Keywords: generalized displacement control method, geometric stiffness matrix,.

The derivation of an explicit geometric stiffness matrix of triangular flat plate element is presented in this study. It is derived based on the physical concepts of rigid body motions. The derived element has abilities to simulate physical properties when it undergoes rigid body motions. Then it is combined with linear stiffness matrices of triangular elements for in-plane effect by Cook [1] and plate bending effect by Batoz, Bathe and Ho [2] to form a tangent stiffness matrix of the flat plate element

The nonlinear incremental equations are solved iteratively by using an effective numerical method, the General Displacement Control (GDC) method, developed by Yang and Shieh [3]. At the same time a skill to trigger the post buckling behaviour of a cylindrical shell structure is also presented.

The cylindrical shell structure subjected uniformly compressive loads in the axial direction is show as Figure 34.1, and the analysis by using the derived element is presented in Figure 34.2.

It shows bifurcation and loops in the analysis. Although the bifurcation point is a little bit deviation from the theoretical value, the post-buckling behaviour compared with the studies done by Yamaki [4] is well enough to present one of the symmetric modes. Because the geometric nonlinear triangular flat plate element has geometric stiffness matrix shown in explicit expressions, it will make engineers appreciate in programming can be guaranteed.

1

R.D. Cook, "A plane hybird element with Rotional D.O.F. and Adjustable stiffenss," International Journal for Numerical Methods in Engineering, 24(8), 499-1508, 1987. doi:10.1002/nme.1620240807

2

J.G. Batoz, K.J. Bathe and L.W. Ho, "A study of three-node triangle plate bending elements," International Journal for Numerical Methods in Engineering., 15, 1771-1812, 1980. doi:10.1002/nme.1620151205

3

Y.B. Yang, and M.S. Shieh, "Solution method for nonlinear problems with multiple critical points," AIAA. Journal, 28(12), 2100-16, 1990. doi:10.2514/3.10529

4

N. Yamaki, "Elastic Stability of Circular Cylindrical Shells", Elsevier Science Publishers B.V., Amsterdam, Netherlands, 1984.

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