The Flow of UCM and Oldroyd-B Fluids Past a Cylinder

2000 ◽  
Author(s):  
Manuel A. Alves ◽  
Fernando T. Pinho ◽  
Paulo J. Oliveira
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Resolution ◽  
Constitutive Equations ◽  
Numerical Procedure ◽  
Plane Flow ◽  
Dependent Variables ◽  
High Resolution Schemes ◽  
Structured Meshes ◽  
Volume Method

Abstract Accurate solutions are obtained with the numerical method of Oliveira et al (1998) for the inertialess plane flow around a confined cylinder. This numerical procedure is based on the finite-volume method in non-orthogonal block-structured meshes with a collocated arrangement of the dependent variables, and makes use of a special interpolation practice to avoid stress-velocity decoupling. Two high-resolution schemes are implemented to represent the convective terms in the constitutive equations for the upper converted Maxwell and Oldroyd-B fluids, and the resulting predictions of the drag coefficient on the cylinder are shown to be as accurate as existing finite-element method predictions based on the very accurate h-p refinement technique.

scholarly journals Influence of Retardation Time on Viscoelastic Behavior of Plane Beams Modeled by the Nonlinear Positional Formulation of the Finite Element Method

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Juliano dos Santos Becho ◽  
Marcelo Greco
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rheological Model ◽  
Iterative Process ◽  
Numerical Procedure ◽  
Viscoelastic Behavior ◽  
Retardation Time ◽  
The Finite Element Method ◽  
Divergence Problem ◽  
Element Method

A numerical procedure is presented to avoid the divergence problem during the iterative process in viscoelastic analyses. This problem is observed when the positional formulation of the finite element method is adopted in association with the finite difference method. To do this, the nonlinear positional formulation is presented considering plane frame elements with Bernoulli–Euler kinematics and viscoelastic behavior. The considered geometrical nonlinearity refers to the structural equilibrium analysis in the deformed position using the Newton–Raphson iterative method. However, the considered physical nonlinearity refers to the description of the viscoelastic behavior through the adoption of the stress-strain relation based on the Kelvin–Voigt rheological model. After the presentation of the formulation, a detailed analysis of the divergence problem in the iterative process is performed. Then, an original numerical procedure is presented to avoid the divergence problem based on the retardation time of the adopted rheological model and the penalization of the nodal position correction vector. Based on the developments and the obtained results, it is possible to conclude that the presented formulation is consistent and that the proposed procedure allows for obtaining the equilibrium positions for any time step value adopted without presenting divergence problems during the iterative process and without changing the analysis of the final results.

scholarly journals NURSE-2 DoF Device for Arm Motion Guidance: Kinematic, Dynamic, and FEM Analysis

2020 ◽  
Vol 10 (6) ◽  
pp. 2139
Author(s):  
Betsy D. M. Chaparro-Rico ◽  
Daniele Cafolla ◽  
Marco Ceccarelli ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Upper Limb ◽  
Numerical Procedure ◽  
Fem Analysis ◽  
Arm Movement ◽  
Assistive Device ◽  
Arm Motion ◽  
Element Method

Patients with neurological or orthopedic lesions require assistance during therapies with repetitive movements. NURSE (cassiNo-qUeretaro uppeR-limb aSsistive dEvice) is an arm movement aid device for both right- and left-upper limb. The device has a big workspace to conduct physical therapy or training on individuals including kids and elderly individuals, of any age and size. This paper describes the mechanism design of NURSE and presents a numerical procedure for testing the mechanism feasibility that includes a kinematic, dynamic, and FEM (Finite Element Method) analysis. The kinematic demonstrated that a big workspace is available in the device to reproduce therapeutic movements. The dynamic analysis shows that commercial motors for low power consumption can achieve the needed displacement, acceleration, speed, and torque. Finite Element Method showed that the mechanism can afford the upper limb weight with light-bars for a tiny design. This work has led to the construction of a NURSE prototype with a light structure of 2.6 kg fitting into a box of 35 × 45 × 30 cm. The latter facilitates portability as well as rehabilitation at home with a proper follow-up. The prototype presented a repeatability of ±1.3 cm that has been considered satisfactory for a device having components manufactured with 3D rapid prototyping technology.

Dynamic Response of Underwater Structures Subject to Impact Loads

2011 ◽  
Author(s):  
Lingyu Sun ◽  
Weiwei Chen ◽  
Xiaojie Wang ◽  
Ning Kang ◽  
Bin Xu ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Response ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Impact Loads ◽  
Main Body ◽  
Energy Absorber ◽  
Volume Method ◽  
Element Method

The present paper studied the dynamic response of an underwater system with its navigation plate rotated relative to the main body until it was blocked by an energy absorber. In this process, the relation between fluid-driving moment and speed of main body, as well as the relation between rotation angle of the plate and design parameters of absorber, was investigated through combined finite element method and finite volume method. Before the plate contacted with the energy absorber, it was modeled by linear elastic material, the movement process was solved by finite volume method with dynamic boundary. When the plate started to contact and crash with the absorber, it was modeled by elastic-plastic material, and the interaction of fluid-structure coupling was simulated by explicit finite element method in LSDYNA and finite volume method in FLUENT. The two-way data exchange on the interface between fluid and structure was carried out through equivalent force and moment on each patch of the interface. In addition, the simulation accuracy on large plastic deformation of absorber was verified through a group of drop hammer experiments. After the energy absorber was crushed to ultimate shape, the open angle of plate reached the maximum value and the plate kept relative static to the rigid body. The maximum structural stress and deformation, the opening time and angle of the plate were evaluated by numerical method. It is demonstrated that the proposed method can effectively predict the dynamic response of underwater system under impact loads, and both the absorption capability of the block and the speed of moving body affect the dynamic response history and structural safety.

A Maxwell's Second Equation Approach to the Finite Element Method Applied to Magnetic Field Determination

1987 ◽  
Vol 24 (3) ◽  
pp. 259-272 ◽  
Author(s):  
José Roberto Cardoso
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Undergraduate Students ◽  
Engineering Students ◽  
Numerical Procedure ◽  
The Finite Element Method ◽  
Cad Cam ◽  
New Formulation ◽  
The Galerkin Method ◽  
Element Method

The burst of modern computing systems like CAD/CAM has given rise to the use of the finite element method (FEM), which is, at present, the most used numerical procedure in the determination of fields in continuous media. Undergraduate students find difficulty in understanding the usual way of demonstrating FEM by variational analysis or the Galerkin method. This paper introduces a new formulation of FEM, based on a direct application of Maxwell's second equation, which can be easily understood by undergraduate engineering students.

Tolerance Induced Performance Variation of a High-Resolution Compliant Micro Stage

2007 ◽  
Author(s):  
Jhy-Cherng Tsai ◽  
Mandy Hsiao ◽  
Jau-Liang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
High Resolution ◽  
Natural Frequency ◽  
Sensitivity Analyses ◽  
Compliant Structure ◽  
Nano Scale ◽  
Leaf Springs ◽  
Performance Variation ◽  
Element Method

Micro stage employs compliant structure is crucial for precision machinery as it can achieve nano-scale resolution fine displacement by deformation. This paper investigates the variations of stiffness and natural frequency due to dimensional tolerances of such a compliant micro stage that is suspended by four leaf springs and rotates with respect to hinges. Performances of the stage are evaluated by finite element method for various dimensions to investigate the effects of dimensions. A series of sensitivity analyses are also performed to investigate how tolerances affect the performance of the stage. It shows that the stiffness and natural frequency of the stage are strongly affected by the dimensions of leaf springs and the hinges. That is, tolerances of these dimensions are crucial and must be well designed and strictly controlled. It further shows that performance variation due to tolerances are nonlinear but can be properly designed with this approach.

Numerical Solution of Multidimensional Compressible Flow by High Order Nodal Discontinuous Galerkin Method

2013 ◽  
Vol 392 ◽  
pp. 100-104 ◽  
Author(s):  
Fareed Ahmed ◽  
Faheem Ahmed ◽  
Yong Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Discontinuous Galerkin ◽  
Finite Volume ◽  
High Order ◽  
Numerical Predictions ◽  
Volume Method ◽  
Element Method

In this paper we present a robust, high order method for numerical solution of multidimensional compressible inviscid flow equations. Our scheme is based on Nodal Discontinuous Galerkin Finite Element Method (NDG-FEM). This method utilizes the favorable features of Finite Volume Method (FVM) and Finite Element Method (FEM). In this method, space discretization is carried out by finite element discontinuous approximations. The resulting semi discrete differential equations were solved using explicit Runge-Kutta (ERK) method. In order to compute fluxes at element interfaces, we have used Roe Approximate scheme. In this article, we demonstrate the use of exponential filter to remove Gibbs oscillations near the shock waves. Numerical predictions for two dimensional compressible fluid flows are presented here. The solution was obtained with overall order of accuracy of 3. The numerical results obtained are compared with experimental and finite volume method results.

A MODIFIED TRIANGULATION ALGORITHM TAILORED FOR THE SMOOTHED FINITE ELEMENT METHOD (S-FEM)

2013 ◽  
Vol 11 (01) ◽  
pp. 1350069 ◽  
Author(s):  
Y. LI ◽  
M. LI ◽  
G. R. LIU
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Advancing Front ◽  
Stiffness Matrices ◽  
Smoothed Finite Element Method ◽  
Complicated Geometry ◽  
Discrete Domains ◽  
Volume Method ◽  
Element Method

Meshing is one of the key tasks in using the finite element method (FEM), the smoothed finite element method (S-FEM), finite volume method (FVM), and many other discrete numerical methods. Linear triangular (T3) mesh is one of the most widely used mesh, because it can be generated and refined automatically for discrete domains of complicated geometry, and hence save significantly the time for model creation. This paper presents a modified triangulation algorithm based on the advancing front technique to provide a comprehensive linear triangular mesh generator with six connectivity lists, including element–node (Ele–N) connectivity, element–edge (Ele–Eg) connectivity, edge–node (Eg–N) connectivity, edge–element (Eg–Ele) connectivity, node–edge (N–Eg) connectivity and node–element (N–Ele) connectivity. These six connectivity lists are generated along the way when the T3 elements are created, and hence it is done in a most efficient fashion. The connectivity is recorded in the usual counter-clockwise convention for convenient utilization in various S-FEM models for effective analyses. In addition, an algorithm is developed for renumbering the nodes in the T3 mesh to obtain a minimized bandwidth of stiffness matrices for both FEM and S-FEM models.

Research and Development of the Porthole-Die Aluminium Alloy Extrusion Processes

2012 ◽  
Vol 472-475 ◽  
pp. 214-218
Author(s):  
Shu Mei Lou ◽  
Lin Jing Xiao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Research And Development ◽  
Aluminium Alloy ◽  
Simulation Method ◽  
Empirical Method ◽  
Arbitrary Lagrangian Eulerian ◽  
Porthole Die ◽  
Lagrangian Finite Element ◽  
Volume Method

The current research on the porthole-die aluminium alloy extrusion is presented here. The empirical method and simulation method are analyzed. Particularly, the Lagrangian Finite Element Method(FEM), Eulerian Finite Volume Method(FVM) and Arbitrary-Lagrangian Eulerian(ALE) algorithm are compared. The development of the porthole-die aluminium is educed.

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