On the stability and accuracy of fully coupled finite element techniques used to simulate the flow of differential viscoelastic fluids: A one‐dimensional model

1992 ◽  
Vol 36 (7) ◽  
pp. 1325-1348 ◽  
Author(s):  
Vincent Legat ◽  
Jean‐Marie Marchal
Keyword(s):  
Finite Element ◽  
Viscoelastic Fluids ◽  
Dimensional Model ◽  
One Dimensional ◽  
The Stability ◽  
Stability And Accuracy ◽  
Fully Coupled

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

Effective Shear Area in One Dimensional Ship Hull Finite Element Models to Predict Natural Frequencies of Vibration

2013 ◽  
Author(s):  
Osvaldo Pinheiro de Souza e Silva ◽  
Severino Fonseca da Silva Neto ◽  
Ilson Paranhos Pasqualino ◽  
Antonio Carlos Ramos Troyman
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Experimental Tests ◽  
Numerical Results ◽  
Computational Method ◽  
Scale Model ◽  
Dimensional Model ◽  
One Dimensional ◽  
Shear Area

This work discusses procedures used to determine effective shear area of ship sections. Five types of ships have been studied. Initially, the vertical natural frequencies of an acrylic scale model 3m in length in a laboratory at university are obtained from experimental tests and from a three dimensional numerical model, and are compared to those calculated from a one dimensional model which the effective shear area was calculated by a practical computational method based on thin-walled section Shear Flow Theory. The second studied ship was a ship employed in midshipmen training. Two models were made to complement some studies and vibration measurements made for those ships in the end of 1980 decade when some vibration problems in them were solved as a result of that effort. Comparisons were made between natural frequencies obtained experimentally, numerically from a three dimensional finite element model and from a one dimensional model in which effective shear area is considered. The third and fourth were, respectively, a tanker ship and an AHTS (Anchor Handling Tug Supply) boat, both with comparison between three and one dimensional models results out of water. Experimental tests had been performed in these two ships and their results were used in other comparison made after the inclusion of another important effect that acts simultaneously: the added mass. Finally, natural frequencies experimental and numerical results of a barge are presented. The natural frequencies numerical results of vertical hull vibration obtained from these approximations of effective shear areas for the five ships are finally discussed.

Stability Considerations in Thermoelastic Contact

1980 ◽  
Vol 47 (4) ◽  
pp. 871-874 ◽  
Author(s):  
J. R. Barber ◽  
J. Dundurs ◽  
M. Comninou
Keyword(s):  
Steady State ◽  
Perturbation Method ◽  
Energy Function ◽  
First Principles ◽  
Dimensional Model ◽  
Contact Conditions ◽  
One Dimensional ◽  
Thermoelastic Contact ◽  
The Stability ◽  
Steady State Solutions

A simple one-dimensional model is described in which thermoelastic contact conditions give rise to nonuniqueness of solution. The stability of the various steady-state solutions discovered is investigated using a perturbation method. The results can be expressed in terms of the minimization of a certain energy function, but the authors have so far been unable to justify the use of such a function from first principles in view of the nonconservative nature of the system.

One-dimensional model for the Rijke tube

1989 ◽  
Vol 202 ◽  
pp. 83-96 ◽  
Author(s):  
C. Nicoli ◽  
P. Pelcé
Keyword(s):  
Heat Transfer ◽  
Transfer Function ◽  
Dimensional Model ◽  
Unsteady Heat Transfer ◽  
Order Unity ◽  
Rijke Tube ◽  
Thermoacoustic Instability ◽  
One Dimensional ◽  
The Stability ◽  
Stability Limits

We develop a simple model in which longitudinal, compressible, unsteady heat transfer between heater and gas is computed in the small-Mach-number limit. This calculation is used to determine the transfer function of the heater, which plays an important role in the stability limits of the thermoacoustic instability of the Rijke tube. The transfer function is determined analytically in the limit of small expansion parameter γ, and numerically for γ of order unity. In the case ρμ/cp = constant, an analytical solution can be found.

scholarly journals A one-dimensional tearing mode equation for pedestal stability studies in tokamaks

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
J. W. Connor ◽  
R. J. Hastie ◽  
C. Marchetto ◽  
C. M. Roach
Keyword(s):  
Cross Section ◽  
Approximate Equation ◽  
Stability Studies ◽  
Dimensional Model ◽  
Tearing Mode ◽  
One Dimensional ◽  
Tearing Modes ◽  
The Stability ◽  
Poloidal Flux

Starting from expressions in Connor et al. (Phys. Fluids, vol. 31, 1988, p. 577), we derive a one-dimensional tearing equation similar to the approximate equation obtained by Hegna & Callen (Phys. Plasmas, vol. 1, 1994, p. 2308) and Nishimura et al. (Phys. Plasmas, vol. 5, 1998, p. 4292), but for more realistic toroidal equilibria. The intention is to use this approximation to explore the role of steep profiles, bootstrap currents and strong shaping in the vicinity of a separatrix, on the stability of tearing modes which are resonant in the H-mode pedestal region of finite aspect ratio, shaped cross-section tokamaks, e.g. the Joint European Torus (JET). We discuss how this one-dimensional model for tearing modes, which assumes a single poloidal harmonic for the perturbed poloidal flux, compares with a model that includes poloidal coupling Fitzpatrick et al. (Nucl. Fusion, vol. 33, 1993, p. 1533).

scholarly journals SUPG Approximation for the Oseen Viscoelastic Fluid Flow with Stabilized Lowest-Equal Order Mixed Finite Element Method

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 128
Author(s):  
Shahid Hussain ◽  
Afshan Batool ◽  
Md. Al Mahbub ◽  
Nasrin Nasu ◽  
Jiaping Yu
Keyword(s):  
Finite Element ◽  
Fluid Flow ◽  
Viscoelastic Fluid ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Constitutive Law ◽  
Optimal Error Estimates ◽  
Fe Method ◽  
The Stability ◽  
Stability And Accuracy

In this article, a stabilized mixed finite element (FE) method for the Oseen viscoelastic fluid flow (OVFF) obeying an Oldroyd-B type constitutive law is proposed and investigated by using the Streamline Upwind Petrov–Galerkin (SUPG) method. To find the approximate solution of velocity, pressure and stress tensor, we choose lowest-equal order FE triples P 1 - P 1 - P 1 , respectively. However, it is well known that these elements do not fulfill the i n f - s u p condition. Due to the violation of the main stability condition for mixed FE method, the system becomes unstable. To overcome this difficulty, a standard stabilization term is added in finite element variational formulation. The technique is applied herein possesses attractive features, such as parameter-free, flexible in computation and does not require any higher-order derivatives. The stability analysis and optimal error estimates are obtained. Three benchmark numerical tests are carried out to assess the stability and accuracy of the stabilized lowest-equal order feature of the OVFF.

Thermo-piezo-elastic analysis of amplified piezoceramic actuators using a refined one-dimensional model

2017 ◽  
Vol 29 (17) ◽  
pp. 3482-3494 ◽  
Author(s):  
Enrico Zappino ◽  
Erasmo Carrera
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Structural Model ◽  
Element Model ◽  
Elastic Analysis ◽  
One Dimensional ◽  
Piezoelectric Effects ◽  
Carrera Unified Formulation ◽  
Strain Stress ◽  
Fully Coupled

The thermo-piezo-elastic analysis of amplified piezoceramic actuators is presented in this article. A refined one-dimensional multi-field finite element model, based on the Carrera Unified Formulation, has been developed. Thermal and piezoelectric effects have been included in the structural model and a fully coupled thermo-piezo-elastic analysis has been performed. The finite element model has been assessed by comparing it with results from open literature The model has also been used to perform the analysis of complex amplified piezoceramic actuators. These actuators are able to amplify the displacements produced by piezoceramic material, but they suffer from high deformations when they undergo high thermal loads. An accurate thermal analysis has been performed to evaluate the strain/stress field. The results show the accuracy of the present model and its capabilities in multi-field analyses.

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