Nonlinear Analysis of 3D Beams: A Comparative Study of Geometrically Exact and the Beam Elements in ABAQUS
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For several decades, the finite element method (FEM) has been widely used in nonlinear analysis of three-dimensional (3D) curved beam-like structural systems, subjected to large displacements and strains. Among the numerous approaches that have been proposed, the vast majority of them have been limited to describing the beam reference geometry as a straight line. In this thesis, the geometrically exact 3D beam element, expanded by Mathisen et al. to be able to model arbitrary shaped curved geometries, has been validated and compared with the beam elements available in ABAQUS. The thesis presents the theory of the Timoshenko beam element, as well as the shear locking phenomena and it s remedies. The theory of solving nonlinear static and dynamic equilibrium equations has also been described.