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Assumed strain stabilization procedure for the 9-node Lagrange shell element. (English) Zbl 0674.73054
Summary: An assumed strain (strain interpolation) method is used to construct a stabilization matrix for the 9-node shell element. The stabilization procedure can be justified based on the Hellinger-Reissner variational method. It involves a projection vector which is orthogonal to both linear and quadratic fields in the local co-ordinate system of each quadrature point. All terms in the development involve \(2\times 2\) quadrature in the 9-node element. Example problems show good accuracy and an almost optimal rate of convergence.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
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[1] Ahmad, Int. j. numer. methods eng. 2 pp 419– (1970)
[2] Bathe, Int. j. numer. methods eng. 21 pp 367– (1985)
[3] Belytschko, Comp. Methods Appl. Mech. Eng. 54 pp 279– (1986)
[4] Belytschko, Comp. Methods Appl. Mech. Eng. 62 pp 275– (1987)
[5] Belytschko, Comp. Struct. 20 pp 121– (1985)
[6] Belytschko, Comp. Methods Appl. Mech. Eng. 44 pp 269– (1984)
[7] Belytschko, Comp. Methods Appl. Mech. Eng. 43 pp 251– (1984)
[8] Belytschko, Comp. Methods Appl. Mech. Eng. 51 pp 221– (1985)
[9] Belytschko, Int. j. numer. methods eng. 19 pp 405– (1983)
[10] Dvorkin, Eng. Comp. 1 pp 77– (1984)
[11] Stresses in Shells, 2nd edn., Springer-Verlag, Berlin, 1973.
[12] Huang, Eng. Comp. 1 pp 369– (1984)
[13] Huang, Int. j. numer. methods eng. 22 pp 73– (1986)
[14] Hughes, Nucl. Eng. Des. 46 pp 203– (1978)
[15] Hughes, Comp. Methods Appl. Mech. Eng. 26 pp 331– (1981)
[16] Hughes, J. Appl. Mech. ASME 48 pp 587– (1981)
[17] Jacquotte, Comp. Methods Appl. Mech. Eng. 55 pp 105– (1986)
[18] ’Improvement of the quadrangular ’JET’ shell element for a particular class of shell problems’, IREM Internal Report 87/1, 1987.
[19] Lee, AIAA J. 16 pp 29– (1978)
[20] ’Vibration of plates’, NASA Technical Report, SP-160, 1969.
[21] Liu, Comp. Methods Appl. Mech. Eng. 55 pp 259– (1986)
[22] MacNeal, Nucl. Eng. Des. 70 pp 3– (1982)
[23] MacNeal, Finite Elements Anal. Des. 11 pp 3– (1985)
[24] Malkus, Comp. Methods Appl. Mech. Eng. 15 pp 63– (1978)
[25] Introduction to the Mechanics of a Continuum Medium, Prentice-Hall, Englewood Cliffs, N.J., 1969.
[26] Theory of Shell and Plate, Handbuch Der Physik, Vol. VI-2, 2nd edn, Springer-Verlag, Berlin, 1972.
[27] ’A consistent control of spurious modes for 9-node Lagrange element’, Ph.D. Thesis, Northwestern University, Evanston, 1986.
[28] Parish, Comp. Methods Appl. Mech. Eng. 20 pp 323– (1979)
[29] Pian, Int. j. numer. methods eng. 20 pp 1685– (1984)
[30] and , ’A new mixed formulation for finite element analysis of thin shell structures’, in and (eds.), Mixed and Hybrid Finite Element Methods, ASME, New York, 1985, pp. 25-38.
[31] Simo, J. Appl. Mech. ASME 53 pp 51– (1986)
[32] ’Continuum-based shell elements’, Ph.D. Thesis, Stanford University, Palo Alto, 1986.
[33] Stolarski, ZAMM 61 pp 651– (1981)
[34] Stolarski, J. Appl. Mech. ASME 49 pp 172– (1982)
[35] Stolarski, Comp. Methods Appl. Mech. Eng. 41 pp 279– (1983)
[36] Stolarkski, Comp. Methods Appl. Mech. Eng. 58 pp 249– (1986)
[37] Verhegghe, Int.j. numer. methods eng. 23 pp 863– (1986)
[38] Wissman, Comp. Mech. 2 pp 289– (1987)
[39] Wong, Eng. Comp. 4 pp 229– (1987)
[40] Zienkiewicz, Int. j. numer. methods eng. 3 pp 275– (1971)
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