11. Slit Open Annular Plate

This test case was proposed by Basar and Ding[19] and is also reported by Buechter and Ramm[20] and by Rebel[21]. It features an annular plate in the xy-plane with a slit, with one side of the slit clamped and the other side subjected to a line load p in the z-direction.

Test case definition

Figure 43. Test case definition


A nonlinear analysis is performed with the following case definition:

cases
  case 1
    analysis              nonlinear
    ebc                   1
    nbc                   1
    max_newton_iterations 50 
    newton_method         conventional
    max_step              500
    step_size_min         0.001
    step_size_init        0.01
  end
end

Figure 44 displays the z-displacements at points A, B, and C plotted against the applied load for a 32x4 mesh of Q4.S.MITC.E4 elements and the final deformed configuration at the maximum load p = 6.

Tip z displacement vs load factor for a 32x4 mesh of Q4.S.MITC.E4 elements and final deformed configuration.

Figure 44. Tip z displacement vs load factor for a 32x4 mesh of Q4.S.MITC.E4 elements and final deformed configuration.




[19] Y. Basar, Y.Ding; Finite-rotation shell elements for the analysis of finite-rotation shell problems; International Journal for Numerical Methods in Engineering, Vol. 34, pp. 165-169, 1992.

[20] N. Buechter and E. Ramm; Shell theory versus degeneration — a comparison in large rotation finite element analysis; International Journal for Numerical Methods in Engineering, Vol. 34, pp. 39–59, 1992.

[21] G. Rebel; Finite rotation shell theory including drill rotations and its finite element implementation; PhD thesis, Delft University Press, 1998.