@article{ZhenLiangStaatetal.2024,
  author    = {Zhen, Manghao and Liang, Yunpei and Staat, Manfred and Li, Quanqui and Li, Jianbo},
  title     = {Discontinuous fracture behaviors and constitutive model of sandstone specimens containing non-parallel prefabricated fissures under uniaxial compression},
  series = {Theoretical and Applied Fracture Mechanics},
  volume    = {131},
  journal   = {Theoretical and Applied Fracture Mechanics},
  publisher = {Elsevier},
  address   = {Amsterdam},
  issn      = {0167-8442},
  doi       = {10.1016/j.tafmec.2024.104373},
  pages     = {Artikel 104373},
  year      = {2024},
  abstract  = {The deformation and damage laws of non-homogeneous irregular structural planes in rocks are the basis for studying the stability of rock engineering. To investigate the damage characteristics of rock containing non-parallel fissures, uniaxial compression tests and numerical simulations were conducted on sandstone specimens containing three non-parallel fissures inclined at 0°, 45° and 90° in this study. The characteristics of crack initiation and crack evolution of fissures with different inclinations were analyzed. A constitutive model for the discontinuous fractures of fissured sandstone was proposed. The results show that the fracture behaviors of fissured sandstone specimens are discontinuous. The stress-strain curves are non-smooth and can be divided into nonlinear crack closure stage, linear elastic stage, plastic stage and brittle failure stage, of which the plastic stage contains discontinuous stress drops. During the uniaxial compression test, the middle or ends of 0° fissures were the first to crack compared to 45° and 90° fissures. The end with small distance between 0° and 45° fissures cracked first, and the end with large distance cracked later. After the final failure, 0° fissures in all specimens were fractured, while 45° and 90° fissures were not necessarily fractured. Numerical simulation results show that the concentration of compressive stress at the tips of 0°, 45° and 90° fissures, as well as the concentration of tensile stress on both sides, decreased with the increase of the inclination angle. A constitutive model for the discontinuous fractures of fissured sandstone specimens was derived by combining the logistic model and damage mechanic theory. This model can well describe the discontinuous drops of stress and agrees well with the whole processes of the stress-strain curves of the fissured sandstone specimens.},
  language  = {en}
}
@article{WegmannHacklStaatetal.2016,
  author    = {Wegmann, Kilian and Hackl, Michael and Staat, Manfred and Mayer, Katharina and M{\"u}ller, Lars-Peter},
  title     = {Double plate osteosynthesis of proximal ulna fractures: biomechanical and clinical results},
  series = {Knee surgery, sports traumatology, arthroscopy},
  volume    = {Volume 24},
  journal   = {Knee surgery, sports traumatology, arthroscopy},
  number    = {Supplement 1},
  publisher = {Springer},
  address   = {Berlin},
  issn      = {0942-2056},
  doi       = {10.1007/s00167-016-4079-0},
  pages     = {58 -- 59},
  year      = {2016},
  abstract  = {While plate fixation of proximal ulna fractures might lead to superior clinical results compared to tension band wiring, regular plates represent an established risk factor for wound complications. The olecranon double plates (Medartis, Basel, CH) might decrease complications related to the osteosynthesis because of their low profile and better anatomical fit. This study aimed to evaluate the biomechanical performance and clinical results of the olecranon double plates.},
  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{VantStaatBaroud2008,
  author    = {Vant, Christianne and Staat, Manfred and Baroud, Gamal},
  title     = {Percutaneous Vertebroplasty: A Review of Two Intraoperative Complications},
  series = {Bioengineering in Cell and Tissue Research / Artmann, Gerhard M. ; Chien, Shu (Eds.)},
  journal   = {Bioengineering in Cell and Tissue Research / Artmann, Gerhard M. ; Chien, Shu (Eds.)},
  publisher = {Springer},
  address   = {Berlin},
  isbn      = {978-3-540-75408-4},
  pages     = {527 -- 539},
  year      = {2008},
  language  = {en}
}
@article{UllrichGrottkeRossaintetal.2010,
  author    = {Ullrich, Sebastian and Grottke, Oliver and Rossaint, Rolf and Staat, Manfred and Deserno, Thomas M. and Kuhlen, Torsten},
  title     = {Virtual Needle Simulation with Haptics for Regional Anaesthesia},
  pages     = {1 -- 3},
  year      = {2010},
  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}
}
@article{TranStaat2013,
  author    = {Tran, Thanh Ngoc and Staat, Manfred},
  title     = {An Edge-Based Smoothed Finite Element Method for Primal-Dual Shakedown Analysis of Structures Under Uncertainties},
  series = {Limit State of Materials and Structures : Direct Methods 2. Saxc{\´e}, G{\´e}ry de (Hrsg.)},
  journal   = {Limit State of Materials and Structures : Direct Methods 2. Saxc{\´e}, G{\´e}ry de (Hrsg.)},
  publisher = {Springer},
  address   = {Dordrecht},
  isbn      = {978-94-007-5424-9},
  pages     = {89 -- 102},
  year      = {2013},
  language  = {en}
}
@inproceedings{TranStaat2012,
  author    = {Tran, Thanh Ngoc and Staat, Manfred},
  title     = {A primal-dual shakedown analysis of 3D structures using the face-based smoothed finite element method},
  series = {Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)},
  booktitle = {Proceedings European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012)},
  editor    = {Eberhardsteiner, J.},
  year      = {2012},
  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}
}
@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}
}
@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{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{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}
}
@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}
}
@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{TranTranMatthiesetal.2016,
  author    = {Tran, Ngoc Trinh and Tran, Thanh Ngoc and Matthies, Hermann G. and Stavroulakis, Georgios Eleftherios and Staat, Manfred},
  title     = {FEM Shakedown of uncertain structures by chance constrained programming},
  series = {PAMM Proceedings in Applied Mathematics and Mechanics},
  volume    = {16},
  booktitle = {PAMM Proceedings in Applied Mathematics and Mechanics},
  number    = {1},
  issn      = {1617-7061},
  doi       = {10.1002/pamm.201610346},
  pages     = {715 -- 716},
  year      = {2016},
  language  = {en}
}
@inproceedings{TranTranMatthiesetal.2016,
  author    = {Tran, Ngoc Trinh and Tran, Thanh Ngoc and Matthies, H. G. and Stavroulakis, G. E. and Staat, Manfred},
  title     = {Shakedown analysis of plate bending analysis under stochastic uncertainty by chance constrained programming},
  series = {ECCOMAS Congress 2016, VII European Congress on Computational Methods in Applied Sciences and Engineering. Crete Island, Greece, 5-10 June 2016},
  booktitle = {ECCOMAS Congress 2016, VII European Congress on Computational Methods in Applied Sciences and Engineering. Crete Island, Greece, 5-10 June 2016},
  editor    = {Papadrakakis, M.},
  pages     = {13 S.},
  year      = {2016},
  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}
}