Weight Functions for Notched Structures with Anti-plane Deformation

  • An, Deuk-Man (School of Mechanical Engineering, Pusan National University) ;
  • Son, In-Ho (School of Mechanical Engineering, Pusan National University)
  • Published : 2007.07.01

Abstract

Weight functions in fracture mechanics represent the stress intensity factors as weighted averages of the externally impressed boundary tractions and body forces. We extended the weight function theory for cracked linear elastic materials to calculate the notch stress intensity factor of a notched structure with anti-plane deformation. The well-known method of deriving weight functions by differentiation cannot be used for notched structures. By combining an appropriate singular field with a regular field, we derived weight functions for the notch stress intensity factor. Closed expressions of weight functions for notched cylindrical bodies are given as examples.

Keywords

References

  1. Bueckner, H. F., 'A novel principle for the computation of stress intensity factors,' Journal of Applied Mathematics and Mechanics, Vol. 50, pp. 529-546, 1970 https://doi.org/10.1016/0021-8928(86)90022-5
  2. Rice, J. R., 'Some remarks on elastic crack-tip stress fields,' International Journal of Solids Structures, Vol. 8, pp. 751-758, 1972 https://doi.org/10.1016/0020-7683(72)90040-6
  3. Parks, D. M. and Kamenetzky, E. M., 'Weight functions from virtual crack extension,' International Journal for Numerical Methods in Engineering, Vol. 14, pp. 1693-1706, 1979 https://doi.org/10.1002/nme.1620141110
  4. Vanderglas, M. L., 'A stiffuess derivative finite element technique for determination of influence functions,' International Journal of Fracture, Vol. 14, pp. R291-294, 1978
  5. Bueckner; H. F., 'Field singularities and related integral representations,' Mechanics of Fracture, Vol. 1, pp. 239-314, 1973
  6. An, D., 'Weight function theory for a rectilinear anisotropic body,' International Journal of Fracture, Vol. 34, pp. 85-109, 1987 https://doi.org/10.1007/BF00019766
  7. Barber, J. R., 'Elasticity,' 2nd Ed., Kluwer Academic, pp. 393-404, 2002
  8. Hildebrand, F. B., 'Advanced Calculus for Applications,' 2nd Ed., Prentice-Hall, pp. 301-302, 1976
  9. Broek, D., 'Elementary engineering fracture mechanics,' Martinus Nijhoff, pp. 73-86, 1982