Application of radial basis functions to linear and nonlinear structural analysis problems

Tiago, Carlos; Leitão, Vitor M.A.

doi:10.1016/j.camwa.2006.04.008

Cited by 30 publications

(14 citation statements)

References 23 publications

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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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“…Nevertheless, the possibility of obtaining numerical solutions without resorting to the mesh-based techniques mentioned above, has been the goal of many researchers throughout the computational mechanics community for the past two decades or so. Radial basis function (RBF) is one of the most recently developed meshless methods that has attracted attention in recent years, especially in the area of computational mechanics [6][7][8]. This method does not require mesh generation which makes them advantageous for 3-D problems as well as problems that require frequent re-meshing such as those arising in non-linear analysis.…”

Section: Introductionmentioning

confidence: 99%

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

Al-Gahtani

Naffa'a

2009

Engineering Analysis with Boundary Elements

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“…The first three vibration modes were then calculated. The application of using radial basis functions to solve twodimensional engineering beam problems were discussed by Tiago and Leita˜o (2006). The present study attempts to solve the more complicated practical engineering problem of calculating the reference pretension forces of a cable-stayed bridge.…”

Section: Introductionmentioning

confidence: 99%

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

Shum¹,

Tsang²

2008

Bridge Structures

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A proposal for a numerical method based on the complete solution collocation method is presented to solve the cable-stayed bridge engineering structural problem. This complete function collocation method is presented from the viewpoint of calculating the pretension forces required for the final completed bridge structure, which is one of the most important and practical considerations in cable-stayed bridge design. The complete function collocation method is used to calculate stay cable forces by solving a set of partial differential equations. The study shows that this mesh-free collocation method can be used to solve practical structural engineering problems and provides an alternative to traditional finite element methods. A simple two-dimensional cable-stayed bridge is presented and is solved to illustrate this numerical method. Governing equations of deformation for a bridge structure are formulated in either Eulerian or Lagrangian coordinate systems according to the situation. Point loads due to stay cables on bridge pylons and bridge deck are modelled by Fourier or Gaussian representations. Transverse natural frequencies of stay cables subject to no body forces and caused by flow-induced vibration due to blowing wind are proposed. The preliminary computational procedure presented in this paper provides the basis for further analysis toward more realistic cable-stayed bridges, which would include nonlinear effects, live loadings and construction stage loadings.

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Application of radial basis functions to linear and nonlinear structural analysis problems

Cited by 30 publications

References 23 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 meshless method for large deflection of thin plates with immovable edges

Complete function collocation method for solving preliminary cable-stayed bridge pretension forces

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