A 3-Node Co-Rotational Triangular Finite Element for Non-Smooth, Folded and Multi-Shell Laminated Composite Structures

Based on the first-order shear deformation theory, a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth, folded and multi-shell laminated composite structures. The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system. In the global coordinate system, two smaller components of one vector, together with the smallest or second smallest component of another vector, of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables, whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell (away from non-smooth intersections) are defined as rotational variables. All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure, and thus improve the computational efficiency in the nonlinear solution of these composite shell structures. Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables, and the second derivatives of the strain energy functional with respect to local nodal variables, symmetric tangent stiffness matrices in local and global coordinate systems are obtained. To overcome shear locking, the assumed transverse shear strains obtained from the line-integration approach are employed. The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests, several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.