The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems

Gu, Yan; Qu, Wenzhen; Chen, Wen; Song, Lina; Zhang, Chuanzeng

doi:10.1016/j.jcp.2019.01.027

Cited by 67 publications

(10 citation statements)

References 45 publications

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“…Figure 10 shows the propagation of the thermal stress along -axis for BEM, GFDM and FEM–NMM in the case of zero fractional order, and non-homogeneous . These findings for thermal stress in functionally graded magnetic thermoelectric materials, show that the BEM findings are in a very good agreement with the GFDM findings of Gu et al 55 , and FEM–NMM findings of An et al 56 . These results show that the BEM results are in a very good agreement to the FEM and NMM results.…”

Section: Numerical Results and Discussionsupporting

confidence: 87%

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RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

Fahmy

Almehmadi

Subhi

et al. 2022

Sci Rep

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The primary goal of this article is to propose a new fractional boundary element technique for solving nonlinear three-temperature (3 T) thermoelectric problems. Analytical solution of the current problem is extremely difficult to obtain. To overcome this difficulty, a new numerical technique must be developed to solve such problem. As a result, we propose a novel fractional boundary element method (BEM) to solve the governing equations of our considered problem. Because of the advantages of the BEM solution, such as the ability to treat problems with complicated geometries that were difficult to solve using previous numerical methods, and the fact that the internal domain does not need to be discretized. As a result, the BEM can be used in a wide variety of thermoelectric applications. The numerical results show the effects of the magnetic field and the graded parameter on thermal stresses. The numerical results also validate the validity and accuracy of the proposed technique.

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Section: Numerical Results and Discussionsupporting

confidence: 87%

“…Table 1 shows a comparison of required computer resources for the current BEM results, GFDM results of Gu et al 55 and FEM–NMM results of An et al 56 of modeling of fractional nonlinear three-temperature (3 T) thermoelectric problems.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

Fahmy

Almehmadi

Subhi

et al. 2022

Sci Rep

View full text Add to dashboard Cite

show abstract

“…It was first proposed by Liszka et al [21,22], later improved and extended by many other authors [23][24][25][26]. Before this study, this method has been successfully applied to heat transfer, elastic analysis and other engineering problems [27][28][29][30][31][32][33][34]. The main idea of the method is to combine the moving-least squares (MLS) approximation and the Taylor series expansion to derive explicit formulae for the required partial derivatives of unknown field variables.…”

Section: Treatment Of the Boundary Conditionsmentioning

confidence: 99%

A SPH-GFDM Coupled Method for Elasticity Analysis

et al. 2021

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SPH (smoothed particle hydrodynamics) is one of the oldest meshless methods used to simulate mechanics of continuum media. Despite its great advantage over the traditional grid-based method, implementing boundary conditions in SPH is not easy and the accuracy near the boundary is low. When SPH is applied to problems for elasticity, the displacement or stress boundary conditions should be suitably handled in order to achieve fast convergence and acceptable numerical accuracy. The GFDM (generalized finite difference method) can derive explicit formulae for required partial derivatives of field variables. Hence, a SPH–GFDM coupled method is developed to overcome the disadvantage in SPH. This coupled method is applied to 2-D elastic analysis in both symmetric and asymmetric computational domains. The accuracy of this method is demonstrated by the excellent agreement with the results obtained from FEM (finite element method) regardless of the symmetry of the computational domain. When the computational domain is multiply connected, this method needs to be further improved.

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“…To ensure the regularity of the matrix U as shown in Eq. (3.2) [33], the number of collocation points (N s +1)…”

Section: Influence Of Several Factors In the Lmfsmentioning

confidence: 99%

Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

Gu¹,

Fan²,

Fu³

2021

AAMM

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A localized version of the method of fundamental solution (LMFS) is devised in this paper for the numerical solutions of three-dimensional (3D) elasticity problems. The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation. Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations. Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies. The advantages, disadvantages and potential applications of the proposed method, as compared with the classical MFS and boundary element method (BEM), are discussed.

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The generalized finite difference method for long-time dynamic modeling of three-dimensional coupled thermoelasticity problems

Cited by 67 publications

References 45 publications

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

RETRACTED ARTICLE: Fractional boundary element solution of three-temperature thermoelectric problems

A SPH-GFDM Coupled Method for Elasticity Analysis

Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory

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