臺灣博碩士論文加值系統

本論文所發展出之特殊裂紋尖端元素，在元素內部之位移及應力與張開型式之界面裂紋尖端有相同特性；在兩種材料彈性係數相同之情況，裂紋尖端之應力及位移會回復到一般1/4點元素(quarter point element)所產生之應力及位移。使用本論文所使用的座標系，能夠快速的計算出元素剛性矩陣(stiffness matrices)，論文中所推導之公式，可利用特殊元素所求得之位移計算出複數型式應力強度因子(complex stress intensity factor)，其計算結果並與已知之解析解比較，所比較的兩個例題都得到良好結果。

In this thesis a special crack tip element has been developed in which displacements and stresses have same behavior as those of bi-material interface cracks with open tips. As the crack is along an interface of materials with identical elastic moduli, the element degenerates into a traditional quarter point element. By using the isoparametric coordinate system specified in this thesis, element stiffness matrices may be easily calculated. Also, it is shown in this study the complex may be obtained. Numerical results are in good agreement with known analytical solutions in two examples.

Chinese Abstract
English Abstract
Table of contents …………………………………………….………Ⅰ
List of Figures …………………………………………………………Ⅲ
List of Tales ……………………………………………….…………Ⅵ
Symbol Explanation ……………………………………………………Ⅶ
CHAPTER 1 Introduction ………………………………………………1
CHAPTER 2 Crack Tip Singularity …………………………………3
CHAPTER 3 Stiffness Matrix Triangular Coordinates…………7
CHAPTER 4 Stiffness Matrix- Coordinates……………………10
4.1 Jacobian Matrix- Coordinates…………………………..10
4.2 Derivatives of u and v - Coordinates……………………12
CHAPTER 5 Complex Stress Intensity Factors …………………16
CHAPTER 6 Results and Discussions ………………………………19
CHAPTER 7 Conclusions ……………………………………………..23
References ……………………………………………………………..24
Appendix 1 ……………………………………………………………..26
Appendix 2 ……………………………………………………………..28
Appendix 3 ……………………………………………………………..29
Appendix 4 ……………………………………………………………..31
Appendix 5 ……………………………………………………………..36
Appendix 6 ……………………………………………………………..37
Appendix 7 ……………………………………………………………..38

Barsoum, R. S., 1976, “On the Use of Iso-Parametric Finite Elements in Linear Fracture Mechanics,” International Journal for Numerical Methods in Engineering,” Vol. 10, pp. 25-37.
Barsoum, R. S., 1977, “Triangular Quarter-Point Elements as Elastic and Perfectly-Plastic Crack Tip Element,” International Journal for Numerical Methods in Engineering,” Vol. 11, pp. 85-98.
Chow, W. T., and Atluri, S. N., 1995, “ Finite Element Calculation of Intensity Factors for Interfacial Crack Using Virtual Crack Closure Integral,” Computational Mechanics,” Vol. 16, pp. 417-425.
Comninou, M., 1977a, “The Interface Crack,” ASME Journal of Applied Mechanics, Vol. 44, pp. 631-638.
Comninou, M., 1977b, “Interface Crack with Friction in the Contact Zone,” ASME Journal of Applied Mechanics, Vol. 44, pp. 780-781.
Comninou, M. and Schmueser, D., 1979, “The Interface Crack in a Combined Tension-Compression and Shear Field,” ASME Journal of Applied Mechanics, Vol. 46, pp. 345-348.
Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989, “Concepts and Applications of Finite Element Analysis”, third edition, John Wiley & Sons, Inc., New York.
Englan, A. H., 1965, “A Crack Between Dissimilar Media,” ASME Journal of Applied Mechanics, Vol. 32, pp. 400-402.
Erdogan, F., 1963, “Stress Distribution in a Non-homogeneous Elastic Plane with Cracks”, ASME, Journal of Applied Mechanics, Vol. 30, pp. 232-236.
Erdogan, F., 1965, “Stress Distributions in Bonded Dissimilar Material with Cracks,” ASME Journal of Applied Mechanics, Vol. 32, pp. 403-410.
Gautesen, A. K., and Dunder, J., 1987, “The Interface Crack in a Tension Field,” ASME Journal of Applied Mechanics, Vol. 54, pp. 93-98.
Gautesen, A. K., and Dunder, J., 1988, “The Interface Crack under Combined Loading,” ASME Journal of Applied Mechanics, Vol. 55, pp. 580-586.
Hutchinson, J. W., Mear, M., and Rice, J. R., 1987, “Crack Paralleling the Interface Between Dissimilar Materials,” ASME Journal of Applied Mechanics, Vol. 54, pp. 828-832.
Ingraffea, A. R., and Manu, C., 1980, “Stress Intensity Factor Computation in Three Dimensions With Quarter Point Elements”, International Journal for Numerical Methods in Engineering, Vol. 15, pp.1427-1445.
Lim, W. K., and Lee, C. S, 1995, “Evaluation of Stress Intensity Factors For a Crack Normal to Bimaterial Interface Using Isoparametric Finite Elements”, Engineering Fracture Mechanics, Vol. 52, No. 1, pp.65-70.
Liu, H. C., and Chen I. F., 1996, “Interface Cracks in a Layered Solid Subjected to Contact Stresses”, ASME Journal of Applied Mechanics, Vol. 63, pp. 271-277.
Malyshev, B. M., and Salganik, R. L., 1965, “The Strength of Adhesive Joints Using the Theory of Crack”, International Journal of Fracture Mechanics, Vol. 1, pp.114-128.
Murakami, Y., etc., 1987, “Stress Intensity Factors Handbook”, Oxford: Pergamon Press, Vol. 1.
Raju, I. S., 1987, “Calculation of Strain-Energy Release Rates with Higher Order and Singular Finite Elements,” Engineering Fracture Mechanics, Vol. 28, No. 3, pp.251-274.
Rice, J. R., 1988, “Elastic Fracture Mechanics Concepts for Interfacial Cracks,” ASME Journal of Applied Mechanics, Vol. 55, pp. 98-103.
Rice, J. R., and Sih, G. C., 1965, “Plane Problems of Cracks in Dissimilar Media,” ASME Journal of Applied Mechanics, Vol. 32, pp. 418-423.
Salganik, R. L., 1963, “The Brittle Fracture of Cemented Bodies”, PMM, Vol. 27, pp. 1468-1478.
Tada, H, Paris, P. C., and Irwin, G. R., 1985, The Stress Analysis of Cracks Handbook, second ed., Paris Productions, Inc., St. Louis.
Williams, M. L., 1959, “The Stresses Around a Fault or Crack in Dissimilar Media,” Bulletin of the Seismological Society of America, Vol. 49, pp. 199-204
Yehia, N. A. B., and Shephard, M. S., 1985, “On the Effect of Quarter Point Element Size on Fracture Criteria”, International Journal for Numerical Methods in Engineering, Vol. 21, pp.1911-1924.