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 ◽  
◽  
◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interpolation Functions ◽  
Element Method

A Lagrangian Uniform-Mesh Finite Element Method Applied to Problems Governed by Poisson’s Equation

2007 ◽  
Author(s):  
Linxia Gu ◽  
Ashok V. Kumar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Weak Form ◽  
Lagrangian Formulation ◽  
Uniform Mesh ◽  
Interpolation Function ◽  
Step Functions ◽  
Surface Integration ◽  
Interpolation Functions ◽  
Element Method

A method is presented for the solution of Poisson’s Equations using a Lagrangian formulation. The interpolation functions are the Lagrangian operation of those used in the classical finite element method, which automatically satisfy boundary conditions exactly even though there are no nodes on the boundaries of the domain. The integration is introduced in an implicit way by using approximated step functions. Classical surface integration terms used in the weak form are unnecessary due to the interpolation function in the Lagrangian formulation. Furthermore, the Lagrangian formulation simplified the connection between the mesh and the solid structures, thus providing a very easy way to solve the problems without a conforming mesh.

An Investigation of the Implementation of the p-Version Finite Element Method

1995 ◽  
Author(s):  
Simon D. Campion ◽  
John L. Jarvis
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Function Method ◽  
Jacobian Matrix ◽  
P Elements ◽  
Load Vector ◽  
Geometry Mapping ◽  
Selection Of ◽  
Interpolation Functions ◽  
Element Method

Abstract The use of the p-version finite element method has become more widespread over the last five years or so, as witnessed by the addition of p-elements to a number of well known commercial codes. A review of the keynote papers on the p-version method is presented which focusses on the use of the hierarchical concept and the selection of the interpolation functions. The importance of accurate geometry mapping is also discussed, and the use of the blending function method is presented. Details of implementation of the p-version method are discussed in the light of the authors efforts to develop a program for solving two-dimensional elastostatic problems. Topics covered include the rules for numerical integration for the p-method, the possible use of numerical rather than explicit differentiation for determining the Jacobian matrix, and the programming of the load vector for the p-method. The lessons learnt are illustrated by simple examples, and will be of benefit to those wishing to program p-elements for other applications.

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.

Applications of the Fractal-Like Finite Element Method to Sharp Notched Plates

2007 ◽  
Author(s):  
Muhammad Treifi ◽  
Derek K. L. Tsang ◽  
S. Olutunde Oyadiji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Finite Elements ◽  
Stress Intensity Factors ◽  
Stress Singularity ◽  
Intensity Factors ◽  
Singular Region ◽  
Interpolation Functions ◽  
Element Method

The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.

Interpolation functions in control volume finite element method

2003 ◽  
Vol 30 (4) ◽  
pp. 303-309 ◽  
Author(s):  
H. Abbassi ◽  
S. Turki ◽  
S. Ben Nasrallah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Control Volume ◽  
Control Volume Finite Element ◽  
Interpolation Functions ◽  
Element Method

Simulation of tuning graphene plasmonic behaviors by ferroelectric domains for self-driven infrared photodetector applications

Nanoscale ◽  
2019 ◽  
Vol 11 (43) ◽  
pp. 20868-20875 ◽  
Author(s):  
Junxiong Guo ◽  
Yu Liu ◽  
Yuan Lin ◽  
Yu Tian ◽  
Jinxing Zhang ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Interfacial Effect ◽  
Infrared Photodetector ◽  
The Finite Element Method ◽  
Ferroelectric Domains ◽  
Element Method

We propose a graphene plasmonic infrared photodetector tuned by ferroelectric domains and investigate the interfacial effect using the finite element method.

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