A New6-node Co-rotational Triangular Composite Shell Element

In modeling of laminated composite plate and shell structures, a6-node co-rotational curved triangular composite shell element based on first-order shear deformation theory is proposed.Using a co-rotational framework, the element rigid-body rotation is excluded in calculating the local nodal variables from the global nodal variables, leading to a simple local element formulation. Geometric nonlinearity induced by the large element rigid-body motion is incorporated in the transformation matrix relating the local and global internal force vectors/tangent stiffness matrix. Since the transformation matrix is independent of the assumptions made for the local element, thus many existing simple elements with high performance can be reused as the core of a co-rotational element formulation, and the resulting formulation can be employed to solve large displacement and large rotation problems.Different from other existing co-rotational element formulations:1) Additive vectorial rotational variables are employed in the present element, thus updating nodal rotational variables is quite simple in a nonlinear incremental solution procedure;2) Symmetric tangent stiffness matrices are achieved in both the local and global coordinate systems owing to the commutativity of the nodal variables in calculating the second derivatives of strain energy with respect to the local nodal variables and, through chain differentiation, with respect to the global nodal variables.Because there exist no Barlow points in a six-node curved triangular shell element, thus no set of integration points that provide zero membrane strain for all cases of pure bending about axes parallel to each of the three edges of the curved triangular element, which makes it difficult to overcome membrane and shear locking problems. A mixed formulation procedure is employed to overcome membrane and shear locking problems.In the incremental solution procedure, the generalized displacement control method and the displacement control method are employed respectively in tracing nonlinear equilibrium path. Several classic examples are solved, and the results are compared with those from other literatures, the proposed element formulation demonstrates its reliability and computational efficiency.