Corotational Formulation for Geometric Nonlinear Analysis of Shell Structures by ANDES Elements

Abstract

The corotational (CR) kinematic description was a recent method for formulation of geometric nonlinear structural problems. Based on the consistent symmetrizable equilibrated (CSE) CR formulation, a linear triangular flat shell element with three translational and three rotational degrees of freedom (DOFs) at each of the three nodes was derived by the assumed natural deviatoric strain (ANDES) formulation, which can be used to the geometric nonlinear analysis of shell structures with large rotations and small strains. By taking variations of the internal energy with respect to nodal freedoms, the equations for the CR nonlinear finite element, including the tangent stiffness matrix and the internal force vector in the global coordinate system, were derived. The nonlinear equations were solved by using the generalized displacement control (GDC) method. It was shown through numerical examples that combing CR formulation and ANDES elements can accurately solve complex geometric nonlinear problems with large body motions. As revealed by the efficiency and reliability of the ANDES elements in tracing the nonlinear structural load–deflection response, it is demonstrated that some membrane elements and plate elements give better performance in the geometric nonlinear analysis of shell structures.