Journal of Zhejiang University SCIENCE A
ISSN 1673-565X(Print), 1862-1775(Online), Monthly

2007   Vol. 8   No. 9   p. 1373~1379

Finite element modeling for analysis of cracked cylindrical pipes

SUNG Wen-pei^†1, GO Cheer-germ², SHIH Ming-hsiang³

(¹Department of Landscape Design and Management, National Chin-Yi University of Technology, Taiping, Taichung 41111, Taiwan, China)
(²Department of Civil Engineering, National Chung Hsing University, Taichung 40227, Taiwan, China)
(³Department of Construction Engineering, National Kaohsiung First University of Science and Technology, Kaohsiung 811, Taiwan, China)
^†E-mail: sung809@ncut.edu.tw
Received Sept. 19, 2006 revision accepted Mar. 15, 2007

Abstract: The characteristic properties of shell element with similar shapes are used to generate a so-called super element for the analysis of the crack problems for cylindrical pressure vessels. The formulation is processed by matrix condensation without the involvement of special treatment. This method can deal with various singularity problems and it also presents excellent results to crack problems for cylindrical shell. Especially, the knowledge of the kind of singular order is not necessary in super element generation; it is very economical in terms of computer memory and programming. This method also exhibits versatility to solve the problem of kinked crack at cylindrical shell.

Key words: Crack shell, Super-element, Pressure vessel
doi:10.1631/jzus.2007.A1373             CLC number: TB6; TK91

References:

[1] Ainsworth, R.A., Ruggles, M.B., Takahashi, Y., 1992. Flaw assessment procedure for high-temperature reactor components. J. Pressure Vessel Technology, Trans. ASME, 114:166-170.

[2] Anderson, T.L., 1991. Fracture Mechanics: Fundamentals and Applications. CRC Press, Boca Raton.

[3] Atluri, S.N., 1986. Computation Methods in the Mechanics of Fracture. North-Holland, Amsterdam.

[4] Chen, W.H., Lin, H.C., 1985. Flutter analysis of thin cracked panels using the finite element method. AIAA J., 23:795-801.

[5] Cook, R.D., Malkus, D.S., Plesha, M.E., 1989. Concepts and Applications of Finite Element Analysis. John Wiley and Sons.

[6] Dutta, B.K., Maiti, S.K., Kakodkar, A., 1990. On the use of one point and two point’s singularity elements in the analysis of kinked crack. Int. J. Numeral Meth. Eng., 29(7):1487-1499.

[7] Folias, E.S., 1999. Failure correlation between cylindrical pressurized vessels and flat plates. Int. J. Pressure Vessels and Piping, 76(11):803-811.

[8] Go, C.G., Chen, G.C., 1992. On the use of an infinitely small element for the three-dimensional problem of stress singularity. Computers & Structures, 45(1):25-30.

[9] Go, C.G., Lin, Y.S., 1991. Infinitely small element for the problem of stress singularity. Computers & Structures, 37:547-551.

[10] Go, C.G., Lin, Y.S., 1994. Infinitely small element for the dynamic problem of a crack beam. Eng. Fracture Mech., 48(4):475-482.

[11] Go, C.G., Lin, C.I., Lin, Y.S., Wu, S.H., 1998. Formulation of a super-element for the dynamic problem of a cracked plate. Commun. Numer. Meth. Engng., 14(12):1143-1154.

[12] Hooton, D.G., Tomkins, B., 1996. Development of structural integrity criteria for austenitic components. Int. J. Pressure Vessels and Piping, 65(3):311-316.

[13] JHGPA (Inc. Japan Hydraulic Gate and Penstock Association), 1986. Technical Standards for Gates and Penstock.

[14] Knott, J.F., 1973. Fundamentals of Fracture Mechanics. Halsted Press.

[15] Kobayashi, A.S., 1973. Experimental Techniques in Fracture Mechanics. SESA (Society for Experimental Stress Analysis) Monographs, No. 1 and 2. Westport, CT.

[16] Lakshminarayana, H.V., Murthy, M.V.V., Srinath, L.S., 1982. On an analytical-numerical procedure for the analysis of cylindrical shell with arbitrary oriented cracks. Int. J. Fracture, 19(4):257-275.

[17] Le Van, A., Royer, J., 1986. Integral equations for three-dimensional problems. Int. J. Fracture, 31(2): 125-142.

[18] Lynn, P.P., Ingraffen, A.R., 1978. Transition elements to be used with quarter point crack tip elements method. Int. J. Numeral Meth. Eng., 12(6):1031-1036.

[19] Minnetyan, L., Chamis, C.C., 1999. Damage tolerance of large shell structures. J. Pressure Vessel Technology, Trans. ASME, 121:188-195.

[20] Mutri, V., Valliappan, S., Lee, I.K., 1985. Stress Intensity factor using Quarter Point Element. ASCE J. Eng. Mech. Div., 111(2):203-217.

[21] Nichols, R.W., 1987. Pressure Vessel Codes and Standards. Elsevier Applied Science Publisher Ltd.

[22] Pilkey, W.D., 1994. Formulas for Stress, Strain, and Structural Matrices. John Wiley and Sons, Inc., p.117.

[23] Shephard, M.S., Gallagher, R.H., Abel, J.F., 1981. Finite element solution to point-load problems. ASCE J. Eng. Mech. Div., 107(5):839-850.

[24] Sih, G.C., 1977. Mechanics of Fracture: Plates and Shells with Cracks—A Collection of Stress Intensity Factor Solutions for Cracks in Plates and Shells (Vol. 3). Noordhoff International Publishing.

[25] Song, C., 2004. A super-element for crack analysis in the time domain. Int. J. Numeral Meth. Eng., 61(8):1332-1357.

[26] Szilard, R., 1974. Theory and Analysis of Plates, Classical and Numerical Methods. Prentice-Hall, Inc., p.3.

[27] Tani, K., Yamada, T., Kawase, Y., 2000. Error estimation for transient finite element method using edge elements. IEEE Transactions on Magnetics, 12th Conference of the Computation of Electromagnetic Fields, 36(4):1488-1491.

[28] Timoshenko, S., 1955. Strength of Materials. Part I (3rd Ed.). D. Van Nostrand Co., New York, USA, p.370.

[29] Timoshenko, S., Woinowsky-Krieger, S., 1959. Theory of Plates and Shells (2nd Ed.). McGraw-Hill, London, UK, p.431.

[30] Ugural, A.C., 1981. Stresses in PLATES and Shells. McGraw-Hill, Inc.

[31] Zhao, J., Hoa, S.V., Xiao, X.R., Hanna, I., 1999. Global/local approach using partial hybrid finite element analysis of stress fields in laminated composites with mid-plane delamination under bending. J. Reinforced Plastics and Composites, 18(9):827-843.

[32] Zheng, J.Y., Chen, Y.J., Deng, G.D., Sun, G.Y., Hu, Y.L., Li, Q.M., 2006. Dynamic elastic response of an infinite discrete multi-layered cylindrical shell subjected to uniformly distributed pressure pulse. Int. J. Impact Engineering, 32(11):1800-1827.