Abstract
Finite element method using SO(3), which is named special orthogonal group, is formulated by decomposing deformation gradient tensor into SO(3) and stretch tensor. Then, tangent stiffness' using four types of stress rates, which are Truesdell, Jaumann, Green and Linear stress rates, are obtained. Next, euler-buckling analyses and post-buckling analyses using beam elements of this formulation are made. As a result, the buckling loads of the beam element using Linear stress rate are perfectly the same as Timoshenko's theoretical solutions and the results of post-buckling analyses of the beam element using Linear stress rate are also perfectly the same as the solutions of elastica.
