Abstract
An integral analytic process from quantification to propagation based on limited uncertain parameters is investigated to deal with practical engineering problems. A new method by use of the smallest interval-set/hyper-rectangle containing all experimental data is proposed to quantify the parameter uncertainties. With the smallest parameter interval-set, the uncertainty propagation evaluation of the most favorable response and the least favorable response of the structures is studied based on the interval analysis. The relationship between the proposed interval analysis method (IAM) and the classical IAM is discussed. Two numerical examples are presented to demonstrate the feasibility and validity of the proposed method.
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References
Jiang, C., Han, X., Lu, G. Y., Liu, J., Zhang, Z., and Bai, Y. C. Correlation analysis of nonprobabilistic convex model and corresponding structural reliability technique. Computer Methods in Applied Mechanics and Engineering, 200(33–36), 2528–2546 (2011)
Elishakoff, I. and Ohsaki, M. Optimization and Anti-optimization of Structures Under Uncertainty, Imperial College Press, London (2010)
Impollonia, N. and Muscolino, M. G. Interval analysis of structures with uncertain-but-bounded axial stiffness. Computer Methods in Applied Mechanics and Engineering, 200(21–22), 1945–1962 (2011)
Degrauwe, D., Roeck, G. D., and Lombaert, G. Uncertainty quantification in the damage assessment of a cable-stayed bridge by means of fuzzy numbers. Computers and Structures, 87(17–18), 1077–1084 (2009)
Zhai, D. Y. and Mendelm, J. M. Uncertainty measures for general type-2 fuzzy sets. Information Science, 181(3), 503–518 (2011)
Kang, Z. and Luo, Y. J. Non-probabilistic reliability-based topology optimization of geometrically nonlinear structures using convex models. Computer Methods in Applied Mechanics and Engineering, 198(41–44), 3228–3238 (2009)
Qiu, Z. P., Ma, L. H., and Wang, X. J. Non-probabilistic interval analysis method for dynamic response analysis of nonlinear systems with uncertainty. Journal of Sound and Vibration, 319(1–2), 531–540 (2009)
Chen, S. H., Ma, L., Meng, G. W., and Guo, R. An efficient method for evaluating the natural frequencies of structures with uncertain-but-bounded parameters. Computers and Structures, 87(9–10), 582–590 (2009)
Luo, Y. J., Kang, Z., and Li, A. Structural reliability assessment based on probability and convex set mixed model. Computers and Structures, 87(21–22), 1408–1415 (2009)
Guo, S. X. Stability analysis and design of time-delay uncertain systems using robust reliability method. Journal of Systems Engineering and Electronics, 22(3), 493–499 (2011)
Luo, Y. J., Kang, Z., Luo, Z., and Li, A. Continuum topology optimization with non-probabilistic reliability constraints based on multi-ellipsoid convex model. Structural and Multidisciplinary Optimization, 39(3), 297–310 (2009)
Ferson, S., Kreinovich, V., Hajagos, J., Oberkampf, W., and Ginzburg, L. Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty, SAND2007-0939, New York (2007)
Aggarwal, C. C. Managing and Mining Uncertain Data, Springer, New York (2009)
Coleman, H. W. and Steele, W. G. Experimentation, Validation, and Uncertainty Analysis for Engineers, Wiley, New Jersey (2009)
Qiu, Z. P. Comparison of static response of structures using convex models and interval analysis method. International Journal for Numerical Methods in Engineering, 56(12), 1735–1753 (2003)
Öben, T. Analysis of critical buckling load of laminated composites plate with different boundary conditions using FEM and analytical methods. Computional Materials Science, 45(4), 1006–1015 (2009)
Goggin, P. R. The elastic constants of carbon-fibre composites. Journal of Materials Science, 8(2), 233–244 (1973)
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Project supported by the National Natural Science Foundation of China (No. 11002013), the 111 Project (No.B07009), and the Defense Industrial Technology Development Program of China (Nos.A2120110001 and B2120110011)
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Wang, Xj., Wang, L. & Qiu, Zp. Response analysis based on smallest interval-set of parameters for structures with uncertainty. Appl. Math. Mech.-Engl. Ed. 33, 1153–1166 (2012). https://doi.org/10.1007/s10483-012-1612-6
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DOI: https://doi.org/10.1007/s10483-012-1612-6
Key words
- quantification analysis
- smallest interval-set/hyper-rectangle
- uncertain structural response
- most favorable response
- least favorable response