A non-incremental finite element procedure for the analysis of large deformation of plates and shells in mechanical system applications

In this investigation, a non-incremental solution procedure for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to plate elements capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. Unlike other existing finite element formulations that lead to a highly nonlinear inertial forces for three-dimensional elements, the proposed formulation leads to a constant mass matrix, and as a result, the centrifugal and Coriolis inertia forces are identically equal to zero. Furthermore, the method relaxes some of the assumptions used in the classical and Mindlin plate models and automatically satisfies the objectivity requirements. By using a general continuum mechanics approach, a relatively simple expression for the elastic forces is obtained. Generalization of the formulation to the case of shell elements is discussed. As examples of the implementation of the proposed method, two different plate elements are presented; one plate element does not guarantee the continuity of the displacement gradients between the nodal points, while the other plate element guarantees this continuity. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotation and deformation analysis of plates and shells. The numerical results, which are compared with the results obtained using existing incremental procedures, show that the solution obtained using the proposed method satisfies the principle of work and energy. These results are obtained using explicit numerical integration method. Potential applications of the proposed method include high-speed metal forming, vehicle crashworthiness, rotor blades, and tires.