A 6-node Co-rotational Triangular Shell Element

An advanced 6-node co-rotational curved triangular shell element for large displacement and large rotation analysis is presented. Considering that the motion of an element can be divided into overall rigid-body motion and element deformation, while the former part has no contribution to the element strain energy, a co-rotational framework is employed to exclude the rigid-body part in calculating the element tangent stiffness matrix. Meanwhile, additive vectorial rotational variables are employed, which are defined as the two smallest components of the normal vector of the mid-surface at each node, and the internal force vector and the element tangent stiffness matrix are achieved by calculating the first derivative and the second derivative of the strain energy with respect to nodal variables, resulting symmetric element tangent stiffness both in the local and global system.In order to overcome locking phenomena, assumed membrane strains and shear strains are employed to replace the corresponding parts of the Green-Lagrange strains specialized for shallow curved shell problems, where the strategy used in the Discrete Strain Gap Method is adopted to calculate these assumed strains. In the incremental solution procedure, the Generalized Displacement Control Method and the displacement control method are employed respectively in tracing the buckling and post-buckling equilibrium path. Finally, 9 flat plate and curved shell problems are solved to test the reliability, computational efficiency and accuracy of the proposed element formulation.