A new higher-order plate/shell element for dynamic analysis of flexible plate and shell with variable thickness

The flexible plate/shell with variable thickness has many advantages, such as reducing the structural weight, improving the load capacity, raising the overall material utilization ratio and optimizing the stress distribution, etc. The absolute nodal coordinate formulation (ANCF) method provides the possibility for the reasonable modeling of variable thickness plate/shell and the study of flexible large deformation mechanisms. However, the traditional modeling and analysis of variable thickness plate/shell mainly focused on the vibration characteristics based on lower-order ANCF plate/shell element, in which the linear interpolation is used in the transverse direction and there exists the locking problem. Given this, a new higher-order plate/shell element with quadratic interpolation in the transverse direction for dynamic analysis of flexible plate and shell with variable thickness denoted as ANCF-VT3833 is developed in this paper. This new element employs an algebraic function h ( x , y ), called the thickness function, to describe any thickness distribution of the plate/shell. With the use of the thickness function, it is convenient to consider changes in thickness in the calculation model of the element matrix. To verify the feasibility of the proposed new element, a flexible pendulum test was carried out. The results obtained by the new element are in good agreement with those obtained by the traditional finite element method. Furthermore, the dynamic simulation analysis of the uniform thickness, linearly and quadratic variable thickness plates is conducted to study the influence of thickness distribution on the deformation and stress of flexible plates. The results show that the thickness distribution significantly influences the dynamic response of flexible plates. Finally, it is concluded that the ANCF-VT3833 element proposed in this paper has advantages in predicting large deformation of the flexible plate and shell with variable thickness, and can be used to analyze the mechanical effects caused by thickness distribution, as well as to provide a theoretical basis for structural optimization and rational design of thickness distribution.