Time domain FE-analysis of viscoelastic structures having constitutive relations involving fractional derivatives

37th AIAA/ASME/ASCE/AHS/ASC Structure, Structural Dynamics and Materials Conference

Volumn , Issue , 1996, Pages 685-694

  Enelund, Mikael ^a   Josefson, B Lennart ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; CONSTITUTIVE EQUATIONS; CONVOLUTION; DEGREES OF FREEDOM (MECHANICS); DIFFERENTIATION (CALCULUS); STRUCTURAL DYNAMICS; VISCOELASTICITY; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; INTEGRATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NUMERICAL ANALYSIS; STRUCTURAL ANALYSIS; TIME DOMAIN ANALYSIS; TIME SERIES ANALYSIS;

CONSTITUTIVE RELATIONS; CONVOLUTION INTEGRALS; FINITE ELEMENT EQUATIONS; FRACTIONAL DERIVATIVE OPERATOR; FRACTIONAL DERIVATIVES; FRACTIONAL DIFFERENTIATION; ISOTROPIC MATERIALS; NUMERICAL PROCEDURES;

TIME DOMAIN ANALYSIS; FLEXIBLE STRUCTURES;

BACKWARD EULER RULE; FRACTIONAL DERIVATIVES; ISOTROPIC MATERIALS; NEWMARK METHOD; VISCOELASTIC STRUCTURES;

EID: 0029722783     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.1996-1394     Document Type: Conference Paper

References (12)

1. Fung, Y. C., 1965, Foundations of Solid Mechanics, Prentice-Hall, Englewood Cliffs, New Jersey.
2. Lesieutre, G. A., and Mingori, D. L., 1990, “Finite element modelling of frequency-dependent material damping using augmenting thermodynamic fields”, AIAA Journal of Guidance Control and Dynamics, vol. 29, p. 1567-1579.
3. Lesieutre, G. A., and Bianchini, E., 1995, “ Time domain modelling of linear viscoelasticity using anelastic displacement fields”, ASME Journal of Vibration and Acoustics, vol. 117, p. 424-430.
4. Bagley, R. L., and Torvik, P. J., 1983, “Fractional calculus-A different approach to the analysis of viscoelastically damped structures”, AIAA Journal, vol. 21, p. 741-748.
5. Enelund, M., and Olsson P., 1995, “Damping described by fading memory models”, In Proceedings 36th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, AIAA, Washinton D.C., Part 1., p207-220.
6. Beyer, EL, and Kempfle, S., 1995, “Definition of physically consistent damping laws with fractional derivatives”, Zeitshrift fur Angewandte Mathematik und Mechanik, vol. 75, p. 623-635.
7. Enelund, M., and Olsson P., 1995, “Damping described by fading memory-analysis and application to fractional derivative models”, Division of Solid Mechanics, Chalmers University of Technology, S-412 96 Göteborg, Sweden, Research Report No. F181.
8. Padovan, J., 1987, “Computational algorithms for FE formulations involving fractional operators”, Computational Mechanics, vol. 2, p. 271-287.
9. Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus, Academic Press, New York.
10. Bateman, H., 1955, Higher Transcendental Functions Vol 3, (Bateman Manuscript Project, California Institute of Technology), McGraw-Hill, New York.
11. Christensen, R. M., 1971, “Theory of Viscoelasticity”, Academic Press, New York.
12. Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, Third Edition, John Wiley and Sons, New York.