@article{tran_direct_2019,
	title = {Direct plastic structural design under lognormally distributed strength by chance constrained programming},
	copyright = {All rights reserved},
	issn = {1389-4420},
	url = {http://link.springer.com/10.1007/s11081-019-09437-2 https://rdcu.be/bxiaz},
	doi = {10.1007/s11081-019-09437-2},
	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.},
	journal = {Optimization and Engineering},
	author = {Trần, Ngọc Trình and Staat, Manfred},
	month = apr,
	year = {2019},
	note = {ZSCC: 0000000},
	keywords = {chance constrained programming, limit analysis, primal dual programming, shakedown analysis, stochastic programming, structural reliability},
}

{"_id":"i6xHCPwJoertffe4q","bibbaseid":"trn-staat-directplasticstructuraldesignunderlognormallydistributedstrengthbychanceconstrainedprogramming-2019","authorIDs":["5dba9b3cdd3901df010000ff","5dbc2e733d8602de01000053","7jhRHDZJ6AgPa9GzF"],"author_short":["Trần, N. T.","Staat, M."],"bibdata":{"bibtype":"article","type":"article","title":"Direct plastic structural design under lognormally distributed strength by chance constrained programming","copyright":"All rights reserved","issn":"1389-4420","url":"http://link.springer.com/10.1007/s11081-019-09437-2 https://rdcu.be/bxiaz","doi":"10.1007/s11081-019-09437-2","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.","journal":"Optimization and Engineering","author":[{"propositions":[],"lastnames":["Trần"],"firstnames":["Ngọc","Trình"],"suffixes":[]},{"propositions":[],"lastnames":["Staat"],"firstnames":["Manfred"],"suffixes":[]}],"month":"April","year":"2019","note":"ZSCC: 0000000","keywords":"chance constrained programming, limit analysis, primal dual programming, shakedown analysis, stochastic programming, structural reliability","bibtex":"@article{tran_direct_2019,\n\ttitle = {Direct plastic structural design under lognormally distributed strength by chance constrained programming},\n\tcopyright = {All rights reserved},\n\tissn = {1389-4420},\n\turl = {http://link.springer.com/10.1007/s11081-019-09437-2 https://rdcu.be/bxiaz},\n\tdoi = {10.1007/s11081-019-09437-2},\n\tabstract = {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.},\n\tjournal = {Optimization and Engineering},\n\tauthor = {Trần, Ngọc Trình and Staat, Manfred},\n\tmonth = apr,\n\tyear = {2019},\n\tnote = {ZSCC: 0000000},\n\tkeywords = {chance constrained programming, limit analysis, primal dual programming, shakedown analysis, stochastic programming, structural reliability},\n}\n\n","author_short":["Trần, N. T.","Staat, M."],"key":"tran_direct_2019","id":"tran_direct_2019","bibbaseid":"trn-staat-directplasticstructuraldesignunderlognormallydistributedstrengthbychanceconstrainedprogramming-2019","role":"author","urls":{"Paper":"http://link.springer.com/10.1007/s11081-019-09437-2 https://rdcu.be/bxiaz"},"keyword":["chance constrained programming","limit analysis","primal dual programming","shakedown analysis","stochastic programming","structural reliability"],"metadata":{"authorlinks":{"staat, m":"https://bibbase.org/show?bib=https%3A%2F%2Fapi.zotero.org%2Fusers%2F6114608%2Fcollections%2FTJTBXR6Y%2Fitems%3Fkey%3DqbBfhA5sX7Oco1IT48KAsV2v%26format%3Dbibtex%26limit%3D100&msg=embed"}},"downloads":0},"bibtype":"article","creationDate":"2019-10-31T08:28:44.310Z","downloads":0,"keywords":["chance constrained programming","limit analysis","primal dual programming","shakedown analysis","stochastic programming","structural reliability"],"search_terms":["direct","plastic","structural","design","under","lognormally","distributed","strength","chance","constrained","programming","trần","staat"],"title":"Direct plastic structural design under lognormally distributed strength by chance constrained programming","year":2019,"biburl":"https://api.zotero.org/users/6114608/collections/TJTBXR6Y/items?key=qbBfhA5sX7Oco1IT48KAsV2v&format=bibtex&limit=100","dataSources":["dAp5WYHoS5SWSKWoa","i5FJs3p7i69258A5p","J85Tv7d2C3MXhGnoK"]}