scholarly journals Method of Images for a Charge inside a Three-Layer Medium and Implementation of a Dirichlet Border Condition

2020 ◽  
Vol 44 (2) ◽  
pp. 7-14
Author(s):  
Fausto Valencia ◽  
Hugo Arcos
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Electric Field ◽  
Boundary Conditions ◽  
Electric Potential ◽  
Finite Element Simulations ◽  
Method Of Images ◽  
Layer Medium ◽  
A Charge ◽  
Good Agreement

A process to apply the method of images for a charge located in a three-layer medium is presented. The images are found according to the boundary conditions between the layers for the electric field. The characteristics of the electric potential are also considered, thus the number of unknown variables becomesa guide to set the image charges needed to solve the problem. The results are compared with finite element simulations through the use of the software FEMM 4.2, showing good agreement. The found limitations of the process are also noted, mainly in regards to the dependence of the images on the coordinates where the field is to be calculated. The model obtained was applied to different cases, where it was seen that it was not limited to three material media only. Finally, the null potential boundary condition was applied, showing how the method of images could be applied to this type of problems.

scholarly journals Stiffness Estimation and Equivalence of Boundary Conditions in FEM Models

2021 ◽  
Vol 11 (4) ◽  
pp. 1482
Author(s):  
Róbert Huňady ◽  
Pavol Lengvarský ◽  
Peter Pavelka ◽  
Adam Kaľavský ◽  
Jakub Mlotek
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Conditions ◽  
Model Updating ◽  
Element Model ◽  
Computational Time ◽  
Stiffness Coefficients ◽  
First Case ◽  
Numerical Approaches

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

Finite Element Analysis of Two-Dimensional Turbulent Asymmetric Near and Far Non-Periodic and Periodic Wakes by κ-ϵ Model of Turbulence

1993 ◽  
Author(s):  
Amlan Kusum Nayak ◽  
N. Venkatrayulu ◽  
D. Prithvi Raj
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Wake Flow ◽  
Two Dimensional ◽  
Galerkin Finite Element Method ◽  
Element Analysis ◽  
Galerkin Finite Element ◽  
Flow Problems ◽  
Newton Raphson ◽  
Good Agreement

Two dimensional time averaged, steady incompressible, adiabatic turbulent asymmetric near and far non-periodic and periodic wake flow problems are solved by Galerkin Finite Element Method. A primitive-variables formulation is adopted using Reynolds-averaged momentum equations, with standard k-ε turbulence model. Finite element equations are solved by Newton-Raphson technique with relaxation, using frontal solver. Periodic boundary condition is specified on the periodic lines of the cascade, and asymptotic boundary condition is specified at the exit. These boundary conditions are applied without much difficulty which are not so straight forward in finite volume (FV) method. The results show good agreement with FV prediction and experimental data.

Unified Solution on Skew Plate Bending with Four Edges Supported under Arbitrary Load

2011 ◽  
Vol 243-249 ◽  
pp. 5994-5998
Author(s):  
Lang Cao ◽  
Xing Jie Xing ◽  
Feng Guang Ge
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Engineering Design ◽  
Plate Bending ◽  
The Finite Element Method ◽  
Arbitrary Load ◽  
Skew Plate ◽  
Good Agreement

According to the bending equation and boundary conditions of skew plate in the oblique coordinates system parallel to the edge of the plate, expanding deflection and load into form of Fourier series, the paper derives and obtains unified solution of bending problem for the four-edge-supported skew plate under arbitrary load. Programmed and calculated by mathematica language, the paper also comes with deflections and moments under the condition of any oblique angles, ratios of side length and Poisson ratios. The results of the paper is compared with those by the finite element method in the example, and they’re in good agreement with each other. The paper extends the bending theory of rectangular plate to the skew plate of any angle. The theory being reliable and the result being accurate, the research of the paper can provide reference for engineering design.

VALIDATION OF LOSS-COEFFICIENT-BASED OUTLET BOUNDARY CONDITIONS FOR SIMULATING AORTIC FLOW

2016 ◽  
Vol 16 (02) ◽  
pp. 1650011 ◽  
Author(s):  
ALI CEMAL BENIM ◽  
FETHI GÜL ◽  
ALEXANDER ASSMANN ◽  
PAYAM AKHYARI ◽  
ARTUR LICHTENBERG ◽  
...  
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Constant Pressure ◽  
Loss Coefficient ◽  
Human Aorta ◽  
Retrograde Perfusion ◽  
Heart Lung Machine ◽  
Perfusion Mode ◽  
Good Agreement ◽  
Outlet Boundary Condition

Flow in a polyurethane model of a human aorta, driven by a heart-lung machine, is analyzed experimentally and computationally for antegrade and retrograde perfusion. The purpose of the analysis is the validation of the previously proposed loss-coefficient-based outlet boundary condition for aortic branches. This model is claimed to be commonly applicable to different perfusion modes of the aorta, unlike the alternative straightforward constant-pressure outlet boundary condition. First, the antegrade perfusion is analyzed computationally and experimentally. This step delivers the loss-coefficients that are to be used in any other perfusion mode of the aorta. Subsequently, a retrograde perfusion is applied to the same aorta, where the flow rates at the outlets of the aortic branches are measured and predicted by applying the loss-coefficient-based outlet boundary conditions. A very good agreement of the predictions with the measurements is observed. The predictions delivered by the standard constant-pressure outlet boundary condition are observed, on the contrary, to be highly in error. Thus, the advocated loss-coefficient-based outlet boundary condition is experimentally validated. It is shown that it is applicable to different perfusion modes with a quite good accuracy, which is much higher compared to the straightforward constant-pressure outlet boundary condition.

scholarly journals Convective Boundary Conditions Effect on Cylindrical Media with Transient Heat Transfer

2021 ◽  
Vol 82 (2) ◽  
pp. 146-156
Author(s):  
Raoudha Chaabane ◽  
Nor Azwadi Che Sidik ◽  
Abdelmajid Jemni
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Convective Boundary Condition ◽  
Distribution Functions ◽  
Convective Boundary ◽  
Thermal Fields ◽  
Fortran 90 ◽  
Boltzmann Method ◽  
Transfer Problems ◽  
Good Agreement

Lattice Boltzmann method is used to solve inside a cylindrical cavity with convective boundary condition is highlighted in this paper. Because of its simple, stable, accurate, efficient and ease for parallelization, we use the thermal Single Relaxation Time Bhatnagar Gross Krook (SRT BGK) mesoscopic approach in order to solve the energy equation. Thermal fields are simulated using D2Q9 scheme. We introduce and demonstrate numerically some usual cases (Dirichlet, Newmann) of Boundary conditions (Bcs). After validation, we extend the present work to the convective case. At the wall of the cavity, the unknown Thermal Distribution Functions (TDF) are exposed to the bounce back concept which is determined consistently by one of the imposed BCs. An in-house Fortran 90 code is used to analyze a variety of BCs inside a two-dimensional cavity. In validation, obtained results highlight a good agreement with literature. The present study is extended to deal with convective boundary condition for conduction transfer problems inside an axisymmetric cylindrical media subjected to heat generation and Newman boundary conditions.

scholarly journals Modeling Electric Field and Potential Distribution of an Model of Insulator in Two Dimensions by the Finite Element Method

2018 ◽  
Vol 3 (1) ◽  
pp. 01
Author(s):  
Nassima M ziou ◽  
Hani Benguesmia ◽  
Hilal Rahali
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Electric Field ◽  
Potential Distribution ◽  
Two Dimensions ◽  
Comsol Multiphysics ◽  
The Finite Element Method ◽  
Good Agreement ◽  
Element Method

The electrical effects can be written by two magnitudes the field and the electrostatic potential, for the determination of the distribution of the field and the electric potential along the leakage distance of the polluted insulator, the comsol multiphysics software based on the finite element method will be used. The objective of this paper is the modeling electric field and potential distribution in Two Dimensions by the Finite Element Method on a model of insulator simulating the 1512L outdoor insulator used by the Algerian company of electricity and gas (SONELGAZ). This model is under different conductivity, applied voltage, position of clean layer and width of clean layer. The computer simulations are carried out by using the COMSOL multiphysics software. This paper describes how Comsol Multiphysics have been used for modeling of the insulator using electrostatic 2D simulations in the AC/DC module. Numerical results showed a good agreement.

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