Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
권호 표지
DOI QR코드

DOI QR Code

Optimal Interpolation Functions of 2-None Hybrid-Mixed Curved Beam Element

두 절점 혼합 곡선 보요소의 보간함수 선정

  • Published : 2000.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we propose a new efficient hybrid-mixed C(sup)0 curved beam element with the optimal interpolation functions determined from numerical tests, which gives very accurate locking-free two-node curved beam element. In the element level, the stress parameters are eliminated from the stationary condition and the nodeless degrees of freedom are also removed by static condensation so that a standard six-by-six stiffness matrix is finally obtained. The numeri cal benchmark problems show that the element with cubic displacement functions and quadratic stress functions is the most efficient.

Keywords

References

  1. Dawe, D. J., 1974, 'Numerical Studies Using Circular Arch Finite Elements,' Comput. Struct., Vol. 4, pp. 729-740 https://doi.org/10.1016/0045-7949(74)90041-8
  2. Stolarski, H. and Belytschko, T., 1983, 'Shear and Membrane Locking in Curved $C^0$ Elements,' Comp. Methods Appl. Mech. Engng., Vol. 41, pp. 279-296 https://doi.org/10.1016/0045-7825(83)90010-5
  3. Noor, A. K. and Peters, J. M., 1981, 'Mixed Models and Reduced/Seletive Integration Displacement Models for Nonlinear Analysis fo Curved Beams,' Int. J. Numer. Methods Eng., Vol. 17, pp. 615-631 https://doi.org/10.1002/nme.1620170409
  4. Noor, A. K., Greene, W. H. and Hartley, S. J., 1977, 'Nonlinear Finite Element Analysis of Curved Beams,' Comp. Methods Appl. Mech. Engng., Vol. 12, pp. 289-307 https://doi.org/10.1016/0045-7825(77)90018-4
  5. Stolarski, H. and Belytschko, T., 1982, 'Membrane Locking and Reduced Integration for Curved Elements,' J. Appl. Mech., Vol. 49, pp. 172-176
  6. 문원주, 김용우, 민옥기, 이강원, 1996, '공간곡선보요소에서의 감차최소화 이론,' 대한기계학회논문집, 제20권, 제12호, pp. 3702-3803
  7. Babu, C. Ramesh and Prathap, G., 1986, 'A Linear Thick Curved Beam Element,' Int. J. Numer. Methods Eng., Vol. 23, pp. 1313-1328 https://doi.org/10.1002/nme.1620230709
  8. Prathap, G. and Babu, C. Ramesh, 1986, 'An Isoparametric Quadratic Thick Curved Beam Element,' Int. J. Numer. Methods Eng., Vol. 23, pp. 1583-1600 https://doi.org/10.1002/nme.1620230902
  9. Prathap, G., 1993, The Finite Element Method in Structural Mechanics, Kluwer, Dordrecht
  10. Tessler, A. and Spiridigliozzi, L., 1986, 'Curved Beam Elements with Penalty Relaxation,' Int. J. Numer. Methods Eng., Vol. 23, pp. 2245-2262 https://doi.org/10.1002/nme.1620231207
  11. 유하상, 신효철, 1996, '변형률에 근거한 2-절점곡선보 요소,' 대한기계학회논문집, 제 18권, 제 8호, pp. 2540-2545
  12. Lee, P. G. and Sin, H. C., 1994, 'Locking-Free Curved Beam Element Based on Curvature,' Int. J. Numer. Methods Eng., Vol. 37, pp. 989-1007 https://doi.org/10.1002/nme.1620370607
  13. Saleeb, A. F. and Chang, T. Y., 1987, 'On the Hybrid-Mixed Formulation $C^0$ Curved Beam Elements,' Comp. Methods Appl. Mech. Engng., Vol. 60, pp. 95-121 https://doi.org/10.1016/0045-7825(87)90131-9
  14. Kim, Y. Y. and Kim, J. G., 1996, 'A Simple and Efficient Mixed Finite Element for Axisymmetric Shell Analysis,' Int. J. Numer. Methods Eng., Vol. 39, pp. 1903-1914 https://doi.org/10.1002/(SICI)1097-0207(19960615)39:11<1903::AID-NME935>3.0.CO;2-I
  15. Kim, J. G. and Kim, Y. Y., 1997, 'A Simple and Efficient Mixed Harmonic Element for Shells of Revolution,' Commum. J. Meth. Engng., Vol. 13, pp. 565-572 https://doi.org/10.1002/(SICI)1099-0887(199707)13:7<565::AID-CNM83>3.0.CO;2-A
  16. Kim, J. G. and Kim, Y. Y., 1998, 'A New Higher-Order Hybrid-Mixed Curved Beam Element,' Int. J. Numer. Methods Eng., Vol. 43, pp. 925-940 https://doi.org/10.1002/(SICI)1097-0207(19981115)43:5<925::AID-NME457>3.0.CO;2-M
  17. Kim, J. G. and Kim, Y. Y., 2000, 'A Higher-Order Hybrid-Mixed Harmonic Shell-of-Revolution Element,' Comp. Methods Appl. Mech. Engng., Vol. 182, pp. 1-16 https://doi.org/10.1016/S0045-7825(99)00082-1
  18. Cook, R. D., Malkus, D. S. and Plesha, M. E., 1989, Concepts And Applications of Finite Element Analysis, 3rd Edition, Wiely, New York
  19. Wolfram, S., 1991, Mathematica, Second Edition, Addisom-Wesley Publishing Company, Inc.