The Method of Fundamental Solutions for Two- and Three-Dimensional Transient Heat Conduction Problems Involving Point and Curved Line Heat Sources

Mohammadi, M

doi:10.1007/s40997-019-00333-9

Cited by 5 publications

(2 citation statements)

References 32 publications

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“…The complex roots with positive imaginary part are denoted by μ 1 and μ 2 , which are used in Eqs. ( 17) and (18). P ik in Eq.…”

Section: Fundamental Solutions Of Two-dimensional Anisotropic Elasticitymentioning

confidence: 99%

“…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. These features make the MFS suitable for problems with moving/unknown boundary [13][14][15], for problems with concentrated loads [16][17][18], and moving load problems [19]. The boundary element method (BEM) is also a boundary-type method, which is based on the fundamental solutions of the problem, as in the MFS, and results in accurate solutions.…”

Section: Introductionmentioning

confidence: 99%

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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

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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.

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“…The complex roots with positive imaginary part are denoted by μ 1 and μ 2 , which are used in Eqs. ( 17) and (18). P ik in Eq.…”

Section: Fundamental Solutions Of Two-dimensional Anisotropic Elasticitymentioning

confidence: 99%

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

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Isogeometric boundary element method for steady-state heat transfer with concentrated/surface heat sources

Zang

Liu

Fraser

et al. 2021

Engineering Analysis with Boundary Elements

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Solving heat conduction problems with a moving heat source in arc welding processes via an overlapping nodes scheme based on the improved element-free Galerkin method

Hostos

Storti

Tourn

et al. 2022

International Journal of Heat and Mass Transfer

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The Method of Fundamental Solutions for Two- and Three-Dimensional Transient Heat Conduction Problems Involving Point and Curved Line Heat Sources

Cited by 5 publications

References 32 publications

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

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

Isogeometric boundary element method for steady-state heat transfer with concentrated/surface heat sources

Solving heat conduction problems with a moving heat source in arc welding processes via an overlapping nodes scheme based on the improved element-free Galerkin method

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