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Extreme structural response analysis of truss structures under material uncertainty via linear mixed 0–1 programming
Author(s) -
Guo Xu,
Bai Wei,
Zhang Weisheng
Publication year - 2008
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2298
Subject(s) - truss , extreme value theory , moduli , linear programming , structural engineering , bounded function , upper and lower bounds , displacement (psychology) , mathematics , modulus , mathematical optimization , bar (unit) , engineering , mathematical analysis , geometry , statistics , geology , physics , oceanography , psychology , quantum mechanics , psychotherapist
This paper concerns the extreme structural response analysis of truss structures taking the possible uncertainties of Young's moduli of the bars into consideration. The uncertainty of Young's modulus is described by a non‐probability but bounded interval model. With the use of this uncertain model, it is shown that the structural responses such as nodal displacement and bar stress will attain their extreme values when Young's moduli of the bars take either their upper or lower bound value. Based on this conclusion and simultaneous analysis and design formulation, a linear mixed 0–1 programming problem can be constructed to find the extreme values of the structural response by the well‐established branch‐and‐bound approach with global optimality. The proposed approach is applied to several test problems for the demonstration of its validity. Copyright © 2008 John Wiley & Sons, Ltd.