Natural element hierarchical models for static and free vibration analysis of cylindrical panels

Most of studies on the hierarchical models were restricted to beam- and plate-like structures using the finite element method. In this context, this study intends to present the hierarchical models for cylindrical panels and investigate their characteristics using 2-D natural element method (NEM). The displacement field of cylindrical panel is decomposed into the triple-vectored in-plane functions and the assumed thickness polynomials, and the hierarchical models are defined by sequentially increasing the maximum orders of thickness polynomials from (1,1,0). The triple-vectored in-plane functions are approximated by applying 2-D NEM to the unfolded rectangular plane of curved mid-surface of cylindrical panels, for which the stiffness matrices corresponding to the membrane and transverse strains and stresses are calculated using the selectively reduced integration technique to avoid shear-membrane locking. The hierarchical models are demonstrated and validated from the comparative numerical experiments of bending and free vibration of cylindrical panels. The present hierarchical models provide the central deflections and the natural frequencies which are in good agreement with the reference solutions. In addition, the characteristics of hierarchical models such as the limit property and the modeling and approximation errors are investigated with respect to the model level and the width-thickness ratio and the grid density. It is found that the hierarchical models show the locking-free robust and spectral variation in the central deflection and natural frequencies.

Automated summary

This study presents hierarchical models for cylindrical panels using the 2-D natural element method, and validates their performance in bending and free vibration through numerical experiments. The hierarchical models are able to accurately predict the central deflections and natural frequencies of the panels.