Advanced3-Node Co-rotational Triangular Shell Element

An advanced3-node co-rotational triangular shell element based on assumed strains method is proposed to solve large-displacement and large-rotation problems.The co-rotational framework is employed in evaluating the local nodal variables from the global ones to exclude the element rigid-body rotation, leading to a simple local element formulation. Geometric nonlinearity caused by the element rigid-body rotation is considered in computing the transformation matrix. The element tangent stiffness matrix in the local co-ordinate system is free of the overall element rigid-body motion, which extends any implementation of a small displacement/rotation element formulation to that of a large displacement/rotation one.The vectorial rotational variables are defined, and all nodal variables are additive. Due to the commutativity of all nodal variables in calculating the second derivative of the element strain energy with respect to nodal variables, symmetric tangent stiffness matrices are obtained in both the local and global coordinate systems, leading to computational efficiency and significant computer storage saving. The element tangent stiffness matrix is updated using the total values of the nodal variables in an incremental solution procedure, making it advantageous for solving dynamic problems.To overcome locking problems, the assumed strain method proposed by MacNeal is utilized. The assumed linear membrane strains and shear strains are obtained respectively by using the line integration approaches, which are then employed to replace the corresponding conforming strains in evaluating the internal force vector and the element tangent stiffness matrix.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, several shell structures undergoing large displacement and large rotation are solved to demonstrate the reliability, computational accuracy and efficiency of the present element formulation.