@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}
}
@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},
  booktitle = {Proceedings of (NACOME2022) The 11th National Conference on Mechanics, Vol. 1. Solid Mechanics, Rock Mechanics, Artificial Intelligence, Teaching and Training},
  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}
}
@article{TranKreissigStaat2009,
  author    = {Tran, Thanh Ngoc and Kreißig, R. and Staat, Manfred},
  title     = {Probabilistic limit and shakedown analysis of thin plates and shells},
  series = {Structural safety. 31 (2009), H. 1},
  journal   = {Structural safety. 31 (2009), H. 1},
  publisher = {-},
  isbn      = {0167-4730},
  pages     = {1 -- 18},
  year      = {2009},
  language  = {en}
}
@article{TranKreissigVuetal.2008,
  author    = {Tran, Thanh Ngoc and Kreißig, R. and Vu, Duc Khoi and Staat, Manfred},
  title     = {Upper bound limit and shakedown analysis of shells using the exact Ilyushin yield surface},
  series = {Computer \& Structures. 86 (2008)},
  journal   = {Computer \& Structures. 86 (2008)},
  isbn      = {0045-7949},
  pages     = {1683 -- 1695},
  year      = {2008},
  language  = {en}
}
@inproceedings{TranNovacekTolbaetal.2011,
  author    = {Tran, Thanh Ngoc and Novacek, V. and Tolba, R. and Klinge, U. and Turquier, F. and Staat, Manfred},
  title     = {Experimental and Computational approach to study colorectal anastomosis. ISB2011, Proceedings of the XXIII Congress of the International Society of Biomechanics, Brussels, Belgium, July 3-7, 2011},
  year      = {2011},
  abstract  = {Summary: This paper presents a methodology to study and understand the mechanics of stapled anastomotic behaviors by combining empirical experimentation and finite element analysis. Performance of stapled anastomosis is studied in terms of leakage and numerical results which are compared to in vitro experiments performed on fresh porcine tissue. Results suggest that leaks occur between the tissue and staple legs penetrating through the tissue.},
  subject      = {Anastomose},
  language  = {en}
}
@inproceedings{TranPhamStaat2008,
  author    = {Tran, Thanh Ngoc and Pham, Phu Tinh and Staat, Manfred},
  title     = {Reliability analysis of shells based on direct plasticity methods},
  year      = {2008},
  abstract  = {Abstracts der CD-Rom Proceedings of the 8th World Congress on Computational Mechanics (WCCM8) and 5th Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) 30.06. - 04.07.2008 Venedig, Italien. 2 Seiten Zusammenfassung der Autoren mit graph. Darst. und Literaturverzeichnis},
  subject      = {Finite-Elemente-Methode},
  language  = {en}
}
@article{TranPhamVuetal.2009,
  author    = {Tran, Thanh Ngoc and Pham, Phu Tinh and Vu, D. K. and Staat, Manfred},
  title     = {Reliability Analysis of Inelastic Shell Structures Under Variable Loads},
  series = {Limit States of Materials and Structures : Direct Methods / Hrsg. Dieter Weichert; Hrsg. Alan Ponter},
  journal   = {Limit States of Materials and Structures : Direct Methods / Hrsg. Dieter Weichert; Hrsg. Alan Ponter},
  publisher = {Springer Netherland},
  address   = {Berlin},
  isbn      = {978-1-4020-9633-4},
  pages     = {135 -- 156},
  year      = {2009},
  language  = {en}
}
@incollection{TranStaat2015,
  author    = {Tran, Thanh Ngoc and Staat, Manfred},
  title     = {Uncertainty multimode failure and shakedown analysis of shells},
  series = {Direct methods for limit and shakedown analysis of structures / eds. Paolo Fuschi ...},
  booktitle = {Direct methods for limit and shakedown analysis of structures / eds. Paolo Fuschi ...},
  publisher = {Springer},
  address   = {Cham},
  isbn      = {978-3-319-12927-3 (print) ; 978-3-319-12928-0 (online)},
  doi       = {10.1007/978-3-319-12928-0_14},
  pages     = {279 -- 298},
  year      = {2015},
  abstract  = {This paper presents a numerical procedure for reliability analysis of thin plates and shells with respect to plastic collapse or to inadaptation. The procedure involves a deterministic shakedown analysis for each probabilistic iteration, which is based on the upper bound approach and the use of the exact Ilyushin yield surface. Probabilistic shakedown analysis deals with uncertainties originated from the loads, material strength and thickness of the shell. Based on a direct definition of the limit state function, the calculation of the failure probability may be efficiently solved by using the First and Second Order Reliability Methods (FORM and SORM). The problem of reliability of structural systems (series systems) is handled by the application of a special technique which permits to find all the design points corresponding to all the failure modes. Studies show, in this case, that it improves considerably the FORM and SORM results.},
  language  = {en}
}
@incollection{TranStaat2014,
  author    = {Tran, Thanh Ngoc and Staat, Manfred},
  title     = {Shakedown analysis of Reissner-Mindlin plates using the edge-based smoothed finite element method},
  series = {Direct methods for limit states in structures and materials / Dieter Weichert ; Alan Ponter, ed.},
  booktitle = {Direct methods for limit states in structures and materials / Dieter Weichert ; Alan Ponter, ed.},
  publisher = {Springer},
  address   = {Dordrecht [u.a.]},
  isbn      = {978-94-007-6826-0 (Print) 978-94-007-6827-7 (Online)},
  doi       = {10.1007/978-94-007-6827-7_5},
  pages     = {101 -- 117},
  year      = {2014},
  abstract  = {This paper concerns the development of a primal-dual algorithm for limit and shakedown analysis of Reissner-Mindlin plates made of von Mises material. At each optimization iteration, the lower bound of the shakedown load multiplier is calculated simultaneously with the upper bound using the duality theory. An edge-based smoothed finite element method (ES-FEM) combined with the discrete shear gap (DSG) technique is used to improve the accuracy of the solutions and to avoid the transverse shear locking behaviour. The method not only possesses all inherent features of convergence and accuracy from ES-FEM, but also ensures that the total number of variables in the optimization problem is kept to a minimum compared with the standard finite element formulation. Numerical examples are presented to demonstrate the effectiveness of the present method.},
  language  = {en}
}