Structural Engineering and Mechanics

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The mixed finite element for quasi-static and dynamic analysis of viscoelastic circular beams

  • Kadioglu, Fethi (Faculty of Civil Engineering, Istanbul Technical University) ;
  • Akoz, A. Yalcin (Faculty of Civil Engineering, Istanbul Technical University)
  • Received : 2002.01.05
  • Accepted : 2003.04.08
  • Published : 2003.06.25
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Abstract

The quasi-static and dynamic responses of a linear viscoelastic circular beam on Winkler foundation are studied numerically by using the mixed finite element method in transformed Laplace-Carson space. This element VCR12 has 12 independent variables. The solution is obtained in transformed space and Schapery, Dubner, Durbin and Maximum Degree of Precision (MDOP) transform techniques are employed for numerical inversion. The performance of the method is presented by several quasi-static and dynamic example problems.

Keywords

References

  1. Addey, R.A. and Brebbia, C.A. (1973), "Efficient method for solution of viscoelastic problem", J. Eng. Mech. Div. ASCE, 99, 1119-1127.
  2. Akoz, A.Y. and , Kadioglu, F.. (1996), "The mixed finite element solutions of circular beam on elastic foundation", Comput. Struct., 60(4), 643-657. https://doi.org/10.1016/0045-7949(95)00418-1
  3. Akoz, A.Y. and , Kadioglu, F. (1999), "The mixed finite element method for the quasi-static and dynamic analysis of viscoelastic Timoshenko beams", Int. J. Numer. Methods Eng., 44, 1909-1932. https://doi.org/10.1002/(SICI)1097-0207(19990430)44:12<1909::AID-NME573>3.0.CO;2-P
  4. Aköz, A.Y., Omurtag, M.H. and , Dogruoglu, A. (1991), "The mixed finite element formulation for threedimensional bars", Int. J. Solids Structures, 28(2), 225-234. https://doi.org/10.1016/0020-7683(91)90207-V
  5. Aral, M.M. and Gulcat, U. (1977), "A finite element Laplace transform solution technique for wave equation", Int. J. Numer. Methods Eng., 11, 1719-1732. https://doi.org/10.1002/nme.1620111107
  6. Chen, T. (1995), "The hybrid Laplace transform/finite element method applied to the quasi-static and dynamic analysis of viscoelastic Timoshenko beams", Int. J. Numer. Methods Eng., 38, 509-522. https://doi.org/10.1002/nme.1620380310
  7. Christensen, R.M. (1982), Theory of Viscoelasticity, 2nd ed., Academic Press, New York.
  8. Dubner, H. and Abate, J. (1968), "Numerical inversion of Laplace transforms by relating them to finite Fourier cosine transform", Journal of the Association for Computing Machinery, 15(1), 115-123. https://doi.org/10.1145/321439.321446
  9. Durbin, F. (1974), "Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate's method", The Computer Journal, 17(4), 371-376 https://doi.org/10.1093/comjnl/17.4.371
  10. Findley, W.N., Lai, J.S. and Onaran, K. (1976), Creep and Relaxation of Nonlinear Visco-elastic Materials, North-Holland, New York.
  11. Flugge, W. (1975), Viscoelasticity, 2nd ed., Springer, Berlin, Heidelberg.
  12. Hetenyi, M. (1946), Beams on Elastic Foundation, The University of Michigan Press, Ann Arbor, Michigan.
  13. Johnson, A.R., Tessler, A. and Dambach, M. (1997), "Dynamics of thick viscoelastic beams", Journal of Engineering Materials and Technology, 119, July, 273-278. https://doi.org/10.1115/1.2812256
  14. Kadioglu, F. (1999), "Quasi-static and dynamic analysis of viscoelastic beams", Ph.D. thesis (in Turkish), Department of Civil Engineering, Istanbul Technical University.
  15. Krylov, V.I. and Skoblya, N.S. (1969), Handbook of Numerical Inversion of Laplace Transforms, Jeruselam by ISST Press, Wiener Bindery Ltd.
  16. Miranda, C.K. and Nair, K. (1966), "Finite beams on elastic foundations", J. Struct. Div., ASCE, 92, 131-142
  17. Narayanan, G.V. and Beskos, D.E. (1982), "Numerical operational methods for time-dependent linear problems", Int. J. Numer. Methods Eng., 18, 1829-1854. https://doi.org/10.1002/nme.1620181207
  18. Oden, J. and Reddy, J.N. (1976), Variational Methods in Theoretical Mechanics, Springer, Berlin.
  19. Rabbatnow, Yu. N. (1980), Element of Hereditary Solid Mechanics, Mir Publishers-Moscow.
  20. Reddy, J.N. (1986), Applied Functional Analysis and Variational Method in Engineering, McGraw-Hill.
  21. Schapery, R.A. (1962), "Approximate methods of transform inversion for viscoelastic stress analysis", Proc. the Fourth U.S. National Congress of Applied Mechanics, 2, Pergamon Press, Oxford, London, New York, Paris, June, 18-21.
  22. Ting, B.Y. and Mockry, E.F. (1983), "Beam on elastic foundation finite element", J. Appl. Mec., ASCE, 109(6), 1390-1402. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:6(1390)
  23. Wang, C.M., Yang, T.Q. and Lam, K.Y. (1997), "Viscoelastic Timoshenko beam solutions from Euler-Bernoulli solutions", July, 746-748.
  24. White, J.L. (1986), "Finite element in linear viscoelasticity", Proc. 2nd Conf. on Matrix Method in Structural Mechanics, AFFDL-TR-68-150, 489-516.

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