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International Journal for Multiscale Computational Engineering
Импакт фактор: 1.016 5-летний Импакт фактор: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Печать: 1543-1649
ISSN Онлайн: 1940-4352

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International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2016015829
pages 215-235


Jianbing Chen
State Key Laboratory of Disaster Reduction in Civil Engineering and School of Civil Engineering, Tongji University, Shanghai, PRC
Pengyan Song
College of Civil Engineering and Architecture, Hebei University, Baoding, Hebei, PRC
Xiaodan Ren
School of Civil Engineering, Tongji University, Shanghai, PRC

Краткое описание

The impact of randomness of structural parameters on structural responses and performance is of paramount importance. In engineering practice, the distributions of most random parameters are nonuniform and non-Gaussian. The probability density evolution method is capable in these cases of capturing the probability density functions of the responses. To optimally select the representative point set, the L2-discrepancy in cubature formulae, which is only applicable to uniform distributions with equal weights, is generalized to: (i) consider general nonuniform, non-Gaussian distributions; and (ii) involve the impact of the assigned probabilities as unequal weights. The extended Koksma-Hlawka inequality is proved rigorously, and the explicit expression for the generalized L2-discrepancy (GL2-discrepancy) is derived. A point selection strategy by minimizing the GL2-discrepancy is proposed. In particular, a two-step approach is suggested, and the existence and uniqueness of optimal assigned probabilities are proved. Numerical examples are illustrated, showing the fair accuracy and efficiency of the proposed method. Particularly, in obvious contrast to most existing random vibration analyses of nonlinear structures where the component-structure two-level models are employed, stochastic response of a structure with a refined model incorporating the stochastic damage constitutive law of concrete material is implemented. Problems to be further studied are discussed.