@article{
 title = {Direct plastic structural design under lognormally distributed strength by chance constrained programming},
 type = {article},
 year = {2020},
 keywords = {chance constrained programming,limit analysis,primal dual programming,shakedown analysis,stochastic programming,structural reliability},
 pages = {131-157},
 volume = {21},
 websites = {http://link.springer.com/10.1007/s11081-019-09437-2,https://rdcu.be/bxiaz},
 id = {6f0ba919-3796-3b2a-afcf-ff1d77357145},
 created = {2019-04-04T06:55:43.054Z},
 file_attached = {false},
 profile_id = {93ec0d5b-403c-3f87-b702-40b6362f05e6},
 last_modified = {2020-01-23T18:12:53.224Z},
 read = {false},
 starred = {false},
 authored = {true},
 confirmed = {true},
 hidden = {false},
 citation_key = {Tran2020},
 private_publication = {false},
 abstract = {We propose the so-called chance constrained programming model of stochastic programming 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.},
 bibtype = {article},
 author = {Trần, Ngọc Trình and Staat, Manfred},
 doi = {10.1007/s11081-019-09437-2},
 journal = {Optimization and Engineering},
 number = {1}
}

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