Formulation and integration of the standard linear viscoelastic solid with fractional order rate laws

International Journal of Solids and Structures

Volumn 36, Issue 16, 1999, Pages 2417-2442

  Enelund, Mikael ^a   Mähler, Lennart ^a   Runesson, Kenneth ^a   Josefson, B Lennart ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DAMPING; DIFFERENTIATION (CALCULUS); DYNAMIC RESPONSE; FINITE ELEMENT METHOD; INTEGRATION; MATHEMATICAL MODELS;

FRACTIONAL ORDER RATE LAWS; SOLID MECHANICS;

VISCOELASTICITY;

EID: 0033149442     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(98)00111-5     Document Type: Article

References (21)

1. ABAQUS/Explicit Version 5.5 (1995). Providence, RI.
2. ABAQUS/Explicit Version 5.4 (1995). Providence, RI.
3. Bagley, R. L. and Calico, R. A. (1991) Fractional order state equations for the control of viscoelastically damped structures, AIAA Journal of Guidance, Control, and Dynamics 14, 304-311.
4. Bagley R. L., Torvik P. J. AIAA Journal. 21:1983;741-748.
5. Bateman, H. (1955) Higher Transcendental Functions, Vol. 3. McGraw-Hill, New York. Bateman Manuscript Project, California Institute of Technology.
6. Boltzmann, L. (1876) Zur theorie der elastichen nachwirkung. Annalen der Physik und Chemie 27, 624-654.
7. Cook, R. D., Malkhus, D. S. and Plesha, M. E. (1989) Concepts and Applications of Finite Element Analysis. John Wiley and Sons, New York.
8. Day W. A. Archive for Rational Mechanics and Analysis. 31:1968;1-34.
9. Day W. A. Archive for Rational Mechanics and Analysis. 34:1969;85-96.
10. Enelund M. ASCE Journal of Engineering Mechanics. 34:1997;407-409.
11. Enelund M., Josefson B. L. AIAA Journal. 35:1997;1630-1637.
12. Enelund, M. and Lesieutre, G. A. (1995) Time domain modeling of damping using an elastic displacement fields and fractional calculus. Report f188, Division of Solid Mechanics, Chalmers University of Technology, Göteborg, Sweden.
13. Enelund, M. and Olsson, P. (1995) Damping described by fading memory models. Proceedings AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, New Orleans, LA. AIAA, Washington, DC, pp. 207-220.
14. Fenander . AIAA Journal. 34:1996;1051-1058.
15. Gelfand, I. M. and Shilov, G. E. (1964) Generalized Functions, Volume I, Properties and Operations. Academic Press, San Diego, LA.
16. Hughes, T. J. R. (1987) The Finite Element Method, Linear, Static and Dynamic Finite Element Analysis. Prentice Hall, Englewood Cliffs, NJ.
17. Koeller R. C. ASME Journal of Applied Mechanics. 51:1984;299-307.
18. Oldham, K. B. and Spanier, J. (1974) The Fractional Calculus. Academic Press, New York.
19. Padovan, J. (1987) Computational Algorithms for Fe Formulations Involving Fractional Operators 2, 271-287.
20. Rabotnov, Y. N. (1980) Elements of Hereditary Solid Mechanics. Mir Publishers, Moscow.
21. Reed, M. and Simon, B. (1975) Methods of Modern Mathematical Physics, Vol. II. Academic Press, New York.