scholarly journals Application of the hp-finite element method to modeling thermal fields of high voltage underground cables buried in multi-layer soil

2013 ◽  
Vol 16 (3) ◽  
pp. 72-83
Author(s):  
Tu Phan Vu ◽  
Long Van Hoang Vo
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Adaptive Mesh ◽  
Higher Order ◽  
New Approach ◽  
Underground Cables ◽  
Thermal Fields ◽  
Transfer Problems ◽  
Interpolation Functions ◽  
Element Method

In this paper, we investigate the application of the adaptive higher-order Finite Element Method (hp-FEM) to heat transfer problems in electrical engineering. The proposed method is developed based on the combination of the Delaunay mesh and higher-order interpolation functions. In which the Delaunay algorithm based on the distance function is used for creating the adaptive mesh in the whole solution domain and the higher-order polynomials (up to 9th order) are applied for increasing the accuracy of solution. To evaluate the applicability and effectiveness of this new approach, we applied the proposed method to solve a benchmark heat problem and to calculate the temperature distribution of some typical models of buried double- and single -circuit power cables in the homogenous and multi-layer soils, respectively.

A New Approach to the Rigid Finite Element Method in Modeling Spatial Slender Systems

2018 ◽  
Vol 18 (02) ◽  
pp. 1850017 ◽  
Author(s):  
Iwona Adamiec-Wójcik ◽  
Łukasz Drąg ◽  
Stanisław Wojciech
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Nonlinear Dynamic Analysis ◽  
New Approach ◽  
Static And Dynamic Analysis ◽  
Rigid Finite Element Method ◽  
Longitudinal Flexibility ◽  
Element Method

The static and dynamic analysis of slender systems, which in this paper comprise lines and flexible links of manipulators, requires large deformations to be taken into consideration. This paper presents a modification of the rigid finite element method which enables modeling of such systems to include bending, torsional and longitudinal flexibility. In the formulation used, the elements into which the link is divided have seven DOFs. These describe the position of a chosen point, the extension of the element, and its orientation by means of the Euler angles Z[Formula: see text]Y[Formula: see text]X[Formula: see text]. Elements are connected by means of geometrical constraint equations. A compact algorithm for formulating and integrating the equations of motion is given. Models and programs are verified by comparing the results to those obtained by analytical solution and those from the finite element method. Finally, they are used to solve a benchmark problem encountered in nonlinear dynamic analysis of multibody systems.

scholarly journals MDFEM: Multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficients using higher-order QMC and FEM

2021 ◽  
Author(s):  
Dong T.P. Nguyen ◽  
Dirk Nuyens
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Monte Carlo ◽  
Convergence Rates ◽  
Higher Order ◽  
Elliptic Pdes ◽  
Infinite Dimensional ◽  
Quasi Monte Carlo ◽  
Higher Order Convergence ◽  
Element Method

We introduce the \emph{multivariate decomposition finite element method} (MDFEM) for elliptic PDEs with lognormal diffusion coefficients, that is, when the diffusion coefficient has the form $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\bsy) = \sum_{j \ge 1} y_j \, \phi_j$ with $y_j \sim \calN(0,1)$ and a given sequence of functions $\{\phi_j\}_{j \ge 1}$. We use the MDFEM to approximate the expected value of a linear functional of the solution of the PDE which is an infinite-dimensional integral over the parameter space. The proposed algorithm uses the \emph{multivariate decomposition method} (MDM) to compute the infinite-dimensional integral by a decomposition into finite-dimensional integrals, which we resolve using \emph{quasi-Monte Carlo} (QMC) methods, and for which we use the \emph{finite element method} (FEM) to solve different instances of the PDE.   We develop higher-order quasi-Monte Carlo rules for integration over the finite-di\-men\-si\-onal Euclidean space with respect to the Gaussian distribution by use of a truncation strategy. By linear transformations of interlaced polynomial lattice rules from the unit cube to a multivariate box of the Euclidean space we achieve higher-order convergence rates for functions belonging to a class of \emph{anchored Gaussian Sobolev spaces} while taking into account the truncation error. These cubature rules are then used in the MDFEM algorithm.   Under appropriate conditions, the MDFEM achieves higher-order convergence rates in term of error versus cost, i.e., to achieve an accuracy of $O(\epsilon)$ the computational cost is $O(\epsilon^{-1/\lambda-\dd/\lambda}) = O(\epsilon^{-(p^* + \dd/\tau)/(1-p^*)})$ where $\epsilon^{-1/\lambda}$ and $\epsilon^{-\dd/\lambda}$ are respectively the cost of the quasi-Monte Carlo cubature and the finite element approximations, with $\dd = d \, (1+\ddelta)$ for some $\ddelta \ge 0$ and $d$ the physical dimension, and $0 < p^* \le (2 + \dd/\tau)^{-1}$ is a parameter representing the sparsity of $\{\phi_j\}_{j \ge 1}$.

scholarly journals Calculation of thermal field and ampacity of overhead power transmission lines using finite element method

2014 ◽  
Vol 17 (1) ◽  
pp. 16-29
Author(s):  
Long Van Hoang Vo ◽  
Tu Phan Vu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transmission Lines ◽  
Power Transmission ◽  
Power Lines ◽  
Power Transmission Lines ◽  
Thermal Fields ◽  
Overhead Power Transmission Lines ◽  
Transmission And Distribution ◽  
Element Method

The population explosion and development of the national economy are two main causes of increasing the power demand. Besides, the Distributed Generations (DG) connected with the power transmission and distribution networks increase the transmission power on the existing lines as well. In general, for solving this problem, power utilities have to install some new power transmission and distribution lines. However, in some cases, the install of new power lines can strongly effect to the environment and even the economic efficiency is low. Nowadays, the problem considered by scientists, researchers and engineers is how to use efficiently the existing power transmission and distribution lines through calculating and monitoring their current carrying capacity at higher operation temperature, and thus the optimal use of these existing lines will bring higher efficiency to power companies. Generally, the current carrying capacity of power lines is computed based on the calculation of their thermal fields illustrated in IEEE [1], IEC [2] and CIGRE [3]. In this paper, we present the new approach that is the application of the finite element method based on Comsol Multiphysics software for modeling thermal fields of overhead power transmission lines. In particular, we investigate the influence of environmental conditions, such as wind velocity, wind direction, temperature and radiation coefficient on the typical line of ACSR. The comparisons between our numerical solutions and those obtained from IEEE have been shown the high accuracy and applicability of finite element method to compute thermal fields of overhead power transmission lines.

scholarly journals Cover interpolation functions and h-enrichment in finite element method

2017 ◽  
Vol 2 (1) ◽  
pp. 72-79
Author(s):  
H. Arzani ◽  
E. Khoshbavar rad ◽  
M. Ghorbanzadeh ◽  
◽  
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...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interpolation Functions ◽  
Element Method
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