@book{StaatHeitzerYanetal.2000,
  author    = {Staat, Manfred and Heitzer, M. and Yan, Ai-Min and Khoi, Vu Duc and Nguyen, Dang Hung and Valdoire, F. and Lahousse, A.},
  title     = {Limit Analysis of Defects},
  publisher = {Forschungszentrum J{\"u}lich},
  address   = {J{\"u}lich},
  issn      = {0944-2952},
  pages     = {89 S.},
  year      = {2000},
  language  = {en}
}
@article{StaatVu2004,
  author    = {Staat, Manfred and Vu, Duc-Khoi},
  title     = {An Algorithm for Shakedown Analysis for Materials with Temperature Dependent Yield Stress},
  series = {Proceedings in Applied Mathematics and Mechanics (PAMM). 4 (2004), H. 1},
  journal   = {Proceedings in Applied Mathematics and Mechanics (PAMM). 4 (2004), H. 1},
  isbn      = {1617-7061},
  pages     = {231 -- 233},
  year      = {2004},
  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}
}
@article{StaatVu2007,
  author    = {Staat, Manfred and Vu, Duc-Khoi},
  title     = {Limit analysis of flaws in pressurized pipes and cylindrical vessels. Part I: Axial defects},
  series = {Engineering Fracture Mechanics. 74 (2007), H. 3},
  journal   = {Engineering Fracture Mechanics. 74 (2007), H. 3},
  isbn      = {0013-7944},
  pages     = {431 -- 450},
  year      = {2007},
  language  = {en}
}
@article{VuStaatTran2007,
  author    = {Vu, Duc Khoi and Staat, Manfred and Tran, Ich Thinh},
  title     = {Analysis of pressure equipment by application of the primal-dual theory of shakedown},
  series = {Communications in Numerical Methods in Engineering. 23 (2007), H. 3},
  journal   = {Communications in Numerical Methods in Engineering. 23 (2007), H. 3},
  isbn      = {1069-8299},
  pages     = {213 -- 225},
  year      = {2007},
  language  = {en}
}
@article{VuStaat2007,
  author    = {Vu, Duc Khoi and Staat, Manfred},
  title     = {Shakedown analysis of structures made of materials with temperature-dependent yield stress},
  series = {International Journal of Solids and Structures. 44 (2007), H. 13},
  journal   = {International Journal of Solids and Structures. 44 (2007), H. 13},
  isbn      = {0020-7683},
  pages     = {4524 -- 4540},
  year      = {2007},
  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{PhamVuTranetal.2010,
  author    = {Pham, Phu Tinh and Vu, Khoi Duc and Tran, Thanh Ngoc and Staat, Manfred},
  title     = {A primal-dual algorithm for shakedown analysis of elastic-plastic bounded linearly kinematic hardening bodies},
  pages     = {1 -- 7},
  year      = {2010},
  language  = {en}
}
@article{StaatVu2012,
  author    = {Staat, Manfred and Vu, Duc Khoi},
  title     = {Limit analysis of flaws in pressurized pipes and cylindrical vessels Part II: Circumferential defects},
  series = {Engineering Fracture Mechanics ; 97(2013), H. 1},
  volume    = {97},
  journal   = {Engineering Fracture Mechanics ; 97(2013), H. 1},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0013-7944},
  doi       = {10.1016/j.engfracmech.2012.05.017},
  pages     = {314 -- 333},
  year      = {2012},
  abstract  = {Upper and lower bound theorems of limit analyses have been presented in part I of the paper. Part II starts with the finite element discretization of these theorems and demonstrates how both can be combined in a primal-dual optimization problem. This recently proposed numerical method is used to guide the development of a new class of closed-form limit loads for circumferential defects, which show that only large defects contribute to plastic collapse with a rapid loss of strength with increasing crack sizes. The formulae are compared with primal-dual FEM limit analyses and with burst tests. Even closer predictions are obtained with iterative limit load solutions for the von Mises yield function and for the Tresca yield function. Pressure loading of the faces of interior cracks in thick pipes reduces the collapse load of circumferential defects more than for axial flaws. Axial defects have been treated in part I of the paper.},
  language  = {en}
}