Structural Engineering and Mechanics

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Adaptive finite elements by Delaunay triangulation for fracture analysis of cracks

  • Received : 2002.05.20
  • Accepted : 2003.03.14
  • Published : 2003.05.25
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Abstract

Delaunay triangulation is combined with an adaptive finite element method for analysis of two-dimensional crack propagation problems. The content includes detailed descriptions of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around the crack tips and large elements in the other regions. Three examples for predicting the stress intensity factors of a center cracked plate, a compact tension specimen, a single edge cracked plate under mixed-mode loading, and an example for simulating crack growth behavior in a single edge cracked plate with holes, are used to evaluate the effectiveness of the procedure. These examples demonstrate that the proposed procedure can improve solution accuracy as well as reduce total number of unknowns and computational time.

Keywords

References

  1. Anderson, T.L. (1991), Fracture Mechanics: Fundamentals and Applications, CRC Press, Florida.
  2. ASTM 1996 (1996), Annual Book of ASTM Standards, American Society for Testing and Materials, Philadelphia.
  3. Barsoum, R.S. (1977), "Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements", Int. J. Numer. Methods Eng., 11, 85-98. https://doi.org/10.1002/nme.1620110109
  4. Bittencourt, T.N., Wawrzynek, P.A., Ingraffea, A.R. and Sousa, J.L. (1996), "Quasi-automatic simulation of crack propagation for 2D LEFM problems", Eng. Fract. Mech., 55, 321-334. https://doi.org/10.1016/0013-7944(95)00247-2
  5. Borouchaki, H. and George, P.L. (1997), "Aspects of 2-D Delaunay mesh generation", Int. J. Numer. Methods Eng., 40, 1957-1975. https://doi.org/10.1002/(SICI)1097-0207(19970615)40:11<1957::AID-NME147>3.0.CO;2-6
  6. Bowyer, A. (1981), "Computing Dirichlet tessellations", Comp. J., 24(2), 162-166. https://doi.org/10.1093/comjnl/24.2.162
  7. Chan, S.K., Tuba, I.S. and Wilson, W.K. (1970), "On the finite element method in linear fracture mechanics", Eng. Fract. Mech., 2, 1-17. https://doi.org/10.1016/0013-7944(70)90026-3
  8. Dechaumphai, P. (1996), "Improvement of plane stress solutions using adaptive finite elements", J. Chin. Inst. Eng., 19, 375-380. https://doi.org/10.1080/02533839.1996.9677798
  9. Erdogan, F. and Sih, G.C. (1963), "On the crack extension in plates under plane loading and transverse shear", J. Basic Eng., 85, 519-527. https://doi.org/10.1115/1.3656897
  10. Frey, W.H. (1987), "Selective refinement: a new strategy for automatic node placement in graded triangular meshes", Int. J. Numer. Methods Eng., 24, 2183-2200. https://doi.org/10.1002/nme.1620241111
  11. Guinea, G.V., Planas, J. and Elices, M. (2000), "$K_I$ evaluation by the displacement extrapolation technique", Eng. Fract. Mech., 66, 243-255. https://doi.org/10.1016/S0013-7944(00)00016-3
  12. Isida, M. (1971), "Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions", Int. J. Fract., 7, 301-316.
  13. Karamete, B.K., Tokdemir, T. and Ger, M. (1997), "Unstructured grid generation and a simple triangulation algorithm for arbitrary 2-D geometries using object oriented programming", Int. J. Numer. Methods Eng., 40, 251-268. https://doi.org/10.1002/(SICI)1097-0207(19970130)40:2<251::AID-NME62>3.0.CO;2-U
  14. Lawson, C.L. (1977), Software for $C^1$ Surface Interpolation. Mathematical Software III, Academic Press, New York.
  15. Peraire, J., Vahdati, M., Morgan, K. and Zienkiewicz, O.C. (1987), "Adaptive remeshing for compressible flow computations", J. Comput. Phys., 72, 449-466. https://doi.org/10.1016/0021-9991(87)90093-3
  16. Phongthanapanich, S. and Dechaumphai, P. (2002), Underwater Explosion Simulation by Transient Adaptive Delaunay Triangulation Meshing Technique, Technical Report submitted to the Royal Thai Navy, TR-3894. Bangkok.
  17. Rao, B.N. and Rahman, S. (2000), "An efficient meshless method for fracture analysis of cracks", Comput. Mech., 26, 398-408. https://doi.org/10.1007/s004660000189
  18. Sloan, S.W. (1993), "A fast algorithm for generating constrained Delaunay triangulations", Comp. Struct., 47, 441-450. https://doi.org/10.1016/0045-7949(93)90239-A
  19. Watson, D.F. (1981), "Computing the n-dimensional Delaunay tessellation with application to Voronoi polytopes", Comp. J., 24(2), 167-172. https://doi.org/10.1093/comjnl/24.2.167
  20. Weatherill, N.P. and Hassan, O. (1994), "Efficient three-dimension Delaunay triangulation with automatic point creation and imposed boundary constraints", Int. J. Numer. Methods Eng., 37, 2005-2039. https://doi.org/10.1002/nme.1620371203
  21. Zienkiewicz, O.C. and Taylor, R.L. (2000), Finite Element Method, Fifth Edition, Butterworth-Heinemann, Woburn.

Cited by

  1. J-integral calculation by domain integral technique using adaptive finite element method vol.28, pp.4, 2008, https://doi.org/10.12989/sem.2008.28.4.461