Research of Flow-Induced Vibration of Flexible Plate Based on Fluid-Solid Interaction Method

2014 ◽  
Vol 945-949 ◽  
pp. 642-645
Author(s):  
Ren Qiang Xi ◽  
Xue Dong Jiang ◽  
Yun Song He
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Degrees Of Freedom ◽  
Data Transfer ◽  
Stokes Equations ◽  
Linear Equations ◽  
Solution Procedure ◽  
Element Formulation ◽  
Flexible Plate ◽  
Arbitrary Lagrangian Eulerian

This work is concerned with the modelling of the interaction of fluid flow with flexible solid structures. The fluid flow considered is governed by the incompressible Navier-Stokes equations and modelled with stabilised low order velocity-pressure finite elements. The governing equation of fluid movement is described by an arbitrary Lagrangian-Eulerian (ALE) strategy. The structure is represented by means of an appropriate standard finite element formulation. A simple data transfer strategy based on a finite element type interpolation of the interface degrees of freedom guarantees kinematic consistency and equilibrium of the stresses along the interface. The resulting strongly coupled set of non-linear equations is solved by means of a partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates the full linearization of the overall incremental problem.

Numerical Simulation of Glottal Flow in Interaction with Self Oscillating Vocal Folds: Comparison of Finite Element Approximation with a Simplified Model

2012 ◽  
Vol 12 (3) ◽  
pp. 789-806 ◽  
Author(s):  
P. Sváček ◽  
J. Horáček
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Finite Element Approximation ◽  
Vocal Folds ◽  
Multistep Method ◽  
Element Approximation ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Stabilized Finite Element Method

AbstractIn this paper the numerical method for solution of an aeroelastic model describing the interactions of air flow with vocal folds is described. The flow is modelled by the incompressible Navier-Stokes equations spatially discretized with the aid of the stabilized finite element method. The motion of the computational domain is treated with the aid of the Arbitrary Lagrangian Eulerian method. The structure dynamics is replaced by a mechanically equivalent system with the two degrees of freedom governed by a system of ordinary differential equations and discretized in time with the aid of an implicit multistep method and strongly coupled with the flow model. The influence of inlet/outlet boundary conditions is studied and the numerical analysis is performed and compared to the related results from literature.

Finite Element Simulation of a Gust Response of an Ultralight 2-DOF Airfoil

2014 ◽  
Author(s):  
Jaromír Horáček ◽  
Petr Sváček
Keyword(s):  
Finite Element ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Turbulent Viscosity ◽  
Equations Of Motion ◽  
Sudden Change ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian

Flexibly supported two-degrees of freedom (2-DOF) airfoil in two-dimensional (2D) incompressible viscous turbulent flow subjected to a gust (sudden change of flow conditions) is considered. The structure vibration is described by two nonlinear ordinary differential equations of motion for large vibration amplitudes. The flow is modeled by Reynolds averaged Navier-Stokes equations (RANS) and by k–ω turbulence model. The numerical simulation consists of the finite element (FE) solution of the RANS equations and the equations for the turbulent viscosity. This is coupled with the equations of motion for the airfoil by a strong coupling procedure. The time dependent computational domain and a moving grid are taken into account with the aid of the arbitrary Lagrangian-Eulerian formulation. In order to avoid spurious numerical oscillations, the SUPG and div-div stabilizations are applied. The solution of the ordinary differential equations is carried out by the Runge-Kutta method. The resulting nonlinear discrete algebraic systems are solved by the Oseen iterative process. The aeroelastic response to a sudden gust is numerically analyzed with the aid of the developed FE code. The gust responses exhibit similar oscillations as those found in literature.

Numerical Simulation of Airfoil Vibrations Induced by Turbulent Flow

2014 ◽  
Vol 17 (1) ◽  
pp. 146-188 ◽  
Author(s):  
Miloslav Feistauer ◽  
Jaromír Horáček ◽  
Petr Sváček
Keyword(s):  
Numerical Simulation ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Vertical Direction ◽  
Turbulence Models ◽  
Computational Domain ◽  
Arbitrary Lagrangian Eulerian ◽  
Element Discretization ◽  
Flow Equations

AbstractThe subject of the paper is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. The airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the finite element solution of the Reynolds averaged Navier-Stokes equations combined with Spalart-Allmaras or κ–ω turbulence models, coupled with a system of nonlinear ordinary differential equations describing the airfoil motion with consideration of large amplitudes. The time-dependent computational domain and approximation on a moving grid are treated by the Arbitrary Lagrangian-Eulerian formulation of the flow equations. Due to large values of the involved Reynolds numbers an application of a suitable stabilization of the finite element discretization is employed. The developed method is used for the computation of flow-induced oscillations of the airfoil near the flutter instability, when the displacements of the airfoil are large, up to ±40 degrees in rotation. The paper contains the comparison of the numerical results obtained by both turbulence models.

scholarly journals Self-updated four-node finite element using deep learning

2021 ◽  
Author(s):  
Jaeho Jung ◽  
Hyungmin Jun ◽  
Phill-Seung Lee
Keyword(s):  
Finite Element ◽  
Deep Learning ◽  
Iterative Solution ◽  
Solution Procedure ◽  
Element Formulation ◽  
Zero Energy ◽  
Energy Mode ◽  
Bending Modes ◽  
Solution Accuracy ◽  
Iterative Solution Procedure

AbstractThis paper introduces a new concept called self-updated finite element (SUFE). The finite element (FE) is activated through an iterative procedure to improve the solution accuracy without mesh refinement. A mode-based finite element formulation is devised for a four-node finite element and the assumed modal strain is employed for bending modes. A search procedure for optimal bending directions is implemented through deep learning for a given element deformation to minimize shear locking. The proposed element is called a self-updated four-node finite element, for which an iterative solution procedure is developed. The element passes the patch and zero-energy mode tests. As the number of iterations increases, the finite element solutions become more and more accurate, resulting in significantly accurate solutions with a few iterations. The SUFE concept is very effective, especially when the meshes are coarse and severely distorted. Its excellent performance is demonstrated through various numerical examples.

scholarly journals A Kollár and Pluzsik anisotropic composite beam theory for arbitrary multicelled cross sections

2016 ◽  
Vol 35 (23) ◽  
pp. 1696-1711 ◽  
Author(s):  
Danilo S Victorazzo ◽  
Andre De Jesus
Keyword(s):  
Finite Element ◽  
Cross Sections ◽  
Composite Beam ◽  
Linear Equations ◽  
Beam Theory ◽  
Element Formulation ◽  
Compliance Matrix ◽  
Asymmetric System ◽  
Anisotropic Composite ◽  
Stiffness Matrices

In this paper we extend Kollár and Pluzsik’s thin-walled anisotropic composite beam theory to include multiple cells with open branches and booms, and present a finite element formulation utilizing the stiffness matrix obtained from this theory. To recover the 4 × 4 compliance matrix of a beam containing N closed cells, we solve an asymmetric system of 2N + 4 linear equations four times with unitary section loads and extract influence coefficients from the calculated strains. Finally, we compare 4 × 4 stiffness matrices of a multicelled beam using this method against matrices obtained using the finite element method to demonstrate accuracy. Similarly to its originating theory, the effects of shear deformation and restrained warping are assumed negligible.

Sign in / Sign up

Export Citation Format

Share Document