A Finite Element Analysis of Flow-induced Vibration in Nonlinear Elastic Structures

Abstract

This study investigates 2D flow-induced vibrations in solid structures undergoing large elastic deformations. Finite Element Analysis provides a robust numerical framework capable of accurately modeling such complex, coupled fluid-structure problems. The governing mass and momentum equations are formulated for both fluid and solid domains, accompanied by their respective constitutive laws. A semi-Lagrangian (SL) scheme is adopted to ensure unconditional numerical stability. In the solid domain, a quadratic triangular mesh is employed within a dynamic simulation, with the governing equations suitably linearized for the finite element discretization. In the fluid domain, second-order spatial accuracy for the velocity field is achieved through P2-P1 triangular elements, which satisfy the classical LBB stability condition. Due to strong mesh deformation caused by the solid motion in the surrounding fluid, an adaptive strategy is required to prevent excessive distortion. For this purpose, the Arbitrary Lagrangian-Eulerian (ALE) method is implemented assuring a sharp interface transition across the fluid-structure domain.