Reduction of system matrices of plate in absolute nodal coordinate formulation by component mode synthesis method

Abstract

In this paper, we present a reduction method of the system matrix of a flexible thin plate element of 48 degrees of freedom, which is formulated on the basis of the absolute nodal coordinate method (ANCF) by use of the component mode synthesis method. We focus that the bending stiffness matrix expressed by the ANCF plate element is constant when the continuum mechanics approach is adopted and the in-plane strain is not so large. This feature allows applying the Craig-Bampton method to the equation of motion of the plate expressed by ANCF, and then it enable to reduce the dimension size of the system matrix of the plate. Three numerical examples that compare the presented method and the conventional ANCF plate are demonstrated to examine the performance and the accuracy of the presented method. From these examples, it is verified that the presented method can describe the large deformation and rotation effects as well as the conventional ANCF plate does. The use of the presented method is also verified to be able to reduce the computing time against the conventional ANCF plate. This feature is effective for carrying out numerical simulations for the structure composed of multiple plate elements when the number of elements increases.