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Abstrakty
In the paper a non-statistical approach for eigenproblems of cracked cross-sectional beam systems with random parameters is proposed. The methodology is based on the mean-centered second moment analysis of a random variable expanded in the second-order perturbation form. The system random parameters are defined by their first two statistical moments. A hierarchical system of equations is obtained and solved for the first two statistical moments for the eigenpairs. An exact solution of the first- and second-order sensitivity equations is presented. Analytical and computational issues of the stochastic formulation are discussed. Comprehensive numerical results are given for cantilever and fixed-hinged beams. The efficient technique may be employed directly for a wide class of problems in fracture mechanics.
Słowa kluczowe
Rocznik
Tom
Strony
69--88
Opis fizyczny
Bibliogr. 28 poz., rys.
Twórcy
autor
autor
- Technical University of Szczecin, Szczecin, Poland, Faculty of Maritime Technology, Al. Piastów 41, 71-065 Szczecin
Bibliografia
- 1. Knott J. F., Fundamentals of Fracture Mechanics, Butterworth, 1976.
- 2. Tada H., Paris P. C., Irwin G. R., The Stress Analysis of Cracks. Handbook, Hellertown, 1973.
- 3. Nowacki W Dynamika budowli, Arkady, 1972.
- 4. Kobayashi A. S., Photoelastic studies of fracture, [in:] Liebowitz H. (ed.), Fracture, Vol. 3, Chapter 5, Acad. Press, 1971.
- 5. Drewko J., Sperski M., Vibration of multi-chamber Shell structures with discontinuously variable crosssections, Eng frans., 39, 1991, 163—180.
- 6. Drewko J. , Elastic hinge modelling in vibration analysis of beams with crosssections weakened by cracks, Marine Tech. Trans., 10, 1999, 93—103.
- 7. Drewko J Vibration analysis of beams with cracks, VISNYK L VIV UNIE, Ser. Mech. Math., 55, 1999, 30-34.
- 8. Drewko J., Analysis of models of elastic-plastic hinges, Marine Tech. Trans., 11, 2000, 107-1 14.
- 9. MSC, NASIR4N. Reference Manuał. ven 70, MacNeal-Schwendler, 1994.
- 10. Hisada T. , Nakagiri S., Stochastic finite element method developed for structural safety and reliability, Proc. 3rd Inn Conf on Struct. Safety and Reliahility, 1981, 395=402.
- 11. Vanmarcke E. H., Grigoriu M.. Stochastic finite element analysis of simple beams, J. Eng. Mech., ASCE, 109(S), 1983, 1203-1214.
- 12. Liu W _ K., Belytschko T., Mani A. , Random field finite elements, Int. J. Num. Meth. Eng., 23, 1986, 1831-1845.
- 13. Tocher K. D., TheArt ofSimu1ation, McGraw-Hill, 1968.
- 14. Liu W. K.„ Belytschko T., Besterfield G. H., A variational principle for probabilistic mechanics, [in:] T. J. R. Hughes and E. Hinton (eds.), Finite Element Method for Plate and Shell Structures, Vol. 2: Formulations and Algorithms, Pineridge Press, 1986, 285-311.
- 15. Liu W. K., Besterfield G. H., Belytschko T.. Variational approach to probabilistic finite elements, Engrg Mech., 1 14(12), 1988, 2115—2133.
- 16. Kleiber M., Hien T. D. , The Stochastic Finite Element Method, Wiley, 1992.
- 17. Hien T. D, Kleiber M., Finite element analysis based on stochastic Hamilton variational principle, Comput. & Structures, 37(6), 1990, 893—902.
- 18. Hien T. D., Kleiber M., Stochastic finite element modelling in linear transient heat transfer, Comput. Meth. Appl. Mech. Engrg., 144, 1997, 111—124.
- 19. Hien T. D., Kleiber M., On solving nonlinear heat transient heat transfer problems with random parameters, Comput Meth Appl Mech. Engrg., 151, 1998. 287-299.
- 20. Collins J. D, -1 hornson W. T. , The eigenvalue problem for structural systems with Statistical propenies, AIAA J.. 7(4), 1969, 642-648.
- 21. Kleiber M., Hien T. D., Parameter sensitivity of inelastic buckling and post-buckling response, Comput. Meth Appl_ Mech. Engrg., 145. 1997, 239—262.
- 22. Liu P.-L., Der Kiureghian A., Multivariate distribution models with prescribed marginals and covariances, Prohah. Engrg. Mech.. I (2), 1986, 105—112.
- 23. Der Kiureghian A. , Jyh-Bin Ke, 'Ihe stochastic finite element method in structural reliability, Probab. Engrg Mech., 3(2), 1988, 83-91.
- 24. LawTence M. A., Basic random variables in finite element analysis, Int J. Num Meth. Eng., 24, 1987, 1849-1863.
- 25. Der Kiureghian A., Liu P.-L, First- and second-order finite element reliability methods in structural reliability, [in:] Liu W. K., Belytschko T. (eds.), Compulational Mechanics of Probabilistic and Reliability Analysis Elmepress Int., 1989, 281-298.
- 26. Nelson R. B., Simplified calculation of eigenvector derivatives, AIAA J., 14(9), (1976), 1201-1205
- 27. Hidebrand F. B., Introduction to Numerical Analysis. Mc Graw Hill, 1956.
- 28. Sih G. C. , Handhook of Srress Intensity Faclors, Bethlehem: Lihigh Univ., 1973.
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Bibliografia
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bwmeta1.element.baztech-article-BWM2-0061-0049