Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Stress intensity factors for 3-D axisymmetric bodies containing cracks by p-version of F.E.M.

  • Woo, Kwang S. (Department of Civil Engineering, Chonnam National University) ;
  • Jung, Woo S. (Department of Civil Engineering, Chonnam National University)
  • Published : 1994.09.25
⟨ Previous Next ⟩

Abstract

A new axisymmetric crack model is proposed on the basis of p-version of the finite element method limited to theory of small scale yielding. To this end, axisymmetric stress element is formulated by integrals of Legendre polynomial which has hierarchical nature and orthogonality relationship. The virtual crack extension method has been adopted to calculate the stress intensity factors for 3-D axisymmetric cracked bodies where the potential energy change as a function of position along the crack front is calculated. The sensitivity with respect to the aspect ratio and Poisson locking has been tested to ascertain the robustness of p-version axisymmetric element. Also, the limit value that is an exact solution obtained by FEM when degree of freedom is infinite can be estimated using the extrapolation equation based on error prediction in energy norm. Numerical examples of thick-walled cylinder, axisymmetric crack in a round bar and internal part-thorough cracked pipes are tested with high precision.

Keywords

References

  1. Basu, P.K, Woo, K. S. and Ahmed, N.U. (1990), "LEFM analysis of cracked plates and membranes using p-version of the finite element method," Numerical Methods in Engineering: Theory & Applications, II, Ed. G.N. Pande & J. Middleton, pp.1066-1073, Elsevier Applied Science.
  2. Hellen, T.K. (1975), "On the method of virtual crack extensions," Int. J. Numer. Mech. Eng., 9, pp.181-207.
  3. Meyer, C. (1987), "Finite element idealization", ASCE.
  4. Peano, A.G. (1976), "Hierarchies of conforming finite elements for plane elasticity and plate bending," Comput. Math. Appl. 2, pp.211-224, https://doi.org/10.1016/0898-1221(76)90014-6
  5. Robinson, J. (1976), "Single element test", CMAME, 7, pp.191-200.
  6. Rossow, M.P., Chen, K.C. and Lee, J.C. (1976), "Computer implementation of the constraint method," Comput. Struct. 6, pp.203-209. https://doi.org/10.1016/0045-7949(76)90031-6
  7. Surana, K.S. and Orth, N.J. (1991), "p-version hierarchical axisymmetric shell element." Comput. Strnct., 39(3/4), pp.257-268. https://doi.org/10.1016/0045-7949(91)90024-G
  8. Szabo, B.A and Mehta, K.A. (1978), "p-convergent finite element approximations in fracture mechanics," Int. J. Numer. Meth. Eng., 12, pp.551-561. https://doi.org/10.1002/nme.1620120313
  9. Tada, H., Paris, P. and Irwin, G.R. (1985), The Stress Analysis of Cracks Handbook, Second Edition, Paris Production.
  10. Timoshenko, S.P. and Goodier, F.W. (1984), Theory of Elasticity, 3rd Edition, McGRAW-HILL.
  11. Woo, K.S. and Busu, P.K. (1989), "Analysis of singular cylindrical shells by p-version of FEM," Int. J. Solids Structures, 25(2), pp.151-165., https://doi.org/10.1016/0020-7683(89)90004-8
  12. Zahoor, A (1985), "Closed form expressions for fracture mechanics analysis of cracked pipes," Technical Briefs, Journal of Pressure Vessel Technology, 107, pp.203-205. https://doi.org/10.1115/1.3264435
  13. Zienkiewicz, O.C., Iron, B.M., Campbell, J. and Scott, F. (1970) "Three dimensional stress analysis," In High Speed Computing of Elastic Structure, 1, pp.413-432, Proceedings of the Symposium of International Union of Theoretical and Applied Mechanics, Liege.

Cited by

  1. J-integral and fatigue life computations in the incremental plasticity analysis of large scale yielding by p-version of F.E.M. vol.17, pp.1, 2004, https://doi.org/10.12989/sem.2004.17.1.051
  2. An extended equivalent domain integral method for mixed mode fracture problems by thep-version of FEM vol.42, pp.5, 1998, https://doi.org/10.1002/(SICI)1097-0207(19980715)42:5<857::AID-NME390>3.0.CO;2-#
  3. Error estimates and adaptive finite element methods vol.18, pp.5/6, 2001, https://doi.org/10.1108/EUM0000000005788