scholarly journals Peridynamic Formulation for Coupled Thermoelectric Phenomena

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Migbar Assefa ◽  
Xin Lai ◽  
Lisheng Liu ◽  
Yang Liao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Partial Differential Equations ◽  
Analytical Solutions ◽  
Current Flow ◽  
Numerical Technique ◽  
Electrical Current ◽  
Numerical Examples ◽  
Electrical Current Flow ◽  
Thermoelectric Convertor

Modeling of heat and electrical current flow simultaneously in thermoelectric convertor using classical theories do not consider the influence of defects in the material. This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes at the discontinuities. The usual way of solving such PDEs is by using numerical technique, like Finite Element Method (FEM). Although FEM is robust and versatile, it is not suitable to model evolving discontinuities. To avoid such shortcomings, we propose the concept of peridynamic theory to derive the balance of energy and charge equations in the coupled thermoelectric phenomena. Therefore, this paper presents the transport of heat and charge in thermoelectric material in the framework of peridynamic (PD) theory. To illustrate the reliability of the PD formulation, numerical examples are presented and results are compared with those from literature, analytical solutions, or finite element solutions.

Bond Based Peridynamic Formulation for Thermoelectric Materials

2017 ◽  
Vol 883 ◽  
pp. 51-59 ◽  
Author(s):  
Migbar Assefa Zeleke ◽  
Lai Xin ◽  
Li Sheng Liu
Keyword(s):  
Finite Element Method ◽  
Current Flow ◽  
Numerical Technique ◽  
Electrical Current ◽  
Stress Fields ◽  
External Criterion ◽  
Conservation Of Energy ◽  
Electrical Current Flow ◽  
Crack Tips ◽  
Thermoelectric Convertor

Modeling of heat and electrical current flow simultaneously in thermoelectric convertor using classical theories do not consider the influence of defects in the material. This is because traditional methods are developed based on partial differential equations (PDEs) and lead to infinite fluxes and stress fields at the crack tips. The usual way of solving such PDEs is by using numerical technique, like Finite Element Method (FEM). Although FEM is robust and versatile, it is not suitable to model evolving discontinuities since discontinuous fields are mathematically singular at the crack tip and required an external criterion for the prediction of crack growth. In this paper, we follow the concept of peridynamic (PD) theory to overcome the shortcomings above. Therefore, the main aim of this paper is to develop the peridynamic equations for the generalized Fourier’s and Ohm’s laws. Furthermore, we derived the peridynamic equations for the conservation of energy and charge for the coupled thermoelectric phenomena.

The Equilibrium Cell-Based Smooth Finite Element Method for Shakedown Analysis of Structures

2019 ◽  
Vol 16 (05) ◽  
pp. 1840013 ◽  
Author(s):  
P. L. H. Ho ◽  
C. V. Le ◽  
T. Q. Chu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Optimization Problem ◽  
Conic Programming ◽  
Equilibrium Equations ◽  
Shakedown Analysis ◽  
Numerical Examples ◽  
Elastic Stresses ◽  
Gauss Points ◽  
Element Method

This paper presents a novel equilibrium formulation, that uses the cell-based smoothed method and conic programming, for limit and shakedown analysis of structures. The virtual strains are computed using straining cell-based smoothing technique based on elements of discretized mesh. Fictitious elastic stresses are also determined within the framework of finite element method (CS-FEM)-based Galerkin procedure, and equilibrium equations for residual stresses are satisfied in an average sense at every cell-based smoothing cell. All constrains are imposed at only one point in the smoothing domains, instead of Gauss points as in a standard FEM-based procedure. The resulting optimization problem is then handled using the highly efficient solvers. Various numerical examples are investigated, and obtained solutions are compared with available results in the literature.

Hot Forging Comparative Analyses by Using a Combined Finite Element Method

2007 ◽  
Vol 340-341 ◽  
pp. 737-742
Author(s):  
Yong Ming Guo
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Hot Forging ◽  
Rigid Plastic ◽  
Numerical Examples ◽  
Comparative Analyses ◽  
Single Action ◽  
Element Method

In this paper, single action die and double action die hot forging problems are analyzed by a combined FEM, which consists of the volumetrically elastic and deviatorically rigid-plastic FEM and the heat transfer FEM. The volumetrically elastic and deviatorically rigid-plastic FEM has some merits in comparison with the conventional rigid-plastic FEMs. Differences of calculated results for the two forging processes can be clearly seen in this paper. It is also verified that these calculated results are similar to those of the conventional rigid-plastic FEM in comparison with analyses of the same numerical examples by the penalty rigid-plastic FEM.

scholarly journals A Numerical Solution to Fractional Diffusion Equation for Force-Free Case

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
O. Tasbozan ◽  
A. Esen ◽  
N. M. Yagmurlu ◽  
Y. Ucar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Exact Analytical Solution ◽  
Fractional Diffusion ◽  
Fractional Diffusion Equation ◽  
Spline Functions ◽  
B Spline ◽  
Numerical Examples ◽  
Free Case

A collocation finite element method for solving fractional diffusion equation for force-free case is considered. In this paper, we develop an approximation method based on collocation finite elements by cubic B-spline functions to solve fractional diffusion equation for force-free case formulated with Riemann-Liouville operator. Some numerical examples of interest are provided to show the accuracy of the method. A comparison between exact analytical solution and a numerical one has been made.

Electrical current flow at conductive nanowires formed in GaN thin films by a dislocation template technique

2010 ◽  
Vol 96 (19) ◽  
pp. 193109 ◽  
Author(s):  
Shin-ichi Amma ◽  
Yuki Tokumoto ◽  
Keiichi Edagawa ◽  
Naoya Shibata ◽  
Teruyasu Mizoguchi ◽  
...  
Keyword(s):  
Thin Films ◽  
Current Flow ◽  
Electrical Current ◽  
Electrical Current Flow

scholarly journals Local Elastic and Geometric Stiffness Matrices for the Shell Element Applied in cFEM

2017 ◽  
Author(s):  
Dávid Visy ◽  
Sándor Ádány
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Shell Element ◽  
Numerical Examples ◽  
Geometric Stiffness ◽  
Stiffness Matrices ◽  
Plane Element ◽  
Unusual Combination ◽  
Shell Finite Element ◽  
Lagrange Strain

In this paper local elastic and geometric stiffness matrices of ashell finite element are presented and discussed. The shell finiteelement is a rectangular plane element, specifically designedfor the so-called constrained finite element method. One of themost notable features of the proposed shell finite element isthat two perpendicular (in-plane) directions are distinguished,which is resulted in an unusual combination of otherwise classicshape functions. An important speciality of the derived stiffnessmatrices is that various options are considered, whichallows the user to decide how to consider the through-thicknessstress-strain distributions, as well as which second-order strainterms to consider from the Green-Lagrange strain matrix. Thederivations of the stiffness matrices are briefly summarizedthen numerical examples are provided. The numerical examplesillustrate the effect of the various options, as well as theyare used to prove the correctness of the proposed shell elementand of the completed derivations.

scholarly journals Elasto - plastic analysis of anisotropic hardening materials by finite element method

1985 ◽  
Vol 7 (1) ◽  
pp. 8-13
Author(s):  
Tran Duong Hien
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Program ◽  
Yield Criterion ◽  
Element Model ◽  
Isotropic Hardening ◽  
Anisotropic Hardening ◽  
Numerical Examples ◽  
Plastic Analysis ◽  
Hill's Yield Criterion

An elasto- plastic analysis for general three dimes10nal problems using a finite element model is presented. The analysis is based on Hill's yield criterion which included anisotropic materials displaying kinematic - isotropic hardening. The validity and practical applicability of the algorithm are illustrated by a number of numerical examples, calculated by a computer program written in fortran.

Effect of Current Direction on the Reliability of Different Capped Cu Interconnects

2005 ◽  
Vol 863 ◽  
Author(s):  
C. L. Gan ◽  
C. Y. Lee ◽  
C. K. Cheng ◽  
J. Gambino
Keyword(s):  
Failure Analysis ◽  
Current Flow ◽  
Void Nucleation ◽  
Electrical Current ◽  
Nucleation Site ◽  
Time To Failure ◽  
Current Direction ◽  
Electron Current ◽  
Electrical Current Flow ◽  
Better Than

AbstractThe reliability of Cu M1-V1-M2-V2-M3 interconnects with SiN and CoWP cap layers was investigated. Similar to previously reported results, the reliability of CoWP capped structures is much better than identical SiN capped structures. However, it was also observed that the reliability of CoWP capped interconnects was independent of the direction of electrical current flow. This phenomenon is different from what was observed for SiN capped structures, where M2 lines with electron current flow in the upstream configuration (“via-below”) have about three times larger median-time-to-failure than identical lines in the downstream configuration (“viaabove”). This is because the Cu/SiN interface is the preferential void nucleation site and provides the fastest diffusion pathway in such an architecture. Failure analysis has shown that fatal partially-spanned voids usually had formed directly below the via for “via-above” configuration, and fully-spanned voids occurred in the lines above the vias for “via-below” configuration.On the other hand, failure analysis for CoWP-coated Cu structures showed that partiallyspanned voids below the via do not cause fatal failures in the downstream configuration. This is because the CoWP layer is conducting, and thus able to shunt current around the void. As a result, a large fully-spanning void is required to cause a failure, just like the upstream configuration. Thus the lifetime of an interconnect with a conducting cap layer is independent of whether the current is flowing upstream or downstream.

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