A Beam Finite Element for Static and Dynamic Analysis of Composite and Stiffened Structures with Bending-Torsion Coupling

This research presents a new beam finite element capable of predicting static and dynamic behavior of beam structures with bending-torsion coupling. The model here derived establishes a relation between the bending and torsional nodal degree of freedom of a two node beam element. The equilibrium equations are derived neglecting the non-linear terms while the stiffness and mass matrices are derived with Galerkin's method. The shape functions are obtained considering Timoshenko's hypothesis and the torsional moment constant along the element. The model has been validated through numerical and experimental results for static and dynamic simulation. The comparison revealed a relative difference mostly lower than 5% for static deformations and natural frequency prediction, while the Modal Assurance Criterion (MAC) confirmed the consistency with numerical and experimental results in terms of mode shape similarity.

Automated summary

This research introduces a new beam finite element model that can predict the static and dynamic behavior of beam structures with bending-torsion coupling. The derived model establishes a relation between the bending and torsional nodal degree of freedom of a two node beam element. The equilibrium equations are derived neglecting non-linear terms, while the stiffness and mass matrices are derived using Galerkin's method. The model has been validated through numerical and experimental results, showing good agreement for static deformations, natural frequency prediction, and mode shape similarity.