Application of method of fundamental solutions for elasto-plastic torsion of prismatic rods

Kołodziej, Jan Adam; Gorzelańczyk, Piotr

doi:10.1016/j.enganabound.2011.06.010

Cited by 29 publications

(21 citation statements)

References 21 publications

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“…Even the BEM utilized in [16] requires that the boundary be discretized and, hence, is not purely meshless. Although studies such as [17] utilize the RBF as an interpolant of the non-homogeneous term of the governing equation, the fact still remains that they use this approach in conjunction with another to obtain the overall solution. For instance, in Ref.…”

Section: Analysis Of Elasto-plastic Torsionmentioning

confidence: 99%

“…Description of the data for this problem is given in Ref. [17]. Same values of the parameter m (0.0, 0.1, 0.2, 0.5 and 1.0) and the Poisson ratio of m ¼ 0:3 as used in [17] are used here.…”

Section: Numerical Examplementioning

confidence: 99%

“…Only the end results are summarized here. The approach used in [17] is based on the assumption that the displacements are the same as in the case of elastic torsion. The resulted governing equation is the following Poisson equation with a nonlinear right hand side involving the plastic strains.…”

Section: Governing Equationsmentioning

confidence: 99%

“…[17] MFS is used as the main solution technique with the RBF used only to interpolate the right hand side of the governing equation. Hence, the study presented in this paper makes use of the RBF alone in solving elasto-plastic torsion of bars and the result verified against an FDM solution and that reported in [17]. As will be seen, the RBF approach results into an enormous reduction in the computational effort compared to that using MFS.…”

Section: Analysis Of Elasto-plastic Torsionmentioning

confidence: 99%

“…Boundary element method (BEM), a mesh reduction method that requires boundary-only discretization, was applied by Sapountzakis and Tsipiras [16] to analyze non-linear elasticplastic uniform torsion problem. MFS was used by Kolodziej and Gorzelanczyk [17] to analyze both elastic and elasto-plastic torsion of bars. The non-linear torsion problem in plastic region was solved by means of the Picard iteration.…”

Section: Analysis Of Elasto-plastic Torsionmentioning

confidence: 99%

See 4 more Smart Citations

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: Analysis Of Elasto-plastic Torsionmentioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

Section: Governing Equationsmentioning

confidence: 99%

Section: Analysis Of Elasto-plastic Torsionmentioning

confidence: 99%

Section: Analysis Of Elasto-plastic Torsionmentioning

confidence: 99%

See 3 more Smart Citations

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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Growth of Yield Front of Functionally Graded Non-uniform Bars Under Thermal Load

Nayak

Saha

2019

Lecture Notes on Multidisciplinary Industrial Engineering

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A meshless procedure for analysis of fluid flow and heat transfer in an internally finned square duct

Grabski

2019

Heat Mass Transfer

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Application of the method of fundamental solutions in combination with the global radial basis function collocation method for analysis of fluid flow and heat transfer in an internally finned square duct is presented in the paper. Fluid flow problem is solved using the modified method of fundamental solutions. After that, the average fluid velocity and product of friction factor and Reynolds number can be determined. Heat transfer problem in the fluid is governed by a nonlinear equation with linear boundary conditions. The Picard iteration method is employed in the paper in order to transform the nonlinear problem into a sequence of inhomogeneous problems. At each iteration step, the general solution is obtained using the modified method of fundamental solutions and the particular solution is obtained using the global radial basis function collocation method. When the iteration process is stopped, the Nusselt number can be determined. Nomenclature aHalf of internal width of channel [m] bThickness of wall [m]

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Application of method of fundamental solutions for elasto-plastic torsion of prismatic rods

Cited by 29 publications

References 21 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

Growth of Yield Front of Functionally Graded Non-uniform Bars Under Thermal Load

A meshless procedure for analysis of fluid flow and heat transfer in an internally finned square duct

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