A boundary collocation method for cracked plates

Computers and Structures

Volumn 81, Issue 28-29, 2003, Pages 2621-2630

  Wang, Y H ^a   Tham, L G ^b   Lee, P K K ^b   Tsui, Y ^b  

^a HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Bending plate; Boundary collocation method; Complex stress functions; Stress intensity factors

Indexed keywords

BOUNDARY CONDITIONS; CRACKS; LEAST SQUARES APPROXIMATIONS; STRESS INTENSITY FACTORS;

COLLOCATION METHODS;

PLATES (STRUCTURAL COMPONENTS);

EID: 0142043356     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(03)00324-9     Document Type: Article

References (37)

1. Sih G.C. Handbook of stress intensity factors. 1973;Leheigh University, Bethlehem.
2. Tada H., Paris P.C., Irwin G.R. The stress analysis of cracks handbook. 1973,1985;Del Research Corp, Hellertown.
3. Rook D.P., Cartwright D.J. Compendium of stress intensity factors. 1976;Her Majesty's Stationary Office, London.
4. Murakami Y. Stress intensity factor handbook, vol. 2. New York: Pergamon Press; 1987.
5. Timoshenko S., Woinowsky-Krieger S. Theory of plates and shells. 1959;McGraw-Hill, New York.
6. Williams M.L. The bending stress distribution at the base of a stationary crack. J. Appl. Mech. 28:1961;78-82.
7. Sih G.C., Paris P.C., Erdogan F. Crack-tip stress-intensity factors for plane extension and plate bending problems. J. Appl. Mech. 29:1962;306-312.
8. Isida M. Interaction of arbitrary array of cracks in wide plates under classical bending. Sih G.C. Plate and shells with cracks. 1977;1-43 Noordhoff, Leyden.
9. van Vroonhoven J.C.W. Stress intensity factors for curvilinear cracks loaded by bending and torsional moments. Int. J. Fract. 68:1994;193-218.
10. Barsoum R.S. A degenerate solid element for linear fracture analysis of plate bending and general shells. Int. J. Numer. Meth. Eng. 10:1976;551-564.
11. Yagawa G., Nishioka T. Finite element analysis of stress intensity fracture factors for plane extension and plate bending problems. Int. J. Numer. Meth. Eng. 14:1979;727-740.
12. Ahmad J., Loo F.T.C. Solution of plate bending problems in fracture mechanics using a specialized finite element technique. Eng. Fract. Mech. 11:1979;661-673.
13. Murthy M.V.V., Raju K.N., Viswanath S. On the bending stress distribution at the tip of a stationary crack from Reissner's theory. Int. J. Fract. 17:1981;537-552.
14. Rhee H.C., Atluri S.N. Hybrid stress finite element analysis of bending of a plate with a through flaw. Int. J. Numer. Meth. Eng. 18:1982;259-271.
15. Chen W.H., Chen P.Y. A hybrid-displacement finite element model for the bending analysis of thin cracked plates. Int. J. Fract. 24:1984;83-106.
16. Ye T.Q., Gallagher R.H. A singular finite element for analysis of plate bending problem in fracture mechanics. Int. J. Fract. 24:1984;137-147.
17. Chen W.H., Shen C.M. A finite element alternating approach to the bending of thin plates containing mixed mode cracks. Int. J. Solids Struct. 30:1993;2261-2276.
18. Jiang C.P., Cheung Y.K. A special bending crack tip finite element. Int. J. Fract. 61:1995;57-69.
19. Portela A. Dual boundary element analysis of crack growth. 1993;Computational Mechanics Publications, Southampton, UK and Boston, USA.
20. Keer L.M., Sve C. On the bending of cracked plates. Int. J. Solids Struct. 6:1970;1545-1549.
21. Barta J. Über die näherungsweise Lösung einiger zweidimensionaler Elastizitätsaufgaben. Zeitschrift für angewandte Mathematik und Mechanik. 17:1937;184-185.
22. Conway H.D. The approximate analysis of certain boundary-value problems. J. Appl. Mech. 27:1960;275-277.
23. Leissa A.W., Lo C.C., Niedenfuhr F.W. Uniformly loaded plates of regular polygonal shape. AIAA J. 3:1965;566-567.
24. Conway H.D., Farnham K.A. Deflections of uniformly loaded circular plates with combination of clamped simply supported and free boundary conditions. Int. J. Mech. Sci. 9:1967;661-671.
25. Leissa A.W., Clausen W.E. Deflection of a circular plate having mixed boundary conditions. AIAA J. 5:1967;2287-2288.
26. Kolodziej J.A. Review of application of boundary collocation methods in mechanics of continuous media. Solid Mech. Arch. 12:1987;187-231.
27. Hutchinson J.R. Analysis of plates and shells by boundary collocation. Beskos D.E. Boundary element analysis of plates and shells. 1991;Springer-Verlag, Berlin Heidelberg.
28. Gross B, Srawley JE. Stress-intensity factors for a single-edge-notch tension specimen by boundary collocation of a stress function. NASA TN D-2395; 1964.
29. Kobayashi A.S., Cherepy A.S., Kinsal W.C. A numerical procedure for estimating the stress intensity factor of a crack in a finite plate. ASME J. Basic Eng. 86:1964;681-684.
30. Newman JC. An improved method of collocation for the stress analysis of cracked plate with various shaped boundaries. NASA TN D-6376; 1971.
31. Wang YH. The elastic and elasto-plastic fracture analysis by method of weighted residuals and elasto-viscoplasticity. PhD Thesis, The University of Hong Kong, Hong Kong; 1988.
32. Muskhelishvili N.I. Some basic problems of mathematical theory of elasticity. 1975;Noordhoff, Leyden.
33. Lekhnitskii S.G. Anisotropic plates. English translation of the original Russian. 1968;Gordon & Breach, Science Publishers, Inc, New York.
34. Lekhnitskii SG. Theory of elasticity of an anisotropic elastic body. Translated by Fern P. San Francisco: Holden-Day, Inc., 1963.
35. Savin G.N. Stress concentration around holes. 1961;Pergamon Press, Oxford.
36. Liu C.T., Jiang C.P. Fracture mechanics for plates and shells. 2000;National Defense Press, Beijing. (in Chinese).
37. Qu Q.Z., Zhang Q., Ji Q.Y., Liang X.F. Theory of elastic plates. 2000;People's Communication Press, Beijing. (in Chinese).