Calculation of the normal modes of closed waveguides

2020 ◽  
Vol 28 (1) ◽  
pp. 62-76
Author(s):  
Mikhail D. Malykh ◽  
Dmitriy V. Divakov ◽  
Alexandre A. Egorov ◽  
Yaroslav Yu. Kuziv
Keyword(s):  
Finite Element Method ◽  
Optical Waveguides ◽  
Normal Modes ◽  
Computer Algebra Systems ◽  
The Finite Element Method ◽  
Hollow Waveguide ◽  
Smooth Functions ◽  
Software Packages ◽  
Microwave Transmission ◽  
Wide Range

The aim of the work is the development of numerical methods for solving waveguiding problems of the theory of waveguides, as well as their implementation in the form of software packages focused on a wide range of practical problems from the classical issues of microwave transmission to the design of optical waveguides and sensors. At the same time, we strive for ease of implementation of the developed methods in computer algebra systems (Maple, Sage) or in software oriented to the finite element method (FreeFem++). The work uses the representation of electromagnetic fields in a waveguide using four potentials. These potentials do not reduce the number of sought functions, but even in the case when the dielectric permittivity and magnetic permeability are described by discontinuous functions, they turn out to be quite smooth functions. A simple check of the operability of programs by calculating the normal modes of a hollow waveguide is made. It is shown that the relative error in the calculation of the first 10 normal modes does not exceed 4%. These results indicate the efficiency of the method proposed in this article.

Calculation of the normal modes of closed waveguides

2020 ◽  
Vol 28 (1) ◽  
pp. 62-76
Author(s):  
Mikhail D. Malykh ◽  
Dmitriy V. Divakov ◽  
Alexandre A. Egorov ◽  
Yaroslav Yu. Kuziv
Keyword(s):  
Finite Element Method ◽  
Optical Waveguides ◽  
Normal Modes ◽  
Computer Algebra Systems ◽  
The Finite Element Method ◽  
Hollow Waveguide ◽  
Smooth Functions ◽  
Software Packages ◽  
Microwave Transmission ◽  
Wide Range

The aim of the work is the development of numerical methods for solving waveguiding problems of the theory of waveguides, as well as their implementation in the form of software packages focused on a wide range of practical problems from the classical issues of microwave transmission to the design of optical waveguides and sensors. At the same time, we strive for ease of implementation of the developed methods in computer algebra systems (Maple, Sage) or in software oriented to the finite element method (FreeFem++). The work uses the representation of electromagnetic fields in a waveguide using four potentials. These potentials do not reduce the number of sought functions, but even in the case when the dielectric permittivity and magnetic permeability are described by discontinuous functions, they turn out to be quite smooth functions. A simple check of the operability of programs by calculating the normal modes of a hollow waveguide is made. It is shown that the relative error in the calculation of the first 10 normal modes does not exceed 4%. These results indicate the efficiency of the method proposed in this article.

scholarly journals Calculation of the normal modes of closed waveguides

2020 ◽  
Vol 28 (1) ◽  
pp. 62-76
Author(s):  
Mikhail D. Malykh ◽  
Dmitriy V. Divakov ◽  
Alexandre A. Egorov ◽  
Yaroslav Yu. Kuziv
Keyword(s):  
Finite Element Method ◽  
Optical Waveguides ◽  
Normal Modes ◽  
Computer Algebra Systems ◽  
The Finite Element Method ◽  
Hollow Waveguide ◽  
Smooth Functions ◽  
Software Packages ◽  
Microwave Transmission ◽  
Wide Range

The aim of the work is the development of numerical methods for solving waveguiding problems of the theory of waveguides, as well as their implementation in the form of software packages focused on a wide range of practical problems from the classical issues of microwave transmission to the design of optical waveguides and sensors. At the same time, we strive for ease of implementation of the developed methods in computer algebra systems (Maple, Sage) or in software oriented to the finite element method (FreeFem++). The work uses the representation of electromagnetic fields in a waveguide using four potentials. These potentials do not reduce the number of sought functions, but even in the case when the dielectric permittivity and magnetic permeability are described by discontinuous functions, they turn out to be quite smooth functions. A simple check of the operability of programs by calculating the normal modes of a hollow waveguide is made. It is shown that the relative error in the calculation of the first 10 normal modes does not exceed 4%. These results indicate the efficiency of the method proposed in this article.

Local Hydrostatic Pressure Test for Cylindrical Vessels

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
H. Al-Gahtani ◽  
A. Khathlan ◽  
M. Sunar ◽  
M. Naffa'a
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Hydrostatic Pressure ◽  
Cylindrical Vessel ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Wide Range ◽  
Pressure Test ◽  
Local Test ◽  
Alternative Test

The juncture of a small cylindrical nozzle to a large cylindrical vessel is very common in the pressure vessel industry. Upon fabrication, it is required that the whole structure is subjected to pressure testing. The test can be expensive as it necessitates pressurizing the whole structure typically having a large volume. Hence, it is proposed to make a “local test,” which is considerably simpler as it involves capping the small nozzle and testing only a relatively small portion of the structure. This paper investigates the accuracy and reliability of such an alternative test, using the finite-element method. Two different finite-element types are used in the study, specifically a shell-based element and a solid-based element. The verification of the finite-element results for two different cases shows that the models used in the study are valid. It also proves that the two element types yield very similar stress results. In addition, the study includes a numerical investigation of more than 40 different nozzle-to-vessel junctures with a wide range of parameters for the nozzle and vessel. The results indicate that the use of cylindrical caps that are slightly larger than the nozzle is not recommended as it produces stresses that are significantly different from those for the original required pressure test. As such, the study provides an estimate of the smallest size of the cap that may be used in the local test to generate stresses that agree with the full test. For most practical geometries, it is shown that the size of the cap needs to be at least 2–30 times larger than that of the nozzle, depending on the geometrical parameters of the juncture.

The Convergence of the H-P Version of the Finite Element Method with Quasi-Uniform Meshes for Three Dimensional Poisson Problems with Edge Singularity

2014 ◽  
Vol 644-650 ◽  
pp. 1551-1555
Author(s):  
Jian Ming Zhang ◽  
Yong He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weighted Sobolev Spaces ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Smooth Functions ◽  
Edge Singularity ◽  
Theoretical Predictions ◽  
Theoretical Results ◽  
Element Method

This paper is concerned with the convergence of the h-p version of the finite element method for three dimensional Poisson problems with edge singularity on quasi-uniform meshes. First, we present the theoretical results for the convergence of the h-p version of the finite element method with quasi-uniform meshes for elliptic problems on polyhedral domains on smooth functions in the framework of Jacobi-weighted Sobolev spaces. Second, we investigate and analyze numerical results for three dimensional Poission problems with edge singularity. Finally, we verified the theoretical predictions by the numerical computation.

scholarly journals Finite Element Analysis of Square Aquifers Containing Pumped Wells and Comparison with Finite Difference Method

1983 ◽  
Vol 14 (2) ◽  
pp. 85-92 ◽  
Author(s):  
Tilahun Aberra
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Difference ◽  
Discrete Time ◽  
Surface Element ◽  
Dimensionless Time ◽  
The Finite Element Method ◽  
Element Analysis ◽  
Wide Range ◽  
Element Method

The numerical solution of the behaviour of discrete time steps in digital computer analysis of square aquifers containing pumped wells is examined by using the finite element method with a 4 node linear quadrilateral isoparametric surface element. A wide range of time steps are used in the computation. The calculations show that discrete time steps can cause errors and oscillations in the calculations particularly when wells start and stop pumping. Comparison with known results obtained by theoretical and finite difference procedures has been considered. The main objective of this paper is to demonstrate comparison of the finite element and finite difference simulation results over a regular linear 4 node quadrilateral mesh suitable to represent the two numerical schemes with a marked similarity. The dimensionless time drawdown results of the finite element method agreed well with the finite difference and analytical results for small time increment. However, for large time increments, there are from slight to significant oscillations in the results and notable discrepancies are observed in the solutions of the two numerical methods.

Stresses in Thick Pressure Vessel Heads

1990 ◽  
Vol 112 (1) ◽  
pp. 108-114
Author(s):  
A. V. Singh ◽  
V. Kumar
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Finite Element ◽  
Pressure Vessel ◽  
The Finite Element Method ◽  
Solid Of Revolution ◽  
Wide Range ◽  
Radial Thrust ◽  
Thrust Load ◽  
Spherical Pressure

The finite element method is used to study stresses in two types of spherical pressure vessel heads having very wide range of applications in industries. The first problem involves a nozzle to sphere intersection reinforced by a pad and subjected to radial thrust load. The second problem deals with a pressurized thick hemispherical drumhead with a circular manhole. These structures are modeled using eight-node axisymmetric solid of revolution finite elements. Numerical values of circumferential and meridional stresses from the present analysis show excellent agreement with experimental data from the literature.

scholarly journals Grouping and analysis of chair quality and their basic elements

2009 ◽  
pp. 147-154 ◽  
Author(s):  
Dusan Skakic ◽  
Igor Dzincic
Keyword(s):  
Finite Element Method ◽  
Decision Making ◽  
Finite Element ◽  
Numerical Optimization ◽  
Optimal Solution ◽  
Engineering Practice ◽  
The Finite Element Method ◽  
Wide Range ◽  
Decision Making Processes ◽  
Selection Of

Both the scientific experience and the engineering practice indicate that the decision making processes in the course of solving complex designing problems require an analysis of a great number of different construction variants. These types of decision-making processes are time consuming and do not always result in the selection of an optimal solution. That is why the methods of numerical optimization are applied in a wide range of technical sciences to assist in the selection of the best solution. The first step in solving the problem by using the Finite element method is to determine the type of chair earmarked for modeling, and to determine the dimensions of the chair elements.

Development of software based on NX Open for assessing the reliability of REA designs

2018 ◽  
Author(s):  
С.А. Пименов ◽  
П.П. Зорков
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Methods ◽  
Statistical Modelling ◽  
Probabilistic Methods ◽  
The Finite Element Method ◽  
Random Loading ◽  
Random Load ◽  
Wide Range ◽  
Element Method

Рассматриваются основные алгоритмы и численные методы решения задач оценки надежности конструкций радиоэлектронной аппаратуры. Алгоритмы реализованы в виде расчетного программного обеспечения АРКОН для проведения оценки надежности конструкций в условиях случайного нагружения с применением численных методов: метода конечных элементов и метода статистического моделирования. The paper deals with the development of new software which allows us to use probabilistic methods for evaluating the reliability of CEA designs. The main algorithms and numerical methods for solving problems of reliability assessment of REA structures are considered. The reason for conducting the study was the presence of the lag in development of the program-technical complexes aimed at assessment of the strength reliability in relation to the tasks being solved. At the moment, analytical methods for estimating the probability of failure-free operation have been developed. Their implementation requires the existence of a law for the distribution of random load parameters and the system itself. This method is deprived of the method of statistical modelling with the calculation of stresses using the finite element method. The algorithms are implemented in the form of computational software for assessing the reliability of structures under random loading conditions. To implement this method, an open CAE was chosen — a system with the ability to program its own modules — the NX Open system. The developed software is displayed on the NX panel in the form of a special icon tray Reliability. The developed software is intended for analysis of the strength of reliability of CEA structures with random loading. The software does not have domestic or foreign alternatives. The main advantages are universality (the ability to perform calculations for a wide range of designs, taking into account the statistical nature of the initial data), the reliability of the estimated estimates, confirmed by the use of modern numerical methods: the finite element method and the statistical modelling method.

Fundamentals and Applications of the Finite-Element Method in Analyzing Structural and Nonstructural Marine Problems

1982 ◽  
Vol 19 (03) ◽  
pp. 272-292
Author(s):  
Donald Liu ◽  
Yung-Kuang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Element Formulation ◽  
The Finite Element Method ◽  
Static And Dynamic Analysis ◽  
Marine Industry ◽  
Wide Range ◽  
Element Method

The finite-element method has become a popular and effective tool not only for structural analysis, but also for a wide range of physical problems which are of particular interest to the marine industry. A brief review of the finite-element formulation for structural and nonstructural problems is presented. Applications to marine structures, including static and dynamic analysis and fracture mechanics, are given. Nonstructural applications to heat transfer and ship hydrodynamic problems are also demonstrated. Recent developments in the coupled fluid-structural interaction problem using the boundary integral method, which is considered as an extension of the finite-element method, are also described.

Unloading of an Elastic-Plastic Loaded Spherical Contact

2004 ◽  
Author(s):  
Yuri Kligerman ◽  
Izhak Etsion ◽  
Yuri Kadin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Simulations ◽  
The Finite Element Method ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Contact Loads ◽  
Wide Range ◽  
Residual Curvature ◽  
Loading And Unloading

The process of unloading an elastic-plastic loaded sphere in contact with a rigid flat is studied by the Finite Element Method. The sphere material is assumed isotropic with elastic-linear hardening. The numerical simulations cover a wide range of loading interference deformation of various values of Young’s modulus and Poisson ratios of the sphere material. The contact loads, stresses, and deformations in the sphere during both loading and unloading, are calculated for the range of interferences. Empirical dimensionless expressions are presented for the unloading load-deformation relation, the residual axial displacement and the residual curvature of the sphere after complete unloading.

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