Efficient co-rotational formulation for 3D composite beams with two-directional interlayer slip

In this paper, we present a novel 3D nonlinear formulation for two-layered composite beams that accounts for interlayer slip in both longitudinal and lateral directions. Warping effects are included in a simplified manner, assuming that the warping of each layer does not contribute to the stress resultants of each section, allowing the use of the classical St. Venant warping function to define the warping shape of each subsection. The second-order approximation of the Green–Lagrange strain tensor, combined with linear constitutive laws, is integrated into the principle of virtual work to derive the tangent stiffness matrix of the composite element and its corresponding internal force. To address membrane and slip locking issues, we propose a new averaging strain technique, complemented by quadratic interpolation functions for the axial displacement of the two layers. To account for large displacements and rotations, the co-rotational approach is adopted. The co-rotated local reference frame is constructed by connecting end nodes located at the shear center of the bottom layer of the composite beam. As a result, special treatments are employed to address eccentric forces applied to the top layer of the composite beam. Finally, the performance of the proposed formulation is evaluated using four representative examples.