A New ANCF/CRBF Fully Parameterized Plate Finite Element

Abstract

In this paper, the consistent rotation-based formulation (CRBF) is used to develop a new fully parametrized plate finite element (FE) based on the kinematic description of the absolute nodal coordinate formulation (ANCF). The ANCF/CRBF plate element has a general geometric description which is consistent with the basic principles of continuum mechanics, defines a unique rotation field, ensures the continuity of the rotation and strains at the element nodes, can describe an arbitrarily large displacement, and is consistent with computational geometry methods allowing for correctly describing complex shapes as demonstrated in this paper. The proposed ANCF/CRBF finite element does not suffer from the serious and fundamental problems encountered when using other large rotation vector formulations (LRVF) including the coordinate redundancy and violation of the principle of non-commutativity of the finite rotations which cannot be treated as vectors. The proposed bi-cubic ANCF/CRBF plate element employs, as nodal coordinates, three position coordinates and three finite rotation parameters. This element is obtained from a fully parameterized ANCF plate element by writing the position vector gradients of the ANCF plate element in terms of three finite rotation parameters using a nonlinear velocity transformation that systematically reduces the number of the element coordinates. The resulting element captures stretch, bending, and twist deformation modes and it allows for systematically describing complex curved geometry. Because of the lower dimensionality of the resulting ANCF/CRBF plate element, it does not capture complex deformation modes that can be captured using the more general ANCF finite elements. Furthermore, the ANCF/CRBF element mass matrix is not constant, leading to nonlinear Coriolis and centrifugal inertia forces. The new element is validated by examining its performance using several examples that include pendulum plate, free falling plate, and tire models. The results obtained using this new element are compared with the results obtained using the bi-cubic fully parameterized ANCF plate element, the bi-linear shell element, and the conventional solid element implemented in the commercial software ANSYS.