@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}
}
@article{StaatWoltersBongartsetal.1990,
  author    = {Staat, Manfred and Wolters, J and Bongarts, W. and Hennings, W. (u.a.)},
  title     = {{\"U}berarbeitete probabilistisch orientierte Sicherheitsanalyse f{\"u}r den HTR-Modul},
  series = {Jahrestagung Kerntechnik '90 / Kerntechnische Gesellschaft e.V. ; Deutsches Atomforum e.V},
  journal   = {Jahrestagung Kerntechnik '90 / Kerntechnische Gesellschaft e.V. ; Deutsches Atomforum e.V},
  publisher = {INFORUM},
  address   = {Bonn},
  pages     = {143 -- 146},
  year      = {1990},
  language  = {de}
}
@article{TopcuMadabhushiStaat2022,
  author    = {Top{\c{c}}u, Murat and Madabhushi, Gopal S.P. and Staat, Manfred},
  title     = {A generalized shear-lag theory for elastic stress transfer between matrix and fibres having a variable radius},
  series = {International Journal of Solids and Structures},
  volume    = {239-240},
  journal   = {International Journal of Solids and Structures},
  number    = {Art. No. 111464},
  publisher = {Elsevier},
  address   = {New York, NY},
  issn      = {0020-7683},
  doi       = {10.1016/j.ijsolstr.2022.111464},
  year      = {2022},
  abstract  = {A generalized shear-lag theory for fibres with variable radius is developed to analyse elastic fibre/matrix stress transfer. The theory accounts for the reinforcement of biological composites, such as soft tissue and bone tissue, as well as for the reinforcement of technical composite materials, such as fibre-reinforced polymers (FRP). The original shear-lag theory proposed by Cox in 1952 is generalized for fibres with variable radius and with symmetric and asymmetric ends. Analytical solutions are derived for the distribution of axial and interfacial shear stress in cylindrical and elliptical fibres, as well as conical and paraboloidal fibres with asymmetric ends. Additionally, the distribution of axial and interfacial shear stress for conical and paraboloidal fibres with symmetric ends are numerically predicted. The results are compared with solutions from axisymmetric finite element models. A parameter study is performed, to investigate the suitability of alternative fibre geometries for use in FRP.},
  language  = {en}
}
@article{TranStaat2020,
  author    = {Tran, Ngoc Trinh and Staat, Manfred},
  title     = {Direct plastic structural design under lognormally distributed strength by chance constrained programming},
  series = {Optimization and Engineering},
  volume    = {21},
  journal   = {Optimization and Engineering},
  number    = {1},
  publisher = {Springer Nature},
  address   = {Cham},
  issn      = {1573-2924},
  doi       = {10.1007/s11081-019-09437-2},
  pages     = {131 -- 157},
  year      = {2020},
  abstract  = {We propose the so-called chance constrained programming model of stochastic programming theory to analyze limit and shakedown loads of structures under random strength with a lognormal distribution. 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) is used with three-node linear triangular elements.},
  language  = {en}
}
@article{TranStaat2021,
  author    = {Tran, Ngoc Trinh and Staat, Manfred},
  title     = {Direct plastic structural design under random strength and random load by chance constrained programming},
  series = {European Journal of Mechanics - A/Solids},
  volume    = {85},
  journal   = {European Journal of Mechanics - A/Solids},
  number    = {Article 104106},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0997-7538},
  doi       = {10.1016/j.euromechsol.2020.104106},
  year      = {2021},
  language  = {en}
}
@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}
}
@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}
}
@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}
}
@article{TranStaat2010,
  author    = {Tran, Thanh Ngoc and Staat, Manfred},
  title     = {Shakedown analysis of two dimensional structures by an edge-based smoothed finite element method},
  pages     = {1 -- 7},
  year      = {2010},
  language  = {en}
}