×
Fabro, A. T.; Ritto, T. G.; Sampaio, R.; Arruda, J. R. F.

Stochastic analysis of a cracked rod modeled via the spectral element method. (English) Zbl 1272.74379

Mech. Res. Commun. 37, No. 3, 326-331 (2010).
Summary: The spectral element method is used to model a cracked rod, where the crack is modeled as a localized flexibility. The crack flexibility is derived using Castigliano’s theorem, and the uncertainties are modeled by the parametric probabilistic approach. The probabilistic model is constructed directly for the variable of interest, i.e., the crack flexibility. Two different probabilistic models, where the probability density functions are constructed using the Maximum Entropy Principle, are used and compared. It is shown that the model with more uncertainty is the one constructed with less information. Monte Carlo simulations are performed in order to estimate the frequency response function envelopes.

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74R10 Brittle fracture
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
74S25 Spectral and related methods applied to problems in solid mechanics

Keywords:

wave propagation; uncertainty quantification; stochastic analysis; spectral element method
PDF BibTeX XML Cite
\textit{A. T. Fabro} et al., Mech. Res. Commun. 37, No. 3, 326--331 (2010; Zbl 1272.74379)
Full Text: DOI Link

References:

[1] Craig, R. R.: Structural dynamics: an introduction to computer methods, (1981)
[2] Doyle, J. F.: Wave propagation in structures, (1997) · Zbl 0876.73018
[3] Jaynes, E.: Information theory and statistical mechanics, The physical review 106, No. 4, 1620-1630 (1957)
[4] Jaynes, E.: Information theory and statistical mechanics II, The physical review 108, 171-190 (1957) · Zbl 0084.43701
[5] Kapur, J. N.; Kesavan, H. K.: Entropy optimization principles with applications, (1992) · Zbl 0718.62007
[6] Krawczuk, M.; Grabowska, J.; Palacz, M.: Longitudinal wave propagation. Part I – comparison of rod theories, Journal of sound and vibration 295, 461-478 (2006)
[7] Krawczuk, M.; Grabowska, J.; Palacz, M.: Longitudinal wave propagation. Part II – analysis of crack influence, Journal of sound and vibration 295, 479-490 (2006)
[8] Ostachowicz, W. M.: Damage detection of structures using spectral finite element method, Computers & structures 86, 454-462 (2008) · Zbl 1161.74415
[9] Palacz, M.; Krawczuk, M.: Analysis of longitudinal wave propagation in a cracked rod by the spectral element method, Computers & structures 80, 1809-1816 (2002)
[10] Rubinstein, R. Y.; Kroese, D. P.: Simulation and the Monte Carlo method, (2008) · Zbl 1147.68831
[11] Shannon, C. E.: A mathematical theory of communication, Bell system technical journal 27, 379-423 (1948) · Zbl 1154.94303
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.