FINITE ELEMENTS IN ANALYSIS AND DESIGN, vol.206, 2022 (Peer-Reviewed Journal)
Article / Article
FINITE ELEMENTS IN ANALYSIS AND DESIGN
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Modal analysis, Incompressible elastic waves, Eigenvalue problems, Stabilized finite element methods, LINEAR ELASTICITY, RECTANGULAR PLATE, LOCKING, APPROXIMATION, FORMULATION, DYNAMICS
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.