DOI QR코드

DOI QR Code

Numerical Computation of Dynamic Stress Intensity Factors Based on the Equations of Motion in Convolution Integral

시간적분형 운동방정식을 바탕으로 한 동적 응력확대계수의 계산

  • Published : 2002.05.01

Abstract

In this paper, the dynamic stress intensity factors of fracture mechanics are numerically computed in time domain using the FEM. For which the finite element formulations are derived applying the Galerkin method to the equations of motion in convolution integral as has been presented in the previous paper. To assure the strain fields of r$^{-1}$ 2/ singularity near the crack tip, the triangular quarter-point singular elements are imbedded in the finite element mesh discretized by the isoparametric quadratic quadrilateral elements. Two-dimensional problems of the elastodynamic fracture mechanics under the impact load are solved and compared with the existing numerical and analytical solutions, being shown that numerical results of good accuracy are obtained by the presented method.

Keywords

Dynamic Stress Intensity Factor;FEM;Convolution Integral;Singular Element

References

  1. Paris, C.P. and Sih, G.C., 1965, 'Stress Analysis of Cracks,' Fracture Toughness Testing and Its Applications, ASTM STP 381, American Society for Testing and Materials, Philadelphia
  2. Aberson, J.A., Anderson J.M., and King, W.W., 1977, 'Dynamic Analysis of Cracked Structures Using Singularity Finite Elements,' Sih, G.C. (ed.), Mechanics of Fracture 4, Elastodynamic Crack Problems, Noorhoff, Leyden
  3. Tan, M. and Meguid, S.A., 1996, 'Dynamic Analysis of Cracks Perpendicular to Bimaterial Interfaces Using a New Singular Finite Elements,' Fin. El. Anal. Des., Vol. 22, pp. 69-83 https://doi.org/10.1016/0168-874X(95)00060-7
  4. Dauksher, W. and Emery, A.F., 2000, 'The Solution of Elastostatic and Elastodynamic Problems with Chebyshev Spectral Finite Elements,' Comp. Meth. Appl. Mech. Eng., Vol. 188, pp. 217-233 https://doi.org/10.1016/S0045-7825(99)00149-8
  5. Chen, Y.M., 1975, 'Numerical Computation of Dynamic Stress Intensity Factors by a Largrangian Finite Difference Method (the HEMP code),' Eng. Frac. Mech., Vol. 7, pp. 653-660 https://doi.org/10.1016/0013-7944(75)90021-1
  6. Barsum, R.S., 1977, 'Triangular Quarter Point Elements as Elastic and Perfectly Plastic Crack Tip Elements,' Int. J. Num. Meth. Eng., Vol. 11, No. 1, pp. 85-98 https://doi.org/10.1002/nme.1620110109
  7. Tada, H., Paris, P.C., and Irwin, G.R., 1973, The Stress Analysis of Cracks Handbook, Del Research, Hellertown
  8. Parker, A.P., 1981, The Mechanics of Fracture and Fatigue, E. & F.N. Spon Ltd., London
  9. Chen, E.P., and Sih G.C., 1977, 'Transient Response of Cracks to Impact Loads,' Sih, G.C. (ed.), Mechanics of Fracture 4, Elastodynamic Crack Problems, Noordhoff, Leyden
  10. Barsum, R.S., 1976, 'On The Use of Isoparametric Finite Elements in Linear Fracture Mechanics,' Int. J. Num. Meth. Eng., Vol. 10, pp. 25-37 https://doi.org/10.1002/nme.1620100103
  11. Israil, A.S.M. and Banerjee, P.K., 1990, 'Advanced Development of Time-Domain BEM for Two-Dimensional Scalar Wave Propagation,' Int. J. Num. Meth. Eng., Vol. 29, pp. 1003-1020 https://doi.org/10.1002/nme.1620290507
  12. Wang, C.C., Wang, H.C. and Liou, G.S., 1997, 'Quadratic Time Domain BEM Formulation for 2D Elastodynamic Transient Analysis,' Int. J. Solids Structures, Vol. 34, No. 1, pp. 129-151 https://doi.org/10.1016/0020-7683(95)00293-6
  13. 심우진, 이성희, 2001, '과도 선형 동탄성 문제의 시간영역 유한요소해석,' 대한기계학회논문집 A권, 제25권 제4호, pp. 574-581
  14. Dunham, R.S., Nickell, R.E., and Stickler, D.C., 1972, 'Integration Operators for Transient Structural Response,' Computers and Structures, Vol. 2, pp. 1-15 https://doi.org/10.1016/0045-7949(72)90019-3
  15. Atluri S., 1973, 'An Assumed Stress Hybrid Finite Element Model for Linear Elastodynamic Analysis,' AIAA J., Vol. 11, No. 7, pp. 1028-1031 https://doi.org/10.2514/3.6865
  16. Nickell, R.E. and Sackman, J.L., 1968, 'Approximate Solutions in Linear Coupled Thermoelasticity,' Trans. ASME, J. Appl. Mech., Vol. 35, pp. 255-266 https://doi.org/10.1115/1.3601189
  17. Oden, J.T. and Reddy, J.N., 1976, Variational Methods in Theoretical Mechanics, Springer-Verlag, Berlin
  18. Gurtin, M.E., 1964, 'Variational Principles for Linear Elastodynamics,' Archive for Rational Mechanics and Analysis, Vol. 16, No. 1, pp. 34-50 https://doi.org/10.1007/BF00248489
  19. Washizu, K., 1975, Variational Methods in Elasticity and Plasticity (2nd edn.), Pergamon Press, Oxford
  20. Beskos, D.E., 1997, 'Boundary Element Methods in Dynamic Analysis: Part II (1986-1996),' Trans ASME, Appl. Mech. Rev., Vol. 50, No. 3, pp. 149-197 https://doi.org/10.1115/1.3101695
  21. Achenbach, J.D., 1975, Wave Propagation in Elastic Solids, North-Holland, Amsterdam
  22. Manolis, G.D., and Beskos, D.E., 1988, Boundary Element Methods in Elastodynamics, Routledge
  23. Dominguez, J., 1993, Boundary Elements in Dynamics, Elsevier, Amsterdam
  24. Harari, I., Hughes, T.J.R., Grosh, K., Malhotra, M., Pinsky, P.M., Stewart, J.R. and Thompson, L.L., 1996, 'Recent Developments in Finite Element Methods for Structural Acoustics,' Archives of Computational Methods in Engineering, Vol. 3, pp. 131-309 https://doi.org/10.1007/BF03041209
  25. Banerjee, P.K., 1994, Boundary Element Methods in Engineering, McGraw-Hill, London
  26. Bathe, K.J., 1996, Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs
  27. Hughes, T.J.R., 1987, The Finite Element Method, Englewood Cliffs, Prentice-Hall
  28. Belytschko, T. and Hughes, T.J.R. (eds.), 1983, Computational Methods for Transient Analysis, North-Holland, Amsterdam
  29. Zienkiewicz, O.C. and Taylor, R.L., 1991, The Finite Element Method (4th edn.), McGraw-Hill, London
  30. Chen, Y.M. and Wilkins, M.L., 1977, 'Numerical Analysis of Dynamic Crack Problems,' Mechanics of Fracture 4, Elastodynamic Crack Problems, Sih, G.C. (ed.), Noordhoff Int. Publishing, Leyden
  31. Reddy, J.N., 1993, An Introduction to the Finite Element Method (2nd edn.), McGraw-Hill, London