Modeling of Thin Plate Flexural Vibrations by Partition of Unity Finite Element Method

Tong Zhou, Jean Daniel Chazot, Emmanuel Perrey-Debain, Li Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

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 are 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.

Original languageEnglish
Article number2150030
JournalInternational Journal of Applied Mechanics
DOIs
Publication statusAccepted/In press - 2021

Keywords

  • Partition of unity finite element method
  • short wave modeling
  • thin plate flexural vibration
  • wave enriched element

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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