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, cilt.206, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 206
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1016/j.finel.2022.103760
  • Dergi Adı: FINITE ELEMENTS IN ANALYSIS AND DESIGN
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Modal analysis, Incompressible elastic waves, Eigenvalue problems, Stabilized finite element methods, LINEAR ELASTICITY, RECTANGULAR PLATE, LOCKING, APPROXIMATION, FORMULATION, DYNAMICS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

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.