A Finite Element Analysis of Fluid-Structure Interaction With Nonlinear Structures

Abstract

The focus of this study is to evaluate flow-induced vibration in solid structures subjected to high deformation, in the elastic regime. For that, the Finite Element Analysis is a powerful numerical method that allows complex problems to be modelled through a discretization of the domain. First, mass and momentum equations are presented for both fluid and solid domains, along with their respective constitutive relations. The semi-Lagrangian(SL) technique, where unconditional stability is successfully achieved for the numerical solution in different geometries, is developed. For the solid domain, a two-dimensional approach was used with a quadratic triangular element mesh in a dynamic simulation. Since a nonlinear behavior is considered, the governing equation is linearized, and the numerical solution is achieved through an iterative process. As for the fluid domain, a second order spatial convergence is assured for velocity fields, as a quadratic + linear pair of triangular mesh elements is used, fulfilling the well-known LBB condition. Since the movement of the solid body in the fluid requires an adaptative technique to be employed in the mesh, avoiding greater distortion, the Arbitrary Lagrangian-Eulerian method, also known as ALE, was used. For code verification, different cases whose references are found in the literature were simulated for both fluid and solid problems. Since the solid body moves inside the fluid domain, an adaptive mesh is necessary to avoid distortions. The position can be determined for the ALE problem, considering the mesh velocity in the convective velocity. The velocity is then calculated by means of the interpolation of said variable's values in the points of the element that contains the fluid particle at time. Thus, the semi-Lagrangian method, combined with ALE, provides a stable solution for fluidstructure interaction problems, in which stresses and forces can be calculated for the solid body.