Formulation Method for Solid-to-Beam Transition Finite Elements

  • Published : 2001.11.01

Abstract

Various transition elements are used in general for the effective finite element analysis of complicated mechanical structures. In this paper, a solid-to-beam transition finite element, which can b e used for connecting a C1-continuity beam element to a continuum solid element, is proposed. The shape functions of the transition finite element are derived to meet the compatibility condition, and a transition element equation is formulated by the conventional finite element procedure. In order to show the effectiveness and convergence characteristics of the proposed transition element, numerical tests are performed for various examples. As a result of this study, following conclusions are obtained. (1) The proposed transition element, which meets the compatibility of the primary variables, exhibits excellent accuracy. (2) In case of using the proposed transition element, the number of nodes in the finite element model may be considerably reduced and the model construction becomes more convenient. (3) This formulation method can be applied to the usage of higher order elements.

References

  1. Bathe, K. J., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, N. J.
  2. Cook, R. D., Malkus, D. S., Plesha, M. E., 1989, Concept and Applications of finite Element Analysis, 3rd Ed., John Wiley & Sons, New York
  3. Gmur, T. C. and Kauten, R. H., 1993, 'Three-Dimensional Solid-to-Beam Transition Elements for Structural Dynamics Analysis,' International Journal for Numerical Methods in Engineering, Vol. 36, pp. 1429-1444 https://doi.org/10.1002/nme.1620360902
  4. Gupta, A. K., 1978, 'A Finite Element for Transition from a Fine to a Coarse Grid,' International Journal for Numerical Methods in Engineering, Vol. 12, No. 1, pp. 35-45 https://doi.org/10.1002/nme.1620120104
  5. Reddy, J. N., 1993, An Introduction to the Finite Element Method, 2nd Ed., McGraw-Hill, New York
  6. Surana, K. S., 1980, 'Shape Functions for the Isoparametric Transition Elements for Cross Sectional Properties and Stress Analysis of Beams,' International Journal for Numerical Methods in Engineering, Vol, 15, pp. 1403-1407 https://doi.org/10.1002/nme.1620150912