A computational framework for fluid–rigid body interaction: Finite element formulation and applications

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.

A computational framework for free surface fluid flows accounting for surface tension

Computational fluid dynamics (CFD) is increasingly becoming the tool of choice for researchers and engineers facing complex fluid flow problems. One area of CFD that has attracted significant attention in recent years is the development of meshless or mesh-free methods[1]. These methods have so far been used in many applications like fracture mechanics, astrophysics and fluid flow. The key advantage of meshless methods over mesh-based methods like finite volume (FV) and finite element (FE) methods is its non-requirement of pre-specified connectivity between nodes in order to derive approximation and interpolation. This leads to the ability of finite difference (FD) methods to treat irregular domains and boundaries. A direct result of this is another advantage of mesh-free methods having the adaptability for problems involving large movement or wholesale motion of boundaries or embedded bodies. In this area, it has the edge over composite or overset grid methods in being able to use only one coordinate frame.A convecting meshless scheme for boundary driven fluid flow is described. This scheme can be applied to self-propulsion problems, or, in general, flows involving motion of rigid or deformable bodies embedded within the flow.The generalized finite difference method[2] (GFD) was chosen this scheme. A meshless cloud of nodes is embedded around the body surface along with the structured Cartesian background nodes for the entire flow field. By incorporating a subdomain for each node and its neighbours, the use of Taylor series expansion enables the derivatives to be found. Two forms of incompressible momentum equations are used: the standard Eulerian form in primitive variables for the structured nodes and the Arbitrary Lagrangian-Eulerian (ALE) form for the meshless cloud of nodes. GFD with moving least squares approximation is used for spatial discretization of the convecting meshless nodes. The projection method with Crank-Nicolson discretization is used to achieve second order accurate time discretization. Following prescribed body motion or fluid structure interaction, the meshless cloud acquire new locations in the next time step and the momentum equations in ALE form can then be solved.Test cases were performed to verify code usability and method accuracy and convergence. The simulation of the decaying vortex has been a popular benchmark for the gauging of accuracy. Basically the exact solutions of the time-dependent function values are known and both residues and absolute errors were calculated. Solving using different grid sizes proved the present method to be of second order spatial accuracy. The meshless method was then tried on the driven cavity flow at Reynolds number 1000. The results were well-compared with popular benchmark results[4]. In considering the effects of implementing the convecting meshless nodes across a normal flow field, the decaying vortex was again simulated, with a moving patch of nodes within the Cartesian field. The residues were well controlled and the errors were not significantly increased. Finally, a couple of external flows cases were simulated, basically on a flow past a stationary bluff body and a flapping ellipse inside an enclosed body of fluid.Future works in the pipeline include writing a parallel code for larger scale simulation and simulating oscillating cylinders and flapping of elliptic aerofoil(s).

We are interested in the numerical solution of a two-dimensional fluid-structure interaction problem.A special attention is paid to the choice of physically relevant inlet boundary conditions for the case of channel closing.Three types of the inlet boundary conditions are considered.Beside the classical Dirichlet and the do-nothing boundary conditions also a generalized boundary condition motivated by the penalization prescription of the Dirichlet boundary condition is applied.The fluid flow is described by the incompressible Navier-Stokes equations in the arbitrary Lagrangian-Eulerian (ALE) form and the elastic body creating a part of the channel wall is modelled with the aid of linear elasticity.Both models are coupled with the boundary conditions prescribed at the common interface.The elastic and the fluid flow problems are approximated by the finite element method.The detailed derivation of the weak formulation including the boundary conditions is presented.The pseudo-elastic approach for construction of the ALE mapping is used.Results of numerical simulations for three considered inlet boundary conditions are compared.The flutter velocity is determined for a specific model problem and it is shown that the boundary condition with the penalization approach is suitable for the case of the fluid flow in a channel with vibrating walls.

Lock-in and drag amplification phenomena are studied for a flexible cantilever using a simplified fluid-structure interaction approach. Instead of solving the 3D domain, a simplified setup is devised, in which 2D flow problems are solved on a number of planes parallel to the wind direction and transversal to the structure. On such planes, the incompressible Navier-Stokes equations are solved to estimate the fluid action at different positions of the line-like structure. The fluid flow on each plane is coupled with the structural deformation at the corresponding position, affecting the dynamic behaviour of the system. An Arbitrary Lagrangian-Eulerian (ALE) approach is used to take in account the deformation of the domain, and a fractional-step scheme is used to solve the fluid field. The stabilization of incompressibility and convection is achieved through orthogonal quasi-static subscales, an approach that is believed to provide a first step towards turbulence modelling. In order to model the structural problem, a special one-dimensional element for thin walled cross-section beam is implemented. The standard second-order Bossak method is used for the time integration of the structural problem.

The contribution deals with the numerical simulation of the flutter of an airfoil with three degrees of freedom (3-DOF) for rotation around an elastic axis, oscillation in the vertical direction and rotation of a flap. The finite element (FE) solution of two-dimensional (2-D) incompressible Navier-Stokes equations is coupled with a system of nonlinear ordinary differential equations describing the airfoil vibrations with large amplitudes taking into account the nonlinear mass matrix. The time-dependent computational domain and a moving grid are treated by the Arbitrary Lagrangian-Eulerian (ALE) method and a suitable stabilization of the FE discretization is applied. The developed method was successfully tested by the classical flutter computation of the critical flutter velocity using NASTRAN program considering the linear model of vibrations and the double-lattice aerodynamic theory. The method was applied to the numerical simulations of the post flutter regime in time domain showing Limit Cycle Oscillations (LCO) due to nonlinearities of the flow model and vibrations with large amplitudes. Numerical experiments were performed for the airfoil NACA 0012 respecting the effect of the air space between the flap and the main airfoil.

Arbitrary lagrangian-eulerian petrov-galerkin finite elements for nonlinear continua

Abstract. Material Extrusion (MEX) and by extension Fused Deposition Modeling (FDM) is a popular Additive Manufacturing (AM) process used to fabricate complex parts. FDM as of recent is no longer solely utilized for prototyping parts but also used for producing functional components in industrial and research applications. The investigation of material properties of these FDM parts by experimental means is a time-consuming task. Therefore, the use of numerical simulation methods is highly required. Since 1993, various Finite Element Analysis (FEA) models are found in literature attempting to effectively simulate FDM parts utilizing many formulations, each with their pros and cons. The present study aims to compare Lagrangian and Arbitrary Lagrangian-Eulerian (ALE) finite element formulations in simulating tensile loading for FDM parts. The efficiency and precision of the aforementioned methods is evaluated in the numerical simulation of the tensile loading of an ASTM D638 standard geometry ABS specimen utilizing both ABAQUS/Explicit and ABAQUS/Standard. Utilizing a paper from the literature for experimental validation, this study additionally provides insight into explicit and implicit models’ computational efficiency, focusing on the advantages of explicit models for this application. The effects of mesh element type and size on results are also studied for each method. Based on these results, some useful guidelines for selecting the most suitable model of tensile loaded FDM parts are presented.

Thanks to their properties of superelasticity and shape memory effects, SMA wires are often considered for the design of damping devices or actuators coupled to pulleys. In order to dimension such devices for commercialization, it is necessary to develop reliable, robust and fast numerical tools. To this end, simplifying the management of the wire/pulley contact using an Arbitrary Lagrangian–Eulerian (ALE) formulation is an original and effective solution. In this work, the wires are modeled by three-dimensional truss thermo-mechanical finite elements associated with a superelastic law. For each node, the curvilinear abscissa is used as an additional degree of freedom in order to deal with material flow from one element to another. After presenting the ALE formalism and the necessary precautions (advection of variables), as well as the material behavior and thermo-mechanical contact laws at the pulleys, elementary validation tests are studied. Finally, two devices taken from the literature are modeled using the ALE formalism. The results obtained demonstrate the relevance and effectiveness of the approach adopted, as well as the importance of not neglecting friction at the pulleys and thermal effects on the material mechanical response.

Reflection on ‘finite rotation problem’ in plate and shell theories and in finite element formulation – Back to basics

Numerical treatment of frictional contact in ALE formulation for disc brake assemblies

This paper is devoted to the analysis of frictional contact problems with large deformations and displacements between hyper-elastic body and rigid body. The material nonlinearity and contact nonlinearity are separated and, the geometrically nonlinear behavior is described by the total Lagrange formulation. The Coulomb friction law is employed to simulate the friction between rigid vessel and rubber by the use of augmented Lagrange approach with node-to-segment formulation. A formulation of finite element is taken in this paper to describe the frictional contact problem, which is solved by the Newton-Raphson iterative procedure. It is shown that the augmented Lagrange technique significantly avoids locking and over-constraining and provides optimal convergence rate. Finally, the numerical results show that the accuracy and efficiency of augmented Lagrange approach in modeling large deformation frictional contact problem.

An improved ALE and CBS-based finite element algorithm for analyzing flows around forced oscillating bodies

<div class="htmlview paragraph">In this paper methods for the nonlinear dynamic analysis of multibody vehicle systems are presented. A total Lagrangian finite element formulation for deformable bodies of the vehicle systems that undergo large translational and rotational displacements is developed. A set of nonlinear dynamic differential equations are developed in a closed form for each finite element in terms of the reference as well as the nodal elstic coordinates and their time derivatives. These equations are expressed in terms of a set of element invariants that depend on the assumed displacement field. The invariants of the deformable body that undergoes large reference translational and rotational displacements can be obtained by assembling the invariants of its elements using a standard finite element procedure. The nonlinear dynamic equations of the deformable body can then be obtained by assembling the nonlinear element equations. Both the consistent and lumped mass finite element formulations are discussed. The dynamic formulations presented in this paper are exemplified using multibody vehicle systems that consist of interconnected rigid and deformable bodies. Numerical results are obtained using the general purpose computer program <b>DAMS</b> (Dynamic Analysis of Multibody Systems).</div>

An arbitrary Lagrangian–Eulerian finite element formulation for a poroelasticity problem stemming from mixture theory