Post-Buckling Analysis of Beams by Finite-Element Method.

Abstract

In the previous papers, the relationship between the stress rate and the tangent stiffness was derived using the special orthogonal group SO (3) in the finite element formulation. The stress rates used are the Truesdell stress rate, the Jaumann stress rate, the Neo-Green stress rate and the Ishihara stress rate. In that work, the stiffness elements of the tangent stiffnesses of beam elements with SO (3) were given. Those elements include material stiffness ΔδΠm, geometric stiffness of rigid rotation ΔδΠ, geometric stiffness of stretch to stress direction ΔδΠ, geometric stiffness of stretch perpendicular to area ΔδΠ and geometric stiffness of stretch to deformation rate ΔδΠ. In this paper, post-buckling analyses are made using the beam element of Ishihara stress rate. It is shown that the results are almost the same as the results of both 2-dimensional and 3-dimensional analyses of elastica, because the beam element has only geometric stiffness of rigid rotation as geometric stiffness and it can exactly show the nonlinearity of rigid rotation. It is also shown that the beam element without SO (3) can't be used for 3-dimensional large rotation analysis.