TY - CHAP A1 - Staat, Manfred A1 - Tran, Thanh Ngoc A1 - Pham, Phu Tinh T1 - Limit and shakedown reliability analysis by nonlinear programming N2 - 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. KW - Finite-Elemente-Methode KW - Limit analysis KW - Shakedown analysis Y1 - 2008 ER - TY - JOUR A1 - Staat, Manfred A1 - Heitzer, M. T1 - Limit and Shakedown Analysis with Uncertain Data JF - Stochastic optimization techniques : numerical methods and technical applications / Marti, K. [ed] Y1 - 2002 SN - 3-540-42889-5 SP - 241 EP - 254 PB - Springer CY - Heidelberg ER - TY - CHAP A1 - Staat, Manfred T1 - Limit and shakedown analysis under uncertainty T2 - Proceedings International Conference on Advances in Computational Mechanics (ACOME) Y1 - 2012 N1 - International Conference on Advances in Computational Mechanics (ACOME), August 14-16, 2012, Ho Chi Minh City, Vietnam SP - 837 EP - 861 ER - TY - JOUR A1 - Staat, Manfred T1 - Limit and shakedown analysis under uncertainty JF - International journal of computational methods : IJCM Y1 - 2013 SN - 0219-8762 SP - Publ. online PB - World Scientific Publishing CY - Singapore ER - TY - JOUR A1 - Staat, Manfred T1 - Limit and shakedown analysis under uncertainty JF - Tap chi Khoa hoc & ung dung - Dai hoc Ton Duc Thang Y1 - 2012 N1 - = Journal of Applied Sciences - Ton Duc Thang University VL - 19 SP - 45 EP - 47 ER - TY - THES A1 - Tran, Ngoc Trinh T1 - Limit and Shakedown analysis of structures under stochastic conditions Y1 - 2019 U6 - http://dx.doi.org/10.24355/dbbs.084-201902121135-0 PB - Technische Universität Braunschweig CY - Braunschweig ER - TY - CHAP A1 - Tran, Ngoc Trinh A1 - Trinh, Tu Luc A1 - Dao, Ngoc Tien A1 - Giap, Van Tan A1 - Truong, Manh Khuyen A1 - Dinh, Thuy Ha A1 - Staat, Manfred T1 - Limit and shakedown analysis of structures under random strength T2 - 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 N2 - 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. KW - Reliability of structures KW - Stochastic programming KW - Chance constrained programming KW - Shakedown analysis KW - Limit analysis Y1 - 2022 SN - 978-604-357-084-7 SP - 510 EP - 518 PB - Nha xuat ban Khoa hoc tu nhien va Cong nghe (Verlag Naturwissenschaft und Technik) CY - Hanoi ER - TY - THES A1 - Tran, Thanh Ngoc T1 - Limit and shakedown analysis of plates and shells including uncertainties Y1 - 2008 N1 - Chemnitz, Techn. Univ., Diss., 2008 ER - TY - JOUR A1 - Staat, Manfred A1 - Vu, Duc-Khoi T1 - Limit analysis of flaws in pressurized pipes and cylindrical vessels. Part I: Axial defects JF - Engineering Fracture Mechanics. 74 (2007), H. 3 Y1 - 2007 SN - 0013-7944 SP - 431 EP - 450 ER - TY - JOUR A1 - Staat, Manfred A1 - Vu, Duc Khoi T1 - Limit analysis of flaws in pressurized pipes and cylindrical vessels Part II: Circumferential defects JF - Engineering Fracture Mechanics ; 97(2013), H. 1 N2 - 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. Y1 - 2012 U6 - http://dx.doi.org/10.1016/j.engfracmech.2012.05.017 SN - 0013-7944 VL - 97 SP - 314 EP - 333 PB - Elsevier CY - Amsterdam ER -