An intrinsic beam model based on a helicoidal approximation—Part II: Linearization and finite element implementation

The helicoidal beam model developed in the first part of this work is applied here to the development of a mixed finite element for space‐curved and twisted beams undergoing large displacements and finite rotations. Starting from the governing weak form expressed by the principle of virtual work, a consistent linearization is obtained in the following and a novel updated Lagrangian finite element implementation is thoroughly discussed. The unique features and the distinguishing properties previously claimed for the helicoidal model are shown here to imply remarkable numerical consequences. For this purpose, meaningful example problems regarding the non‐linear static response of beams are addressed in the following and the results are compared with those available from the literature. Furthermore, a finite element in time for the rigid body dynamic problem is developed within the framework of the helicoidal geometry. The underlying philosophy of this novel finite element for dynamics is the realization of the helicoidal decomposition of the rigid body motion within a time step.