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On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack

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Abstract

The axisymmetric buckling (delamination) of a circular disk (plate) with a penny-shaped crack is analyzed using a continuum model, piecewise-homogeneous model, and the three-dimensional linearized theory of stability. The FEM is used. The analysis is carried out using various singular and ordinary finite elements. The numerical results obtained indicate that it is not necessary to use singular finite elements to solve the problem

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References

  1. S. D. Akbarov and O. G. Rzayev, “On the buckling of the elastic and viscoelastic composite circular thick plate with a penny-shaped crack,” Europ. J. Mech. A/Solids, 21, 269–279 (2002).

    Article  MATH  Google Scholar 

  2. S. D. Akbarov and O. G. Rzayev, “Delamination of the unidirectional viscoelastic composite materials,” Mech. Comp. Mater., 38, No. 1, 17–24 (2002).

    Article  Google Scholar 

  3. S. D. Akbmov and O. G. Rzayev, “On the delamination of a viscoelastic composite circular plate,” Int. Appl. Mech., 39, No. 3, 368–374 (2003).

    Article  Google Scholar 

  4. V. A. Bazhenov and V. G. Gulyar, “Semianalytic finite-element method in problems of nonlinear continuum mechanics,” Int. Appl. Mech., 39, No. 4, 402–437 (2003).

    Article  Google Scholar 

  5. S. E. Benzley, “Representation of singularities with isoparametric finite elements,” Int. J. Numer. Meth. Eng., 8, 537–545 (1974).

    Article  MATH  Google Scholar 

  6. R. M. Cristensen, Mechanics of Composite Materials, Wiley, New York (1979).

    Google Scholar 

  7. M. Gosz, L. Dolbow, and B. Moran, “Domain integral formulation for stress intensity factor computation along curved three-dimensional interface cracks,” Int. J. Solids Struct., 35, 1763–1783 (1998).

    Article  MATH  Google Scholar 

  8. A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin (1999).

    MATH  Google Scholar 

  9. A. N. Guz, “On two-scale model of fracture mesomechanics of composites with cracks under compression,” Int. Appl. Mech., 41, No. 5, 582–585 (2005).

    Article  MathSciNet  Google Scholar 

  10. A. N. Guz, “Three-dimensional theory of stability of a carbon nanotube in a matrix,” Int. Appl. Mech., 42, No. 1, 19–31 (2006).

    Article  MathSciNet  Google Scholar 

  11. A. N. Guz and I. A. Guz, “Mixed plane problems in linearized solid mechanics: Exact solutions,” Int. Appl. Mech., 40, No. 1, 1–29 (2004).

    Article  MathSciNet  Google Scholar 

  12. A. N. Guz and I. A. Guz, “On models in the theory of stability of multiwalled carbon nanotubes in matrix,” Int. Appl. Mech., 42, No. 6, 617–628 (2006).

    Article  MathSciNet  Google Scholar 

  13. A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, “Fracture and stability of materials and structural members with cracks: Approaches and results,” Int. Appl. Mech., 40, No. 12, 1323–1359 (2004).

    Article  Google Scholar 

  14. A. N. Guz, A. A. Rodger, and I. A. Guz, “Developing a compressive failure theory for nanocomposites,” Int. Appl. Mech., 41, No. 3, 233–255 (2005).

    Article  Google Scholar 

  15. A. N. Guz and V. M. Nazarenko, “Symmetric failure of the half-space with penny-shaped, crack in compression,” Theor. Appl. Frac. Mech., No. 3, 233–245 (1985).

  16. R. D. Henshell and K. G. Shaw, “Crack tip finite elements are unnecessary,” Int. J. Numer. Meth. Eng., 9, 495–507 (1975).

    Article  MATH  Google Scholar 

  17. B. Moran and C. F. Shih, “Crack tip and associated domain integrals from momentum and energy balance,” Eng. Frac. Mech., 27, 615–642 (1987).

    Article  Google Scholar 

  18. O. G. Rzayev and S. D. Akbarov, “Local buckling of the elastic and viscoelastic coating around the penny-shaped interface crack,” Int. J. Eng Sci., 40, No. 13, 1435–1451 (2002).

    Article  Google Scholar 

  19. O. G. Rzayev, “Local buckling around an interface crack in a viscoelastic sandwich plate,” Mech. Comp. Mater., 38, No. 3, 233–242 (2002).

    Article  Google Scholar 

  20. C. F. Shih, B. Moran, and T. Nakamura, “Energy release rate along a three-dimensional crack front in a thermal stressed body,” Int. J. Frac., 30, 79–102 (1986).

    Google Scholar 

  21. O. C. Zienkiewicz and R. L. Taylor, Basic Formulation and Linear Problems. The Finite Element Method, Vol. 1, 4th ed., McGraw-Hill, London (1989).

    Google Scholar 

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Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 120–129, September 2007.

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Akbarov, S.D., Yahnioglu, N. & Rzayev, O.G. On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack. Int Appl Mech 43, 1048–1056 (2007). https://doi.org/10.1007/s10778-007-0106-7

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  • DOI: https://doi.org/10.1007/s10778-007-0106-7

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