TY - JOUR A1 - Tran, Ngoc Trinh A1 - Staat, Manfred T1 - Direct plastic structural design under lognormally distributed strength by chance constrained programming T2 - 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 UR - https://opus.bibliothek.fh-aachen.de/opus4/frontdoor/index/index/docId/8897 SN - 1573-2924 VL - 21 IS - 1 SP - 131 EP - 157 PB - Springer Nature CY - Cham ER -