Non-Incremental Beam Finite Element for Fast Non-Linear analysis of 3D Systems

Many works deal with possible approaches to develop an efficient beam element for large displacement analysis of frame structures. In this work an original non linear FEM approach applied to elastic beams is presented. It is based on the use of rotations only as generalised coordinates. Euler-Rodrigues quaternion approach is used in the case of large displacements. A simplified non-linear theory is presented if the hypothesis of small displacements holds and therefore additive properties of rotations are still valid. Equilibrium equations are written in the deformed configuration, thus permitting a non-incremental approach to be applied. Some cases related to buckling are analyzed from a theoretical point of view and a numerical validation has been finally performed.