The simplest 3-, 6- and 8-noded fully-parameterized ANCF plate elements using only transverse slopes

Abstract

In this paper, the simplest kinematical models of triangular plate finite elements using the absolute nodal coordinate formulation (ANCF) are considered. The ANCF is the finite element approach for simulating large displacements and rotations, in which the nodal position vectors and their derivatives are described in the inertial frame only. This leads to linear kinematics of elements, constant mass matrix and simple expressions for inertia terms in the equations of motion. The elastic forces appear in the ANCF in highly nonlinear form due to using the Green-Lagrange strain tensor. This fact compels researchers to find possibilities of reducing the computational complexity in using the ANCF. One of the ways in this direction is to use simplest fully-parameterized plate elements employing transverse slopes only, without using longitudinal slopes.