Modeling of thin plate flexural vibrations by Partition of Unity Finite Element Method

TL;DR

This paper introduces a Partition of Unity Finite Element Method for modeling thin plate vibrations, enhancing accuracy and efficiency through specialized enrichment functions and polynomial strategies.

Contribution

It develops a novel PUFEM approach with cubic Hermite-type functions and enrichment strategies for improved thin plate vibration simulation.

Findings

High-order polynomials improve accuracy and convergence.

Hybrid wave-polynomial enrichments reduce degrees of freedom.

Numerical results outperform classical FEM in accuracy and efficiency.

Abstract

This paper presents a conforming thin plate bending element based on the Partition of Unity Finite Element Method (PUFEM), for the simulation of steady-state forced vibration. The issue of ensuring the continuity of displacement and slope between elements is addressed by the use of cubic Hermite-type Partition of Unity (PU) functions. With appropriate PU functions, the PUFEM allows the incorporation of the special enrichment functions into the finite elements to better cope with plate oscillations in a broad frequency band. The enrichment strategies consist of the sum of a power series up to a given order and a combination of progressive flexural wave solutions with polynomials. The applicability and the effectiveness of the PUFEM plate elements is first verified via the structural frequency response. Investigation is then carried out to analyze the role of polynomial enrichment orders and enriched plane wave distributions for achieving good computational performance in terms of accuracy and data reduction. Numerical results show that the PUFEM with high-order polynomials and hybrid wave-polynomial combinations can provide highly accurate prediction results by using reduced degrees of freedom and improved rate of convergence, as compared with the classical FEM.