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Exact response bound analysis of truss structures via linear mixed 0‐1 programming and sensitivity bounding technique
Author(s) -
Du Jianming,
Du Zongliang,
Wei Yihai,
Zhang Weisheng,
Guo Xu
Publication year - 2018
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.5913
Subject(s) - bounding overwatch , truss , mathematical optimization , linear programming , upper and lower bounds , bounded function , sensitivity (control systems) , nondeterministic algorithm , mathematics , interval arithmetic , function (biology) , monotonic function , polynomial , computer science , algorithm , engineering , mathematical analysis , structural engineering , artificial intelligence , electronic engineering , evolutionary biology , biology
Summary In the present paper, finding the exact bound of structural response for truss structures is considered under bounded interval type uncertainty. This problem is challenging since seeking the exact bound corresponds to locating the global optima of a multivariate function (generally nonconvex). Traditional treatment of this problem involves the solution of a linear mixed 0‐1 programming problem, which is a highly computationally demanding task especially when large‐scale structures are taken into consideration. In order to alleviate the computational effort, a sensitivity bounding technique is developed in this work using the tools from convex analysis to disclose the monotonicity of concerned structural response function with respect to 0‐1 variables. It is shown that this technique can not only reduce the number of 0‐1 variables substantially but also change the computational complexity of the considered problem from nondeterministic polynomial–hard to nondeterministic polynomial–hard in some cases. The proposed approach provides the possibility of finding the exact bound of structural response for large‐scale truss structures within a reasonable time, and its effectiveness is demonstrated through several numerical examples.