Numerical thermo-elastic analysis of singularities in two-dimensions
- 89 Downloads
- 7 Citations
Abstract
Linear elastic two-dimensional problems with singular points subjected to steady-state temperature distribution are considered. The stress tensor in the vicinity of the singular points exhibits singular behavior characterized by the strength of the singularity and the associated thermal stress intensity factors (TSIFs). It is shown that the TSIFs and the strength of the stress singularity can be obtained using the principle of complementary energy together with the modified Steklov method and the p-version of the finite element method. Importantly, the proposed method is applicable not only to singularities associated with crack tips, but also to multi-material interfaces and non-homogeneous materials. Numerical results of crack-tip singularities in a rectangular plate and singular points associated with a two-material inclusion are presented.
Keywords
Stress Intensity Factor Singular Point Boundary Element Method Thermal Loading Stress SingularityPreview
Unable to display preview. Download preview PDF.
References
- 1.T. Hattori, S. Sakata and G. Murakami, Journal of Electronic Packaging 111 (1989) 243–248.CrossRefGoogle Scholar
- 2.K. Ikegami, Advances in Electronic Packaging, ASME-EEP 1 (1992) 567–573.Google Scholar
- 3.G. C. Sih, Transactions ASME, Journal of Applied Mechanics 29 (1962) 587–589.CrossRefGoogle Scholar
- 4.N. Sumi and T. Katayama, Nuclear Engineering Design 60 (1980) 389–394.CrossRefGoogle Scholar
- 5.C-H. Tsai and C-C. MA, Engineering Fracture Mechanics 41(1) (1992) 27–40.CrossRefGoogle Scholar
- 6.M.M. Michael and R.J. Hartranft, in Proceedings—41st Electronic Components & Technology Conference, Atlanta, GA, USA, pages 273–277. IEEE, Piscataway, NJ, 1991.Google Scholar
- 7.Z. Yosibash and B. A. Szabó, International Journal of Numerical Methods in Engineering 38(12) (1995) 2055–2082.CrossRefGoogle Scholar
- 8.Z. Yosibash, Numerical analysis of singularities and first derivatives for elliptic boundary value problems in two-dimensions. DSc thesis, Sever Institute of Technology, Washington University, St. Louis, Missouri, USA, Aug. 1994.Google Scholar
- 9.B. A. Szabó and Z. Yosibash, Numerical analysis of singularities in two-dimensions. Part 2: Computation of the generalized flux/stress intensity factors. International Journal of Numerical Methods in Engineering, 1996. In press.Google Scholar
- 10.D. Leguillon and E. Sanchez-Palencia, Computation of Singular Solutions in Elliptic Problems and Elasticity John Wiley & Sons, New York, NY, 1987.Google Scholar
- 11.P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman Publishing, England, 1985.Google Scholar
- 12.V. A. Kondratiev, Transactions Moscow Mathematics Society 16 (1967) 227–313.Google Scholar
- 13.B. A. Szabó and I. Babuška, Finite Element Analysis, John Wiley & Sons, New York, 1991.Google Scholar
- 14.I. Babuška and M. Suri, SIAM review 36(4) (1994) 578–632.CrossRefGoogle Scholar
- 15.N. N. V. Prasad, M. H. Aliabadi, and D. P. Rooke, International Journal of Fracture 66 (1994) 255–272.CrossRefGoogle Scholar
- 16.K. Lee and Y. H. Cho, Engineering Fracture Mechanics 37(4) (1990) 787–798.CrossRefGoogle Scholar
- 17.N. Liu and J. Altiero, Applied Mathematical Modelling 16 (1992) 618–628.CrossRefGoogle Scholar
- 18.V.L. Hein and F. Erdogan, International Journal of Fracture 7(3) (1971) 317–330.Google Scholar
- 19.Dai-Heng Chen, Engineering Fracture Mechanics 49(4) (1994) 533–546.CrossRefGoogle Scholar