
  language  = {en}
}
@article{StaatHeitzer1997,
  author    = {Staat, Manfred and Heitzer, M.},
  title     = {Limit and Shakedown Analysis Using a General Purpose Finite Element Code},
  series = {Proceedings of NAFEMS World Congress '97 on Design, Simulation \& Optimisation : reliability \& applicability of computational methods ; Stuttgart, Germany, 9 - 11 April 1997},
  journal   = {Proceedings of NAFEMS World Congress '97 on Design, Simulation \& Optimisation : reliability \& applicability of computational methods ; Stuttgart, Germany, 9 - 11 April 1997},
  publisher = {NAFEMS},
  address   = {Glasgow},
  isbn      = {1-87437-620-4},
  pages     = {522 -- 533},
  year      = {1997},
  language  = {en}
}
@article{Staat2013,
  author    = {Staat, Manfred},
  title     = {Limit and shakedown analysis under uncertainty},
  series = {International journal of computational methods : IJCM},
  journal   = {International journal of computational methods : IJCM},
  publisher = {World Scientific Publishing},
  address   = {Singapore},
  issn      = {0219-8762},
  pages     = {Publ. online},
  year      = {2013},
  language  = {en}
}
@article{Staat2012,
  author    = {Staat, Manfred},
  title     = {Limit and shakedown analysis under uncertainty},
  series = {Tap chi Khoa hoc \& ung dung - Dai hoc Ton Duc Thang},
  volume    = {19},
  journal   = {Tap chi Khoa hoc \& ung dung - Dai hoc Ton Duc Thang},
  pages     = {45 -- 47},
  year      = {2012},
  language  = {en}
}
@phdthesis{Tran2019,
  author    = {Tran, Ngoc Trinh},
  title     = {Limit and Shakedown analysis of structures under stochastic conditions},
  publisher = {Technische Universit{\"a}t Braunschweig},
  address   = {Braunschweig},
  doi       = {10.24355/dbbs.084-201902121135-0},
  pages     = {166 S.},
  year      = {2019},
  language  = {en}
}
@inproceedings{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     = {Limit and shakedown analysis of structures under random strength},
  series = {Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training, Hanoi, December 2-3, 2022},
  booktitle = {Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training, Hanoi, December 2-3, 2022},
  publisher = {Nha xuat ban Khoa hoc tu nhien va Cong nghe (Verlag Naturwissenschaft und Technik)},
  address   = {Hanoi},
  isbn      = {978-604-357-084-7},
  pages     = {510 -- 518},
  year      = {2022},
  abstract  = {Direct methods comprising limit and shakedown analysis is a branch of computational mechanics. It plays a significant role in mechanical and civil engineering design. The concept of direct method aims to determinate the ultimate load bearing capacity of structures beyond the elastic range. For practical problems, the direct methods lead to nonlinear convex optimization problems with a large number of variables and onstraints. If strength and loading are random quantities, the problem of shakedown analysis is considered as stochastic programming. This paper presents a method so called chance constrained programming, an effective method of stochastic programming, to solve shakedown analysis problem under random condition of strength. In this our investigation, the loading is deterministic, the strength is distributed as normal or lognormal variables.},
  language  = {en}
}
@phdthesis{Tran2008,
  author    = {Tran, Thanh Ngoc},
  title     = {Limit and shakedown analysis of plates and shells including uncertainties},
  year      = {2008},
  language  = {en}
}