DOI QR코드

DOI QR Code

Improving the eigenvalue using higher order elements without re-solving

  • Stephen, D.B. (Finite Element Analysis Research Centre, Building J07, Engineering Faculty, University of Sydney) ;
  • Steven, G.P. (Finite Element Analysis Research Centre, Building J07, Engineering Faculty, University of Sydney)
  • Published : 1997.07.25

Abstract

High order finite element have a greater convergence rate than low order finite elements, and in general produce more accurate results. These elements have the disadvantage of being more computationally expensive and often require a longer time to solve the finite element analysis. High order elements have been used in this paper to obtain a new eigenvalue solution with out re-solving the new model. The optimisation of the eigenvalue via the differentiation of the Rayleigh quotient has shown that the additional nodes associated with the higher order elements can be condensed out and solved using the original finite element solution. The higher order elements can then be used to calculate an improved eigenvalue for the finite element analysis.

References

  1. Friberg, P.O. (1986)," An error indicator for the generalized eigenvalue problem using the herarchical finite element method", International Journal for Numerical Methods in Engineering, 23, 91-98. https://doi.org/10.1002/nme.1620230108
  2. Friberg, O., Moller, P., Makovicka, D. and Wiberg, N.E. (1987), "An adaptive procedure for eigenvalue problems using the hierarchical finite element method", International Journal for Numerical Methods in Engineering, 24, 319-335. https://doi.org/10.1002/nme.1620240205
  3. Cook, R.D. (1991)," An error estimate and h-adaptive strategy in vibration analysis", Proceedings from the Sixth International Confrence on Finite Element Methods, K1-K5.
  4. Cook, R.D. (1991), "Error estimation for eigenvalues computed from discretised models of vibration stuctures", AIAA Journal, September, 1527-1529.
  5. Cook, R.D. and Averashi, J. (1992), "Error estimation and adaptive meshing for vibration problems", Computers and Structures, 44, 619-626. https://doi.org/10.1016/0045-7949(92)90394-F
  6. Avrashi, J. and Cook, R.D. (1993), "New error estimation for $C^0$ eigenproblems in finite element analysis", Engineering Computations, 10, 243-256. https://doi.org/10.1108/eb023905
  7. Fried, I. (1971), "Accuracy of finite element eigenproblems", Journal of Sound and Vibration, 18, 289-295. https://doi.org/10.1016/0022-460X(71)90351-8
  8. Stephen, D.B. and Steven, G.P. (1994), "Buckling error estimation using a patch recovery technique", Research Report, FEARC-9402, Finite Element Analysis Research Centre, University of Sydney.
  9. Stephen, D.B. and Steven, G.P. (1994), "Natural frequency error estimation using a patch recovery technique", Research Report, FEARC-9406, Finite Element Analysis Research Centre, University of Sydney.
  10. Stephen, D.B. and Steven, G.P. "Error estimation for natural frequency analysis using plate elements", Engineering Computations, To be published.
  11. Stephen, D.B. and Steven, G.P. "Error estimation for plate vibration elements", Computers and Structures, To be published.
  12. Stephen, D.B. and Steven, G.P. (1997), "Natural frequency error estimation for 3D brick elements", Structural Engineering and Mechanics, 5(2), 137-148. https://doi.org/10.12989/sem.1997.5.2.137
  13. Cook, R.D., Malkus, D.S. and Plesha, M.E. (1989), "Concept and applications of finite element analysis", John Wiley & Sons Inc, New York.
  14. Stephen, D.B. and Steven, G.P. (1995), "Improving the eigenvector in a patch recovery in a patch recovery technique", Engineering Computations, Submitted June.