RBF meshless method for large deflection of thin plates with immovable edges

Al-Gahtani, Husain J.; Naffa'a, Mahmoud

doi:10.1016/j.enganabound.2008.05.004

Cited by 21 publications

(2 citation statements)

References 20 publications

(23 reference statements)

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“…Evaluation of the particular solution for non-homogeneous problems requires combining the boundary-type RBF collocation methods with other techniques such as the dual reciprocity method (DRM) [56] and multiple reciprocity method (MRM) [57]. From application view point, different forms of RBF collocation methods have been applied to several problems in the area of computational mechanics [58][59][60][61][62][63][64][65][66][67][68].…”

Section: Rbf-based Collocation Methodsmentioning

confidence: 99%

Application of radial basis functions to the problem of elasto-plastic torsion of prismatic bars

Mukhtar

Al-Gahtani

2016

Applied Mathematical Modelling

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a b s t r a c tThis paper demonstrates the use of a well-known meshless method, radial basis functions (RBF), to solve the torsion of a prismatic bar having a rectangular/square cross-section. First part of the analysis deals with the elastic solution of the problem formulated using the RBF technique. The result is used in verifying the feasibility of the approach and, subsequently, as an initial guess for the iterative procedure utilized in the analysis of the elasto-plastic torsional behavior of the bar. Verification of the results is made using finite difference method (FDM), method of fundamental solutions (MFS) and the exact elastic solution.

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Section: Rbf-based Collocation Methodsmentioning

confidence: 99%

Application of radial basis functions to the problem of elasto-plastic torsion of prismatic bars

Mukhtar

Al-Gahtani

2016

Applied Mathematical Modelling

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“…The method, however, has not been applied directly to partial differential equations until 1990 by Kansa [15,16]. Since then, many researchers have suggested several variations to the original method [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

RBF-Based Meshless Method for Large Deflection of Elastic Thin Rectangular Plates with Boundary Conditions Involving Free Edges

Al-Tholaia

Al-Gahtani

2016

Mathematical Problems in Engineering

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An RBF-based meshless method is presented for the analysis of thin plates undergoing large deflection. The method is based on collocation with the multiquadric radial basis function (MQ-RBF). In the proposed method, the resulting coupled nonlinear equations are solved using an incremental-iterative procedure. The accuracy and efficiency of the method are verified through several numerical examples. The inclusion of the free edge boundary condition proves that this method is accurate and efficient in handling such complex boundary value problems.

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Different Formulations of the Kansa Method: Domain Discretization

Chen

2013

Recent Advances in Radial Basis Function Collocation Methods

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RBF meshless method for large deflection of thin plates with immovable edges

Cited by 21 publications

References 20 publications

Application of radial basis functions to the problem of elasto-plastic torsion of prismatic bars

Application of radial basis functions to the problem of elasto-plastic torsion of prismatic bars

RBF-Based Meshless Method for Large Deflection of Elastic Thin Rectangular Plates with Boundary Conditions Involving Free Edges

Different Formulations of the Kansa Method: Domain Discretization

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