Generalization of plate finite elements for absolute nodal coordinate formulation

We propose a way to generate new finite elements in the absolute nodal coordinate formulation (ANCF) and use a generalization of displacement fields and degrees of freedom (d.o.f.) of ordinary finite elements used in structural mechanics. Application of this approach to 16- and 12-d.o.f. rectangle plate elements as well as to 9-d.o.f. triangle element gives, accordingly, 48-, 36- and 27-d.o.f. ANCF plate elements. We perform a thorough study of a 48-d.o.f. Hermitian element. Its shape function set is a Cartesian product of sets of one-dimensional shape functions for beam elements. Arguments of the shape functions are decoupled, that is why an explicit calculation of terms of equations of motion leads to single integration only. We develop several models of elastic forces of different complexity with their Jacobian matrices. Convergence and accuracy of the finite element is demonstrated in geometrically nonlinear static and dynamic test problems, as well as in linear analysis of natural frequencies.