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Mathematical Problems in Engineering
Volume 2015, Article ID 484615, 11 pages
Research Article

Structural Response Analysis under Dependent Variables Based on Probability Boxes

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China

Received 29 October 2014; Revised 16 March 2015; Accepted 7 April 2015

Academic Editor: Alessandro Palmeri

Copyright © 2015 Z. Xiao and G. Yang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper considers structural response analysis when structural uncertainty parameters distribution cannot be specified precisely due to lack of information and there are complex dependencies in the variables. Uncertainties in parameter are quantified by probability boxes (-boxes) and dependence among uncertain parameters is modeled by copula. To calculate uncertainty structural response, a sampling-based method is proposed. In this method, a sampling strategy is used to sample random intervals from dependent -boxes according to the copula theory and the metamodel-based optimization method is applied to solve a range of structural interval response problems. Two types of errors are presented to evaluate the error of different -boxes. Four numerical examples are investigated to demonstrate the effectiveness of the present method.