Transient heat transfer analysis of anisotropic material by using Element-Free Galerkin method

Zhang, Jianping; Zhou, Guoqiang; Gong, Shengrong; Wang, Shusen

doi:10.1016/j.icheatmasstransfer.2017.04.003

Cited by 32 publications

(7 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We assume that Ω s is a 3D space domain bounded by a surface 𝜕Ω s = Γ, where Γ = Γ D ∪ Γ N and Γ D ∩ Γ N = ∅. Considering the transient heat conduction problem in anisotropic media in Ω s , the function T(x, t) describing the transient temperature distribution satisfies the following governing equation, 18,39 𝜌c 𝜕T(x, t)…”

Section: Problem Statementmentioning

confidence: 99%

“…We assume that

{\Omega}_s

is a 3D space domain bounded by a surface

\partial {\Omega}_s=\Gamma

, where

\Gamma ={\Gamma}_D\cup {\Gamma}_N

and

{\Gamma}_D\cap {\Gamma}_N=\varnothing

. Considering the transient heat conduction problem in anisotropic media in

{\Omega}_s

, the function

T\left(\mathbf{x},t\right)

describing the transient temperature distribution satisfies the following governing equation, 18,39

\rho c\frac{\partial T\left(\mathbf{x},t\right)}{\partial t}={D}_{ij}\frac{\partial^2T\left(\mathbf{x},t\right)}{\partial {x}_i\partial {x}_j}+Q\left(\mathbf{x},t\right),\kern1.5em \mathbf{x}\in {\Omega}_s,\kern1em t\in \left[{t}_0,{t}_f\right],

where

$$ \m...

…”

Section: Problem Statementmentioning

confidence: 99%

See 1 more Smart Citation

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

Qiu

Wang

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

In this paper, the standard and the localized space‐time radial basis function (RBF) collocation methods are modified and combined with the time‐marching scheme and space‐time domain decomposition technique for simulating the long‐time transient heat conduction in 3D anisotropic composite materials. In the proposed approaches, we set the source points outside the whole space‐time domain in the standard space‐time RBF collocation method or outside the established subdomain in the localized approach by introducing the space and time magnification factors, instead of distributing them inside the original domain. In addition, the space‐time regulating factor is defined and added to the conventional schemes to improve the stability of numerical methods. The modified approaches are resulted in a simple and effective time‐marching process which can achieve long‐time simulation, resting on the property that the coefficient matrices generated by these two methods are only related to the space‐time distance between the collocation points and source points. Our ultimate aim is to develop a computing system for resolving dynamic problems in composite materials by designing a space‐time domain decomposition technique. Numerical experiments are conducted to demonstrate the accuracy, efficiency and stability of the presented methodologies.

show abstract

Section: Problem Statementmentioning

confidence: 99%

“…We assume that

{\Omega}_s

is a 3D space domain bounded by a surface

\partial {\Omega}_s=\Gamma

, where

\Gamma ={\Gamma}_D\cup {\Gamma}_N

and

{\Gamma}_D\cap {\Gamma}_N=\varnothing

. Considering the transient heat conduction problem in anisotropic media in

{\Omega}_s

, the function

T\left(\mathbf{x},t\right)

describing the transient temperature distribution satisfies the following governing equation, 18,39

\rho c\frac{\partial T\left(\mathbf{x},t\right)}{\partial t}={D}_{ij}\frac{\partial^2T\left(\mathbf{x},t\right)}{\partial {x}_i\partial {x}_j}+Q\left(\mathbf{x},t\right),\kern1.5em \mathbf{x}\in {\Omega}_s,\kern1em t\in \left[{t}_0,{t}_f\right],

where

$$ \m...

…”

Section: Problem Statementmentioning

confidence: 99%

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

Qiu

Wang

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…, C M over the main boundary ∂ and we assume that M ≥ N. By satisfying Eqs. (8) and ( 9) at all collocation points on the boundary, the following system of linear equations are obtained:…”

Section: The Mfs Formulation For Two-dimensional Anisotropic Elasticitymentioning

confidence: 99%

“…Meshfree methods can be classified into two major categories [4]. The first category includes meshfree methods based on strong forms of differential equations [5][6][7], while the meshfree methods based on weak forms of governing equations [8,9] fall into the second category. The weak-form meshfree methods need suitable techniques for the computation of domain integrals [10][11][12]; however, the MFS is a strong-form and truly meshfree method without any need for evaluating any domain or boundary integral.…”

Section: Introductionmentioning

confidence: 99%

The Method of Fundamental Solutions for Two-Dimensional Elastostatic Problems with Stress Concentration and Highly Anisotropic Materials

Hematiyan¹,

Jamshidi²,

Mohammadi³

2022

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

The method of fundamental solutions (MFS) is a boundary-type and truly meshfree method, which is recognized as an efficient numerical tool for solving boundary value problems. The geometrical shape, boundary conditions, and applied loads can be easily modeled in the MFS. This capability makes the MFS particularly suitable for shape optimization, moving load, and inverse problems. However, it is observed that the standard MFS lead to inaccurate solutions for some elastostatic problems with stress concentration and/or highly anisotropic materials. In this work, by a numerical study, the important parameters, which have significant influence on the accuracy of the MFS for the analysis of two-dimensional anisotropic elastostatic problems, are investigated. The studied parameters are the degree of anisotropy of the problem, the ratio of the number of collocation points to the number of source points, and the distance between main and pseudo boundaries. It is observed that as the anisotropy of the material increases, there will be more errors in the results. It is also observed that for simple problems, increasing the distance between main and pseudo boundaries enhances the accuracy of the results; however, it is not the case for complicated problems. Moreover, it is concluded that more collocation points than source points can significantly improve the accuracy of the results.

show abstract

“…Studies dealing with thermal properties of wood materials focused mostly on determining the effect of density, temperature, and MC on thermal conductivity, thermal diffusivity, and specific heat capacity [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Applying the EDPS Method to the Research into Thermophysical Properties of Solid Wood of Coniferous Trees

Krišťák

Igaz

Ružiak

2019

Advances in Materials Science and Engineering

View full text Add to dashboard Cite

e results of using the EDPS (extended dynamic plane source) method to determine thermophysical properties of solid wood of coniferous trees growing in Slovakia with 0% and 12% equilibrium moisture content are presented in the paper. Solid wood of two different tree species: Norway spruce (Picea abies L.) and Scots pine (Pinus sylvestris L.) was used in the research. e research was carried out independently in three anatomical planes. Coefficients of thermal conductivity, thermal diffusivity, and specific heat capacity were determined following the research. Comparing the research results to the values determined by other authors and already published models to calculate individual parameters, the fact that the data gathered using the EDPS method can be accepted in case of all studied thermophysical properties can be stated.

show abstract

Transient heat transfer analysis of anisotropic material by using Element-Free Galerkin method

Cited by 32 publications

References 15 publications

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

Modified space‐time radial basis function collocation method for long‐time simulation of transient heat conduction in3Danisotropic composite materials

The Method of Fundamental Solutions for Two-Dimensional Elastostatic Problems with Stress Concentration and Highly Anisotropic Materials

Applying the EDPS Method to the Research into Thermophysical Properties of Solid Wood of Coniferous Trees

Contact Info

Product

Resources

About