Corotational formulation for nonlinear dynamics of beams with arbitrary thin-walled open cross-sections

• A nonlinear dynamic formulation for beams with arbitrary thin-walled cross-section.
• The corotational kinematic description is used to derive internal and inertia terms.
• The warping deformations and the eccentricity of the shear center are considered.
• Each node has 7 degrees of freedom; cubic interpolations are used in local system.
• The predictions of beam element are in good agreement with Abaqus 3D-solid analyzes.

A new consistent corotational formulation for nonlinear dynamics of beams with arbitrary thin-walled cross-section is presented. The novelty is that the warping deformations and the eccentricity of the shear center are fully taken into account. Therefore, additional terms are introduced in the expressions of the inertia force vector and the tangent dynamic matrix. Their contribution is then investigated considering several numerical examples. Besides, the element has seven degrees of freedom at each node and cubic shape functions are used to interpolate local transverse displacements and axial rotations. The formulation’s accuracy is assessed considering five examples with comparisons against 3D-solid solutions.