Abstract
A variational alternating method which is suitable for analyzing finite three dimensional cracked solid is presented. The stress analysis of the unracked solid is performed by the functional variable displacement solution and the variational method. The stress intensity factor solution for an embedded elliptical crack and a surface flaw in a finite plate for the case of mode-I loading are obtained by the variational alternating method. The results are compared with that of reference.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Benthem, J. P. (1977): State of stress at the vortex of a quarter-infinite crack in a half space. Int. J. Solids Struct. 13, 479–492
Kantorovich, L. V.; Krylov, V. I. (1964): Approximate method of higher analysis. New York: Wiley
Kassir, M. K.; Sih, G. C. (1966): Three-dimensional stress distribution around an elliptical crack under arbitrary loading. J. Appl. Mech. 33 Trans. ASME, 88, Series E, 601–611
Newman, J. C.; Raju, I. S. (1979): Analysis of surface cracks in finite plates under tension or bending loads. NASA TP-1578
Nishioka, T.; Atluri, S. N. (1983 a): Analytical solution for embedded elliptical cracks and finite element - alternating method for elliptical surface cracks subjected to arbitrary loading. Eng. Fract. Mech. 17, 247–268
Nishioka, T.; Atluri, S. N. (1983 b): An alternating method of analysis of surface - flawed aircraft structural components. AIAA J. 21, 749–757
Segedin, C. M. (1968): A note on geometric discontinuities in elasto-statics. Int. J. Eng. Sci. 6, 309–312
Shah, R. C.; Kobayashi, A. S. (1971): Stress intensity factor for an elliptical crack under arbitrary normal loading. Eng. Fract. Mech. 3, 71–96
Shah, R. C.; Kobayashi, A. S. (1972): On the surface flaw problem. In: Swedlow, J. L. (ed.) The surface crack: Physical problems and computational solution. New York: ASME
Shah, R. C.; Kobayashi, A. S. (1973): Stress intensity factor for an elliptical crack approaching the surface of a plate in bending. ASTM STP 513
Sih, G. C.; Liebowitz, H. (1968): Mathematic theories of brittle fracture. In: Liebowitz, H. (ed.) Fracture, vol. II. New York: Academic Press
Smith, F. W.; Emery, A. F. (1967): Stress intensity factors for semi-circular cracks, part-semi-infinite solid. J. Appl. Mech. 34, 953–959
Vijayakumar, K.; Atluri, S. N. (1981): An embedded elliptical flaw in an infinite solid subjected to arbitrary crack-face tractions. J. Appl. Mech. 48, 88–96
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wu, S., Zhang, X. & He, Q. Analysis of stress intensity factors for three-dimensional finite cracked bodies by a variational alternating method. Computational Mechanics 5, 23–32 (1989). https://doi.org/10.1007/BF01046876
Issue Date:
DOI: https://doi.org/10.1007/BF01046876