TY  - CHAP
A1  - Tran, N. T.
A1  - Tran, Thanh Ngoc
A1  - Matthies, M. G.
A1  - Stavroulakis, G. E.
A1  - Staat, Manfred
T1  - Shakedown Analysis Under Stochastic Uncertainty by Chance Constrained Programming
T2  - Advances in Direct Methods for Materials and Structures
N2  - In this paper we propose a stochastic programming method to analyse limit and shakedown of structures under uncertainty condition of strength. Based on the duality theory, the shakedown load multiplier formulated by the kinematic theorem is proved actually to be the dual form of the shakedown load multiplier formulated by static theorem. In this investigation 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) with three-node linear triangular elements is used for structural analysis.
Y1  - 2017
SN  - 978-3-319-59810-9
U6  - http://dx.doi.org/10.1007/978-3-319-59810-9_6
SP  - 85
EP  - 103
PB  - Springer
CY  - Cham
ER  - 
TY  - CHAP
A1  - Tran, Thanh Ngoc
A1  - Staat, Manfred
T1  - Shakedown analysis of Reissner-Mindlin plates using the edge-based smoothed finite element method
T2  - Direct methods for limit states in structures and materials / Dieter Weichert ; Alan Ponter, ed.
N2  - 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.
Y1  - 2014
SN  - 978-94-007-6826-0 (Print) 978-94-007-6827-7 (Online)
U6  - http://dx.doi.org/10.1007/978-94-007-6827-7_5
SP  - 101
EP  - 117
PB  - Springer
CY  - Dordrecht [u.a.]
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  -