A New Hybrid-Mixed Composite Laminated Curved Beam Element

  • Lee Ho-Cheol (School of Mechanical & Automotive Engineering, Catholic University of Daegu) ;
  • Kim Jin-Gon (School of Mechanical & Automotive Engineering, Catholic University of Daegu)
  • 발행 : 2005.03.01

초록

In this study, we present a new efficient hybrid-mixed composite laminated curved beam element. The present element, which is based on the Hellinger-Reissner variational principle and the first-order shear deformation lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees in order to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the ($6{\times}6$) element stiffness matrix. The present study also incorporates the straightforward prediction of interlaminar stresses from equilibrium equations. Several numerical examples confirm the superior behavior of the present composite laminated curved beam element.

키워드

참고문헌

  1. Ashwell, D. G. and Sabir, A. B., 1971, 'Limitations of Certaln Curved Beam Elements When Applied to Arches,' Internat. J. Mech. Sci. , Vol. 13, pp. 133-139 https://doi.org/10.1016/0020-7403(71)90017-8
  2. Cook, R, D., Malkus, D. S. and Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, 3rd Edition, Wiely, New York
  3. Dawe, D. J., 1974, 'Numerical studies Using Circular Arch Finite Elements,' Computers & Structures, Vol. 4, pp. 729-740 https://doi.org/10.1016/0045-7949(74)90041-8
  4. Dorfi, H. R. and Busby, H. R., 1994, 'An Effective Curved Composite Beam Finite Element Based on the Hybrid-Mixed Formulation,' Computers & Structures, Vol. 53, pp. 43-52 https://doi.org/10.1016/0045-7949(94)90128-7
  5. Kant, T. and Manjunath, B. S., 1989, 'Refined Theories for Composite and Sandwich Beams with $C^0$ Finite Elements,' Computers & Structures, Vol. 33, No. 3, pp. 755-764 https://doi.org/10.1016/0045-7949(89)90249-6
  6. Kim, J. G. and Kim, Y. Y., 1998, 'A New Higher-Order Hybrid-Mixed Curved Beam Element,' International Journal for Numerical Methods in Engineering, Vol. 43, pp. 925-940 https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<925::AID-NME457>3.0.CO;2-M
  7. Kim, J. G. and Kang, S. W., 2003, 'A New and Efficient $C^{0}$ Laminated Curved Beam Element,' Transactions of the KSME, A, Vol. 27, No. 4, pp. 559-566 https://doi.org/10.3795/KSME-A.2003.27.4.559
  8. Kim, J. G., 2000, 'Optimal Interpolation Functions of 2-Node Hybrid-Mixed Curved Beam Element,' Transactions of the KSME, A, Vol. 24, No. 12, pp. 3003-3009
  9. Levinson, M., 1981, 'A New Rectangular beam theory, 'Journal of sound and Vlbration, Vol. 74, pp. 81-87 https://doi.org/10.1016/0022-460X(81)90493-4
  10. Levinson, M., 1981, 'Further Results of a New Beam Theory.' Journal of Sound and Vibration, Vol. 77, pp. 440-444 https://doi.org/10.1016/S0022-460X(81)80180-0
  11. Moon, W. J., Kim, Y. W., Min, O. K. and Lee, K. W., 1996, 'Reduced Minimization Theory in Skew Beam Element,' Transactions of the KSME, Vol. 20, No. 12, pp. 3702-3803
  12. Noor, A. K. and Peters, J. M., 1981, 'Mixed Models and Reduced/Selective Integration Displacement Models for Nonlinear Analysis of Curved Beams' International Journal for Numerical Methods in Engineering, Vol, 17, pp. 615-631 https://doi.org/10.1002/nme.1620170409
  13. Pagano, N. J., 1969, 'Exact Solutions for Composite Laminates in Cyhndrical Bending,' Journal of Composite Materials, Vol. 3, pp. 398-411 https://doi.org/10.1177/002199836900300304
  14. Pian, T. H. H. and Chen, D., 1983, 'On the Suppression of Zero Energy Deformation Modes,' International Journal for Numerical Methods in Engineering, Vol. 19, pp. 1741-1752 https://doi.org/10.1002/nme.1620191202
  15. Prathap, G. and Babu, C. Ramesh, 1986, 'An Isoparametric Quadratic Thick Curved Beam EIement,' International Journal for Numerical Methods in Engineering, Vol. 23, pp. 1583-1600 https://doi.org/10.1002/nme.1620230902
  16. Prathap, G., 1993, The Finite Element Method in structural Mechanics, Kluwer, Dordrecht
  17. Rychter, Z., 1987, 'On the Accuracy of a Beam Theory,' Mechanics Research Communications, Vol. 14, pp. 99-105 https://doi.org/10.1016/0093-6413(87)90024-3
  18. Ryu, H. S. and Sin, H. C., 1996, 'A 2-Node Strain B ased Curved Beam Element,' Transactions of the KSME, A, Vol. 18, No. 8, pp. 2540-2545
  19. Saleeb, A. F. and Chang, T. Y., 1987, 'On the Hybrid-Mixed Formulation $C^0$ Curved Beam Elements,' Computer Methods in Applied Mechanics and Engineering, Vol. 60, pp. 95-121 https://doi.org/10.1016/0045-7825(87)90131-9
  20. StePhen, N. G. and Levinson, M., 1979, 'A Second Order Beam Theory,' Journal of Sound and Vibration, Vol. 67, pp. 293-305 https://doi.org/10.1016/0022-460X(79)90537-6
  21. Stolarski, H. and Belytschko, T., 1983, 'Shear and Membrane Locking in Curved Elements,' Computer Methods in Applied Mechanics and Engineering, Vol. 41, pp. 279-296 https://doi.org/10.1016/0045-7825(83)90010-5
  22. Stolarski, H. and Belytschko, T., 1982, 'Membrane Locking and Reduced Integration for Curved Elements,' Journal of Applied Mechanics, Vol. 49, pp. 172-176 https://doi.org/10.1115/1.3161961
  23. Vinson, J. R. and Sierakowski, R. L., 1986, The Behavior of Structures Composed or Composite Materials, Martinus Nijhoff, Dordrecht
  24. Washizu, W., 1986, Variational Methods in Elasticity and Plasticity, 3rd Ed., Pergamon Press, Oxford