The global approximate particular solution meshless method for two-dimensional linear elasticity problems

C. A. Bustamante; H. Power; W. F. Florez; C. Y. Hang

doi:10.1080/00207160.2012.741227

The global approximate particular solution meshless method for two-dimensional linear elasticity problems

C. A. Bustamante
, H. Power
, W. F. Florez
, C. Y. Hang

Research output: Contribution to scientific journal › Article in an indexed scientific journal › peer-review

13 Scopus citations

Abstract

The two-dimensional linear elasticity equations are solved by the global method of approximate particular solution as a new meshless option to the conventional finite element discretization. The displacement components are approximated by a linear combination of the elasticity particular solutions and the stress tensor is obtained by differentiating the displacement expressions in terms of the particular solutions. The multiquadric radial basis function (RBF) is employed as the non-homogeneous term in the governing equation to compute the particular solutions. The cantilever beam and the infinite plate with a hole problem are solved to verify the implemented meshless method. For each situation, the trend of the root mean square error is assessed in terms of the shape parameter and the number of nodes. Unlike most of the RBF collocation strategies, it is found that numerical results are in good agreement with the analytical solutions for a wide range of shape parameter values.

Original language	English
Pages (from-to)	978-993
Number of pages	16
Journal	International Journal of Computer Mathematics
Volume	90
Issue number	5
DOIs	https://doi.org/10.1080/00207160.2012.741227
State	Published - May 2013

Bibliographical note

Funding Information:
This work was partially supported by the Mustang project, A multiple space and time scale approach for the quantification of deep saline formations for CO2 storage funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under grant agreement [227286] as well as by COLCIENCIAS and Empresas Públicas de Medellín (EPM), Colombia, as part of the funding provided to the project Energetic assessment of the San Fernando plant bio-solids.

Keywords

meshless methods
particular solutions
plane elasticity
radial basis functions

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10.1080/00207160.2012.741227

Cite this

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title = "The global approximate particular solution meshless method for two-dimensional linear elasticity problems",

abstract = "The two-dimensional linear elasticity equations are solved by the global method of approximate particular solution as a new meshless option to the conventional finite element discretization. The displacement components are approximated by a linear combination of the elasticity particular solutions and the stress tensor is obtained by differentiating the displacement expressions in terms of the particular solutions. The multiquadric radial basis function (RBF) is employed as the non-homogeneous term in the governing equation to compute the particular solutions. The cantilever beam and the infinite plate with a hole problem are solved to verify the implemented meshless method. For each situation, the trend of the root mean square error is assessed in terms of the shape parameter and the number of nodes. Unlike most of the RBF collocation strategies, it is found that numerical results are in good agreement with the analytical solutions for a wide range of shape parameter values.",

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author = "Bustamante, \{C. A.\} and H. Power and Florez, \{W. F.\} and Hang, \{C. Y.\}",

note = "Funding Information: This work was partially supported by the Mustang project, A multiple space and time scale approach for the quantification of deep saline formations for CO2 storage funding from the European Community{\textquoteright}s Seventh Framework Programme [FP7/2007-2013] under grant agreement [227286] as well as by COLCIENCIAS and Empresas P{\'u}blicas de Medell{\'i}n (EPM), Colombia, as part of the funding provided to the project Energetic assessment of the San Fernando plant bio-solids.",

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AU - Hang, C. Y.

N1 - Funding Information: This work was partially supported by the Mustang project, A multiple space and time scale approach for the quantification of deep saline formations for CO2 storage funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under grant agreement [227286] as well as by COLCIENCIAS and Empresas Públicas de Medellín (EPM), Colombia, as part of the funding provided to the project Energetic assessment of the San Fernando plant bio-solids.

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N2 - The two-dimensional linear elasticity equations are solved by the global method of approximate particular solution as a new meshless option to the conventional finite element discretization. The displacement components are approximated by a linear combination of the elasticity particular solutions and the stress tensor is obtained by differentiating the displacement expressions in terms of the particular solutions. The multiquadric radial basis function (RBF) is employed as the non-homogeneous term in the governing equation to compute the particular solutions. The cantilever beam and the infinite plate with a hole problem are solved to verify the implemented meshless method. For each situation, the trend of the root mean square error is assessed in terms of the shape parameter and the number of nodes. Unlike most of the RBF collocation strategies, it is found that numerical results are in good agreement with the analytical solutions for a wide range of shape parameter values.

AB - The two-dimensional linear elasticity equations are solved by the global method of approximate particular solution as a new meshless option to the conventional finite element discretization. The displacement components are approximated by a linear combination of the elasticity particular solutions and the stress tensor is obtained by differentiating the displacement expressions in terms of the particular solutions. The multiquadric radial basis function (RBF) is employed as the non-homogeneous term in the governing equation to compute the particular solutions. The cantilever beam and the infinite plate with a hole problem are solved to verify the implemented meshless method. For each situation, the trend of the root mean square error is assessed in terms of the shape parameter and the number of nodes. Unlike most of the RBF collocation strategies, it is found that numerical results are in good agreement with the analytical solutions for a wide range of shape parameter values.

KW - meshless methods

KW - particular solutions

KW - plane elasticity

KW - radial basis functions

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M3 - Artículo en revista científica indexada

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SN - 0020-7160

VL - 90

SP - 978

EP - 993

JO - International Journal of Computer Mathematics

JF - International Journal of Computer Mathematics

IS - 5

ER -

The global approximate particular solution meshless method for two-dimensional linear elasticity problems

Abstract

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Keywords

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