Modal analysis of elastic vibrations of incompressible materials using a pressure-stabilized finite element method


Codina R., TÜRK Ö.

FINITE ELEMENTS IN ANALYSIS AND DESIGN, vol.206, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 206
  • Publication Date: 2022
  • Doi Number: 10.1016/j.finel.2022.103760
  • Journal Name: FINITE ELEMENTS IN ANALYSIS AND DESIGN
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Modal analysis, Incompressible elastic waves, Eigenvalue problems, Stabilized finite element methods, LINEAR ELASTICITY, RECTANGULAR PLATE, LOCKING, APPROXIMATION, FORMULATION, DYNAMICS

Abstract

This paper describes a modal analysis technique to approximate the vibrations of incompressible elastic solids using a stabilized finite element method to approximate the associated eigenvalue problem. It is explained why residual based formulations are not appropriate in this case, and a formulation involving only the pressure gradient is employed. The effect of the stabilization term compared to a Galerkin approach is detailed, both in the derivation of the approximate formulation and in the error estimate provided.