Accurate geometric stiffness matrix formulation of beam finite element - Sulaeman, Erwin (IIUM Press, 2011)

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Alternate estimation of beam buckling load is presented in this Chapter. The standard procedure using a variational principle approach is usually utilized a cubic polynomial approach for the beam displacement shape such that the geometric stiffness matrix is a function of the geometric length of the element only. In the present work, the geometric stiffness matrix is developed as function geometric length and pre-assumed buckling load such that the accuracy of the buckling load can be improved by performing iteration. If the pre-assumed buckling load is set to zero, the present work will yield to the standard procedure. Therefore the present work offers a procedure to increase the accuracy of buckling estimation by performing iteration using the buckling load estimated by previous iteration as a good estimate for the pre-assumed buckling load.