TY  - JOUR
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  - FEM shakedown analysis of structures under random strength with chance constrained programming
JF  - Vietnam Journal of Mechanics
N2  - 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.
KW  - limit analysis
KW  - shakedown analysis
KW  - chance constrained programming
KW  - stochastic programming
KW  - reliability of structures
Y1  - 2022
U6  - http://dx.doi.org/10.15625/0866-7136/17943
SN  - 0866-7136
SN  - 2815-5882
VL  - 44
IS  - 4
SP  - 459
EP  - 473
PB  - Vietnam Academy of Science and Technology (VAST)
ER  - 
TY  - JOUR
A1  - Tran, Ngoc Trinh
A1  - Staat, Manfred
T1  - Direct plastic structural design under random strength and random load by chance constrained programming
JF  - European Journal of Mechanics - A/Solids
Y1  - 2021
U6  - http://dx.doi.org/10.1016/j.euromechsol.2020.104106
SN  - 0997-7538
VL  - 85
IS  - Article 104106
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Tran, Ngoc Trinh
A1  - Staat, Manfred
T1  - Direct plastic structural design under lognormally distributed strength by chance constrained programming
JF  - Optimization and Engineering
N2  - 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.
Y1  - 2020
U6  - http://dx.doi.org/10.1007/s11081-019-09437-2
SN  - 1573-2924
VL  - 21
IS  - 1
SP  - 131
EP  - 157
PB  - Springer Nature
CY  - Cham
ER  -