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 - CHAP A1 - Tran, Thanh Ngoc A1 - Staat, Manfred T1 - Uncertainty multimode failure and shakedown analysis of shells T2 - Direct methods for limit and shakedown analysis of structures / eds. Paolo Fuschi ... N2 - 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. KW - Limit analysis KW - Shakedown analysis KW - Reliability analysis KW - Multimode failure KW - Non-linear optimization Y1 - 2015 SN - 978-3-319-12927-3 (print) ; 978-3-319-12928-0 (online) U6 - http://dx.doi.org/10.1007/978-3-319-12928-0_14 SP - 279 EP - 298 PB - Springer CY - Cham ER - 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 - CHAP A1 - Tran, Thanh Ngoc A1 - Pham, Phu Tinh A1 - Staat, Manfred T1 - Reliability analysis of shells based on direct plasticity methods N2 - 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 N2 - Abstracts of the Proceedings of the 8th World Congress on Computational Mechanics (WCCM8) and 5th Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008) June 30th - July, 4th 2008, Venice, Italy. 2 pages with abstracts of the authors, Ill. and references. KW - Finite-Elemente-Methode KW - Limit analysis KW - Shakedown analysis KW - First-order reliability method KW - second-order reliability method KW - Sensitivity Y1 - 2008 ER - TY - JOUR A1 - Staat, Manfred T1 - Basis Reduction for the Shakedown Problem for Bounded Kinematic Hardening Material N2 - Limit and shakedown analysis are effective methods for assessing the load carrying capacity of a given structure. The elasto–plastic behavior of the structure subjected to loads varying in a given load domain is characterized by the shakedown load factor, defined as the maximum factor which satisfies the sufficient conditions stated in the corresponding static shakedown theorem. The finite element dicretization of the problem may lead to very large convex optimization. For the effective solution a basis reduction method has been developed that makes use of the special problem structure for perfectly plastic material. The paper proposes a modified basis reduction method for direct application to the two-surface plasticity model of bounded kinematic hardening material. The considered numerical examples show an enlargement of the load carrying capacity due to bounded hardening. KW - Finite-Elemente-Methode KW - Einspielen KW - Basis Reduktion KW - konvexe Optimierung KW - FEM KW - Druckgeräte KW - Basis reduction KW - Convex optimization KW - FEM KW - Shakedown analysis Y1 - 2000 ER - TY - JOUR A1 - Staat, Manfred T1 - Direct finite element route for design-by-analysis of pressure components N2 - In the new European standard for unfired pressure vessels, EN 13445-3, there are two approaches for carrying out a Design-by-Analysis that cover both the stress categorization method (Annex C) and the direct route method (Annex B) for a check against global plastic deformation and against progressive plastic deformation. This paper presents the direct route in the language of limit and shakedown analysis. This approach leads to an optimization problem. Its solution with Finite Element Analysis is demonstrated for mechanical and thermal actions. One observation from the examples is that the so-called 3f (3Sm) criterion fails to be a reliable check against progressive plastic deformation. Precise conditions are given, which greatly restrict the applicability of the 3f criterion. KW - Einspielen KW - Plastizität KW - Deformation KW - Analytischer Zulaessigkeitsnachweis KW - Einspiel-Analyse KW - fortschreitende plastische Deformation KW - alternierend Verformbarkeit KW - Einspiel-Kriterium KW - Design-by-analysis KW - Shakedown analysis KW - Progressive plastic deformation KW - Alternating plasticity KW - Shakedown criterion Y1 - 2005 ER -