Three-Dimensional Frames subject to Large Rotations

The paper describes a technique to compute the quasi-static deformation of elastic three-dimensional frames under large rotations. The aim of of this implementation is the generalization to 3D of a similar 2D project, which is used to compute the ultimate load capacity of slender frames made of high-strength reinforced concrete, taking into account the inter-action between internal forces and deformation [1]. The description of the deformed geometry is fully Lagrangian. The displacement method with a classical Newton-Raphson algorithm is used for the computation of the equilibrium configurations. Arbitrary large rotations and displacements are considered. The deformations are, however, considered as small. A bar finite element, necessary for the case of non-linear material behaviour, is presented. Partial use of numerical derivatives is made in order to compute the tangential structural stiffness matrix. In the present contribution the treatment of the non-vectorial finite rotations by means of quaternions is emphasized. Illustrative examples are presented.