scholarly journals A consecutive-interpolation finite element method for heat transfer analysis

2015 ◽  
Vol 18 (2) ◽  
pp. 21-28
Author(s):  
Minh Ngoc Nguyen ◽  
Nha Thanh Nguyen ◽  
Tinh Quoc Bui ◽  
Thien Tich Truong
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Heat Transfer Analysis ◽  
Two Dimensional ◽  
Interpolation Condition ◽  
Numerical Examples ◽  
Quadrilateral Finite Element ◽  
Transfer Problems

A consecutive-interpolation 4-node quadrilateral finite element (CQ4) is further extended to solve twodimensional heat transfer problems, taking the average nodal gradients as interpolation condition, resulting in highorder continuity solution without smoothing operation and without increasing the number of degrees of freedom. The implementation is straightforward and can be easily integrated into any existing FEM code. Several numerical examples are investigated to verify the accuracy and efficiency of the proposed formulation in two-dimensional heat transfer analysis.

scholarly journals An enhanced nodal gradient finite element for non-linear heat transfer analysis

2019 ◽  
Author(s):  
Minh Ngoc Nguyen ◽  
Tich Thien Truong ◽  
Tinh Quoc Bui
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Heat Transfer Analysis ◽  
Order Continuity ◽  
Linear Heat ◽  
Non Linear ◽  
Interpolation Procedure ◽  
Transfer Problems

The present work is devoted to the analysis of non-linear heat transfer problems using the recent development of consective-interpolation procedure. Approximation of temperature is enhanced by taking into account both the nodal values and their averaged nodal gradients, which results in an improved finite element model. The novel formulation possesses many desirable properties including higher accuracy and higher-order continuity, without any change of the total number of degrees of freedom. The non-linear heat transfer problems equation is linearized and iteratively solved by the Newton-Raphson scheme. To show the accuracy and efficiency of the proposed method, several numerical examples are hence considered and analyzed.

scholarly journals Higher Order Multiscale Finite Element Method for Heat Transfer Modeling

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3827
Author(s):  
Marek Klimczak ◽  
Witold Cecot
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Higher Order ◽  
Shape Functions ◽  
Multiscale Finite Element Method ◽  
Multiscale Finite Element ◽  
Steady State Heat ◽  
Steady State Heat Transfer

In this paper, we present a new approach to model the steady-state heat transfer in heterogeneous materials. The multiscale finite element method (MsFEM) is improved and used to solve this problem. MsFEM is a fast and flexible method for upscaling. Its numerical efficiency is based on the natural parallelization of the main computations and their further simplifications due to the numerical nature of the problem. The approach does not require the distinct separation of scales, which makes its applicability to the numerical modeling of the composites very broad. Our novelty relies on modifications to the standard higher-order shape functions, which are then applied to the steady-state heat transfer problem. To the best of our knowledge, MsFEM (based on the special shape function assessment) has not been previously used for an approximation order higher than p = 2, with the hierarchical shape functions applied and non-periodic domains, in this problem. Some numerical results are presented and compared with the standard direct finite-element solutions. The first test shows the performance of higher-order MsFEM for the asphalt concrete sample which is subject to heating. The second test is the challenging problem of metal foam analysis. The thermal conductivity of air and aluminum differ by several orders of magnitude, which is typically very difficult for the upscaling methods. A very good agreement between our upscaled and reference results was observed, together with a significant reduction in the number of degrees of freedom. The error analysis and the p-convergence of the method are also presented. The latter is studied in terms of both the number of degrees of freedom and the computational time.

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 Efficient Alternative for Construction of the Linear System Stemming from Numerical Solution of Heat Transfer Problems via FEM

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Estaner Claro Romão
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Linear System ◽  
Numerical Solution ◽  
The Finite Element Method ◽  
Numerical Application ◽  
System Building ◽  
Efficient Alternative ◽  
Transfer Problems

This paper proposes an efficient alternative to construction of the linear system coming from a solution via the Finite Element Method that is able to significantly decrease the time of construction of this system. From the presentation of the methodology used and a numerical application it will be clear that the purpose of this work is to be able to decrease 6-7 times (on average) the linear system building time.

The Finite-Element Method—Part I

1989 ◽  
Author(s):  
Shiro Kobayashi ◽  
Soo-Ik Oh ◽  
Taylan Altan
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Finite Element ◽  
Ritz Method ◽  
Approximate Solutions ◽  
Plane Elasticity ◽  
Heat Transfer Analysis ◽  
Deformation Analysis ◽  
The Finite Element Method ◽  
Element Method

The concept of the finite-element procedure may be dated back to 1943 when Courant approximated the warping function linearly in each of an assemblage of triangular elements to the St. Venant torsion problem and proceeded to formulate the problem using the principle of minimum potential energy. Similar ideas were used later by several investigators to obtain the approximate solutions to certain boundary-value problems. It was Clough who first introduced the term “finite elements” in the study of plane elasticity problems. The equivalence of this method with the well-known Ritz method was established at a later date, which made it possible to extend the applications to a broad spectrum of problems for which a variational formulation is possible. Since then numerous studies have been reported on the theory and applications of the finite-element method. In this and next chapters the finite-element formulations necessary for the deformation analysis of metal-forming processes are presented. For hot forming processes, heat transfer analysis should also be carried out as well as deformation analysis. Discretization for temperature calculations and coupling of heat transfer and deformation are discussed in Chap. 12. More detailed descriptions of the method in general and the solution techniques can be found in References [3-5], in addition to the books on the finite-element method listed in Chap. 1. The path to the solution of a problem formulated in finite-element form is described in Chap. 1 (Section 1.2). Discretization of a problem consists of the following steps: (1) describing the element, (2) setting up the element equation, and (3) assembling the element equations. Numerical analysis techniques are then applied for obtaining the solution of the global equations. The basis of the element equations and the assembling into global equations is derived in Chap. 5. The solution satisfying eq. (5.20) is obtained from the admissible velocity fields that are constructed by introducing the shape function in such a way that a continuous velocity field over each element can be denned uniquely in terms of velocities of associated nodal points.

Sign in / Sign up

Export Citation Format

Share Document