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Singular integral operators method for two-dimensional elasto-plastic stress analysis

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Abstract

The Singular Integral Operators Method is presented for the formulation of the two-dimensional elasto-plastic stress analysis. The formulation of the two-dimensional elasto-plastic problem is stated, by applying the fundamental solutions for an isotropic solid. The most interesting features of this method are the much smaller systems of equations and considerable reduction in the data required to run the elasto-plastic problem. An application is presented, to the determination of the stress field in the neighborhood of a circular hole under internal pressure in an infinite and isotropic solid. A second application is stated, to the determination of the plastic behaviour of a square block compressed by two opposite perfectly rough rigid punches in plane strain.

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References

  1. Cruse, T.A. a.W. Vanburen: Three-dimensional elastic stress analysis of a fracture specimen with an edge crack. Int. J. Fract. Mechan., Vol. 7 (1971) pp. 1/15.

    Google Scholar 

  2. Cruse, T.A.: Numerical solutions in three-dimensional elastostatics. Int. J. Solids Struct., Vol. 5 (1969) pp. 1259/1274.

    Google Scholar 

  3. Cruse, T.A.: Application of the boundary-integral equation method to three-dimensional stress analysis. Comp. Struct., Vol. 3, (1973) pp. 509/527.

    Article  Google Scholar 

  4. Weaver, J.: Three-dimensional crack analysis. Int. J. Solids Struct., Vol. 13 (1977) pp. 321/330.

    Google Scholar 

  5. Ladopoulos, E.G.: On the numerical solution of the multidimensional singular integrals and integral equations used in the theory of linear viscoelasticity. Int. J. Math. Math. Scien., Vol. 11 (1988) pp. 561/574.

    MathSciNet  Google Scholar 

  6. Bui, H.D.: An integral equations method for solving the problem of a plane crack of arbitrary shape. J. Mech. Phys. Solids, Vol. 25 (1977) pp. 29/30.

    MathSciNet  Google Scholar 

  7. Kupradze, V.D.: Three-dimensional problems in the mathematical theory of elasticity and thermoelasticity. Second edit., Nayka, Moscow 1976.

    Google Scholar 

  8. Lachat, J.C. a.J.O. Watson: Effective numerical treatment of boundary integral equations: A formulation for three-dimensional elastostatics. Int. J. Num. Meth. Engng, Vol. 10 (1976) pp. 991/1005.

    Article  Google Scholar 

  9. Zabaras, N. a.S. Mukherjee: An analysis of solidification problems by the boundary element method. Int. J. Num. Meth. Engng, Vol. 24 (1987) pp. 1879/1900.

    Article  Google Scholar 

  10. Heinlein, M., S. Mukherjee a.O. Richmond: A boundary element method analysis of temperature fields and stresses during solidification. Acta Mech., Vol. 59 (1986) pp 58/81.

    Article  Google Scholar 

  11. Brebbia, C.A.: Two-dimensional Elasticity. In: The Boundary Element Method for Engineers. London: Pentech Press 1980.

    Google Scholar 

  12. Wardle, L.J. a.J.M. Crotty: Two-dimensional boundary equation analysis for non-homogeneous mining applications. In: Recent Advances in Boundary Element Methods. London: Pentech Press 1978.

    Google Scholar 

  13. Hartmann, F.: Elastostatics. In Progress in Boundary Element Methods. London: Pentech Press 1981.

    Google Scholar 

  14. Parihar, K.S. aS. Sowdamini: Stress distribution in a two-dimensional infinite anisotropic medium with collinear cracks. J. Elasticity, Vol. 15 (1985) pp. 193/214.

    Article  MathSciNet  Google Scholar 

  15. Aliabadi, M.H., D.P. Rooke a.D.J. Cartwright: An improved boundary element formulation for calculating stress intensity factors: Application to aerospace structures. J. Str. Anal. Vol. 22 (1987) pp. 203/207.

    Google Scholar 

  16. Cruse, T.A.: Two-dimensional BIE fracture mechanic analysis. Appl. Math. Modell., Vol. 2 (1978) pp. 287/293.

    Article  Google Scholar 

  17. Blandford, G.E.: Two-dimensional stress intensity factor computations using the boundary element method. Int. J. Num. Meth. Engn, Vol. 17 (1981) pp. 387/404.

    Google Scholar 

  18. Xanthis, L.S., M.J.M. Bernal a.C. Atkinson: The treatment of singularities in the calculation of stress intensity factors using the boundary element method. Comp. Meth. Appl. Mech. Engng, Vol. 26 (1981) pp. 285/304.

    Article  MathSciNet  Google Scholar 

  19. Sutton, M.A., C.H. Liu, J.R. Dickerson a.S.R. McNeill: The two-dimensional boundary integral equation method in elasticity with a consistent boundary formulation. Engng Anal. Vol. 3 (1986) pp. 73/84.

    Google Scholar 

  20. Gilbert, R.R. a.R. Magnanini: The boundary integral method for two-dimensional orthotropic materials. J. Elasticity, Vol. 18 (1987) pp. 61/82.

    Article  MathSciNet  Google Scholar 

  21. Ahner, J.F. a.G.C. Hsiao: On the two-dimensional boundary-value problems of elasticity. SIAM J. Appl. Math., Vol. 31 (1976) pp. 677/685.

    Article  MathSciNet  Google Scholar 

  22. Zastrow, U.: Solution of the anisotropic elastostatical boundary value problems by singular integral equations. Acta Mech. Vol. 44 (1982) pp. 59/71.

    Article  Google Scholar 

  23. Zastrow, U.: Numerical plane stress analysis by integral equations based on the singularity method. Solid Mech. Arch. Vol. 10 (1985) pp. 113/128.

    Google Scholar 

  24. Ladopoulos, E.G.: On the solution of the two-dimensional problem of a plance crack of arbitrary shape in an anisotropic material. Engng Fract. Mech., Vol. 28 (1987) pp 187/195.

    Article  Google Scholar 

  25. Ladopoulos, E.G.: Singular integral representations of three-dimensional plasticity fracture problem. Theor. Appl. Fract. Mech. Vol. 8 (1987) pp. 205/211.

    Google Scholar 

  26. Chandra, A. a.S. Mukherjee: A boundary element formulation for large strain problems of compressible plasticity. Engng Anal., Vol. 3 (1986) 71/78.

    Google Scholar 

  27. Bui, H.D.: Some remarks about the formulation of three-dimensional thermoelastoplastic problem of integral equations. Int. J. Solids Struct., Vol. 14 (1978) pp. 935/939.

    Google Scholar 

  28. Swedlow, J.L. a.T.A. Cruse: Formulation of boundary integral equation for three-dimensional elasto-plastic body. Int. J. Solids Struct., Vol. 7 (1971) pp. 1673–1683.

    Article  Google Scholar 

  29. Mukherjee, S.: Corrected boundary integral equation in planar thermoelastoplasticity. Int. J. Solids Struct., Vol. 13 (1977) pp. 331–335.

    Article  Google Scholar 

  30. Telles, J.C.F. a.C.A. Brebbia: On the application of the Boundary Element Method to Plasticity. Appl. Math. Modell., Vol. 3 (1973) pp. 466/470.

    Google Scholar 

  31. Ladopoulos, E.G.: On the numerical evaluation of the singular integral equations used in two and three-dimensional plasticity problems. Mech. Res. Commun., Vol. 14 (1987) pp 263/274.

    Article  Google Scholar 

  32. Ladopoulos, E.G.: Singular integral operators method for two-dimensional plasticity problems. Comput. Struct., Vol. 33 (1989) pp. 859/865.

    Article  MathSciNet  Google Scholar 

  33. Muskhelishvilli, N.I.: Singular integral equations. Groningen: P. Noordhoff 1953.

    Google Scholar 

  34. Muskhelishvilli, N.I.: Some basic problems of the mathematical theory of elasticity. 4th edition. Groningen: P. Noordhoff 1963.

    Google Scholar 

  35. Chen, W.F.: Limit analysis and soil plasticity. Amsterdam: Elsevier Scientific Publishing Co. 1975.

    MATH  Google Scholar 

  36. Chen, A.C.T. a.W.F. Chen: Constitutive equations and punch-indentation of concrete. Proc. ASCE, J. Engng. Mech. Div., Vol. 101 (1975) pp. 889/906.

    Google Scholar 

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  1. Dept. of Applied Mathematics, The National Technical University of Athens, Greece

    E. G. Ladopoulos

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  1. E. G. Ladopoulos
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Ladopoulos, E.G. Singular integral operators method for two-dimensional elasto-plastic stress analysis. Forsch Ing-Wes 57, 152–158 (1991). https://doi.org/10.1007/BF02561415

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