A PLATE ELEMENT WITH SECOND-ORDER ABSOLUTE NODAL COORDINATE SLOPES: NUMERICAL COMPUTATION OF SHAPE FUNCTIONS

摘要

In this paper, the procedure of construction of geometrical and structural matrices of plate finite elements employing absolute nodal coordinate formulation (ANCF) is studied. The kinematic and topological properties of an arbitrary plate finite element are described using universal digital code dncm that provides systematic enumeration of finite elements. This code is formed using the element's dimension d, the number of nodes it possesses n, the number of scalar coordinates per node c, and a multiplier describing the process of transforming a conventional finite element to an ANCF element m. The detailed generation of a new type of triangular plate finite element 2343 using numerical computation of shape functions is discussed in the paper. The new triangular element employs position vectors and slope vectors up to second order mixed-derivative slope vector. A detailed derivation of the equations of motion of the element is provided; the examples of numerical simulation and validation are presented. The features of creating the models and numerical methods as well as results obtained by applying both approaches are discussed in the paper.