Numerical simulation of fluid-structure interaction using the finite element method

Abstract

An algorithm to simulate 3D fluid–structure interaction problems using the finite element technique is presented in this work. A two-step Taylor–Galerkin scheme and linear tetrahedra elements are employed to analyze the fluid flow, which may be high or slightly compressible. An arbitrary Lagrangean–Eulerian (ALE) formulation is adopted, which must be compatible with the motion of the fluid–structure interface. A fractional method with velocity correction is used for incompressible fluids. The structure is analyzed using triangular elements with three nodes and six degrees of freedom in each node (three displacement components and three rotation components). Geometrically non-linear effects are included. The Newmark method is employed to integrate in time the dynamic equilibrium equations using an updated Lagrangean description. The algebraic system of equations is solved using the conjugated gradient method and an incremental-iterative scheme is used to solve the non-linear system resulting from finite displacements and rotations. The code is optimized to take advantages of vector processors. Some cases studies have been considered for validation of the computational algorithm. A two-dimensional supersonic flow over a clamped flat plate is analyzed in order to study the aeroelastic behavior of this plate. Vibrations due to wind action of an inflated membrane as well as vortex inducing vibrations in a panel immersed in a slightly compressible fluid are also studied.