Wavelet-based model for stochastic analysis of beam structures

AIAA Journal

Volumn 36, Issue 3, 1998, Pages 465-470

  Mei, Hong ^a   Agrawal, Om P ^a,c   Pai, Shantaram S ^b,c  

^a SOUTHERN ILLINOIS UNIVERSITY   (United States)

^b NASA GLENN RESEARCH CENTER   (United States)

^c AIAA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000486472     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/2.387     Document Type: Article

References (32)

1. Daubechies, I., "Orthonormal Bases of Compactly Supported Wavelets," Communications on Pure and Applied Mathematics, Vol. 41, No. 7, 1988, pp. 909-996.
2. Beylkin, G., Coifman, R., and Rokhlin, V., "Fast Wavelet Transforms and Numerical Algorithms, I," Communications on Pure and Applied Mathematics, Vol. 44, No. 2, 1991, pp. 141-183.
3. Alpert, B. K., "Wavelets and Other Bases for Fast Numerical Linear Algebra," Wavelets - A Tutorial in Theory, and Applications, edited by C. K. Chui, Academic, Boston, MA, 1992, pp. 181-216.
4. Brandt, A., and Lubrecht, A. A., "Multilevel Matrix Multiplication and Fast Solution of Integral Equations," Journal of Computational Physics, Vol. 90, No. 2, 1990, pp. 348-370.
5. Harten, A., and Yad-Shalom, I., "Fast Multiresolution Algorithms for Matrix Vector Multiplication," SIAM Journal on Numerical Analysis, Vol. 31, No. 4, 1994, pp. 1191-1218.
6. Qian, S., and Weiss, J., "Wavelets and the Numerical Solution of Partial Differential Equations," Journal of Computational Physics, Vol. 106, No. 1, 1993, pp. 155-175.
7. Amaratunga, K., Williams, J. R., Qian, S., and Weiss, J., "Wavelet-Galerkin Solution for One-Dimensional Partial Differential Equations," International Journal of Numerical Methods in Engineering, Vol. 37, No. 16, 1994, pp. 2703-2716.
8. Beylkin, G., "Wavelets and Fast Numerical Algorithm," Different perspectives on Wavelets, edited by I. Daubechies, American Mathematical Society, Providence, RI, 1993, pp. 89-117.
9. Greenshields, I. R., and Rosiene, J. A., "Spectral Decomposition by Wavelet Approximation to the Karhunen-Loève Transform," SPIE Ophthalmic Technologies II, Vol. 1644, 1992, pp. 282-286.
10. Wornell, G. W., "A Karhunen-Loève Like Expansion for 1/f Processes via Wavelets," IEEE Transactions on Information Theory, Vol. 36, No. 4, 1990, pp. 859-861.
11. Dijkerman, R. W., and Mazumdar, R. R., "Wavelet Representations of Stochastic Processes and Multiresolution Stochastic Models," IEEE Transactions on Signal Processing, Vol. 42, No. 7, 1994, pp. 1640-1652.
12. Zhang, J., and Walter, G., "A Wavelet-Based KL-Like Expansion for Wide-Sense Stationary Random Processes," IEEE Transactions on Signal Processing, Vol. 42, No. 7. 1994, pp. 1737-1745.
13. Shinozuka, M., and Astill, J., "Random Eigenvalue Problems in Structural Mechanics," AIAA Journal, Vol. 10, No. 4, 1972, pp. 456-462.
14. Shinozuka, M., and Lenoe, E., "A Probabilistic Model for Spatial Distribution of Material Properties," Engineering Fracture Mechanics, Vol. 8, No. 1, 1976, pp. 217-227.
15. Nakagiri, S., and Hisada, T., "Stochastic Finite Element Method Applied to Structural Analysis with Uncertain Parameters," Proceedings of the International Conference on finite Element Methods, Gordon and Breach, New York, 1982, pp. 206-211.
16. Liu, W. K., Besterfield, G., and Belytschko, T., Transient Probabilistic Systems," Computer Methods in Applied Mechanics and Engineering, Vol. 67, 1988, pp. 27-54.
17. Adomian, G., and Malakian, K., "Inversion of Stochastic Partial Differential Operators - the linear case," Journal of Mathematical Analysis and Applications, Vol. 77, No. 2, 1980. pp. 505-512.
18. Benaroya, H., and Rehak, M., "Parametric Excitations I: Exponentially Correlated Parameters," ASCE Journal of Engineering Mechanics, Vol 113, No. 6, 1917, pp. 861-874.
19. Yamazaki, F., and Shinozuka, M., "Neumann Expansion for Stochastic Finite Element Analysis," ASCE Journal of Engineering Mechanics, Vol. 114, No. 8, 1988, pp. 1335-1354.
20. Ghanem, R. G., and Spanos, P. D., "Stochastic Finite-Element Expansion for Random Media," ASCE Journal of Engineering Mechanics, Vol. 115, No. 5, 1989, pp. 1035-1053.
21. Ghanem, R. G., and Spanos, P. D., "Spectral Stochastic Finite-Element Formulation for Reliability Analysis," ASCE Journal of Engineering Mechanics, Vol. 117, No. 10, 1991, pp. 2351-2372.
22. Ghanem, R. G., and Spanos, P. D., Stochastic Finite-Elements: A Spectral Approach, Springer-Verlag, New York, 1991.
23. Burczyński, T., "The Boundary Element Method for Stochastic Potential Problems," Applied Mathematical Modeling, Vol. 9, No. 3, 1985, pp. 189-194.
24. Drewniak, J., "Boundary Elements for Random Heat Conduction Problems," Engineering Analysis, Vol. 2, No. 3, 1985, pp 168-170.
25. Ettouney, M., Benaroya, H., and Wright, H., "Probabilistic Boundary Elemeat Method (PBEM)," Computational Mechanics of Probabilistic and Reliability Analysis, edited by W. K. Liu and T. Belytschko, Empress International, Lausanne, 1989, pp. 141-166.
26. Ettouney, M., Benaroya, H., and Wright, H., "Boundary Element Methods in Probabilistic Structural Analysis (PBEM)," Applied Mathematical Modeling, Vol. 13, No. 7, 1989, pp. 432-441.
27. Cheng, A. H. D., and Lafe, O. E., "Boundary Element Solution for Stochastic Groundwater Flow: Random Boundary Condition and Recharge," Water Resources Research, Vol. 27, No. 2, 1991, pp. 231-242.
28. Kaljević I., and Saigal, S., "Stochastic Boundary Elements in Elastostatics," Computer Methods in Applied Mechanics and Engineering, Vol. 109, Nos. 3-4, 1993, pp. 259-280.
29. Kaljević I., and Saigal, S., "Stochastic Boundary Element Method for Two-Dimensional Potential Flow in Homogeneous Domains," International Journal of Solids and Structures, Vol, 32, No. 13, 1995, pp. 1873-1892.
30. Kaljević, I., and Saigal, S., "Stochastic Boundary Elements for Two-Dimensional Potential Flow in Non-Homogeneous Media," Computer Methods in Applied Mechanics and Engineering,Vol. 121, 1995, pp. 211-230.
31. Agrawal, O. P., and Sonti, V. R., "Modeling of Stochastic Dynamic Systems Using Hamilton's Law of Varying Action," Journal of Sound and Vibration, Vol. 192, No. 2, 1996, PP. 399-412.
32. Van-Trees, H. L., Detection, Estimation, and Modulation Theory, part 1, Wiley, New York, 1968.