A numerical mesh-free model for elasto-plastic contact problems

Belaasilia, Youssef; Timesli, Abdelaziz; Braikat, Bouazza; Jamal, Mohammad

doi:10.1016/j.enganabound.2017.05.010

Cited by 37 publications

(25 citation statements)

References 28 publications

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“…is a quadratic form, which represents the convection term; and F is a given force vector. In the following section, we present the description of the HO‐MFA to solve problem . We show that this HO‐MFA is a powerful continuation method, which can be applied without correction.…”

Section: Mathematical Formulationmentioning

confidence: 99%

“…In other works, the high‐order mesh‐free approach (HO‐MFA) is used for the computation of elasto‐plastic contact problems, the treatment of the frictional contact of two elastic deformable bodies in the static case, and buckling and postbuckling analysis of shells. In another hand, this algorithm is used for the simulation of material mixing observed in friction stir welding (FSW) process in dynamic case …”

Section: Introductionmentioning

confidence: 99%

“…We also present the computation of the solution from a weak formulation using the high order with the finite element method (HO‐FEM) for comparison . To demonstrate the effectiveness and the robustness of the presented algorithm in comparison with an iterative algorithm based on the Newton‐Raphson method with MLS and HO‐FEM, three examples of an incompressible fluid flows are studied.…”

Section: Introductionmentioning

confidence: 99%

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Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

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Summary In this paper, we propose for the first time to extend the application field of the high‐order mesh‐free approach to the stationary incompressible Navier‐Stokes equations. This approach is based on a high‐order algorithm, which combines a Taylor series expansion, a continuation technique, and a moving least squares (MLS) method. The Taylor series expansion permits to transform the nonlinear problem into a succession of continuous linear ones with the same tangent operator. The MLS method is used to transform the succession of continuous linear problems into discrete ones. The continuation technique allows to compute step‐by‐step the whole solution of the discrete problems. This mesh‐free approach is tested on three examples: a flow around a cylindrical obstacle, a flow in a sudden expansion, and the standard benchmark lid‐driven cavity flow. A comparison of the obtained results with those computed by the Newton‐Raphson method with MLS, the high‐order continuation with finite element method, and those of literature is presented.

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Section: Mathematical Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solving the incompressible fluid flows by a high‐order mesh‐free approach

Rammane

Mesmoudi

Tri

et al. 2019

Numerical Methods in Fluids

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“…To overcome these disadvantages, meshless methods have been successfully developed. We use among these MLS meshless presented in [6,7] for approximate the unknowns of the problem at any point M (x, y) of support Ω s as follow:…”

Section: Mls Approximationmentioning

confidence: 99%

“…In addition, this technique consists in considering the point ({V (a max )}, λ(a max ) as being the starting point ({V 0 }, λ 0 ) of the following branch. The whole solution of the problems (10, 11) is determined branch by branch [8,6,7].…”

Section: Continuation Techniquementioning

confidence: 99%

A mesh-free approach for the simulation of incompressible flows

et al. 2019

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In this work, we propose to investigate numerically the incompressible flows by the Asymptotic Numerical Method (ANM) with the Moving Least Square (MLS). The mathematical formulation is based on theNavier-Stokes equations written in a strongly formulation to avoid all difficulties of the numerical integration. The used algorithm is developed to investigate the effective of the ANM with the MLS in the strongly formulation.

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Bifurcation points and bifurcated branches in fluids mechanics by high‐order mesh‐free geometric progression algorithms

Rammane

Mesmoudi

Tri

et al. 2020

Numerical Methods in Fluids

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In this article, we propose to investigate numerically the steady bifurcation points and bifurcated branches in fluid mechanics by employing high‐order mesh‐free geometric progression algorithms. These algorithms are based on the use of the geometric progression (GP) in a high‐order mesh‐free approach. The first proposed algorithm is applied on a strong formulation using the moving least squares (MLS) approximation coupled with GP (HO‐MLS‐GPM). While the second proposed algorithm is applied on a weak formulation using the element‐free Galerkin (EFG) coupled also with GP (HO‐EFG‐GPM). The incompressibility condition is taken by introducing the penalty technique to transform the stationary Navier–Stokes equations verified by the pressure and velocity into ones verified by only the velocity. The high‐order mesh‐free algorithm permits to transform this nonlinear equations into a succession of linear ones. The GP allows to detect with precision the bifurcation points and the Lyapunov–Schmidt reduction is coupled with HO‐MLS‐GPM and HO‐EFG‐GPM as a continuation procedure to follow the many bifurcated branches. The aim of this resolution strategy concerns the treatment of the bifurcation phenomena for a fluid flow through an expansion in several geometries, where the steady flow becomes unstable after a critical Reynolds value. The obtained results are compared with those presented in literature and with those computed using the high‐order finite element algorithm coupled with GP.

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A numerical mesh-free model for elasto-plastic contact problems

Cited by 37 publications

References 28 publications

Solving the incompressible fluid flows by a high‐order mesh‐free approach

Solving the incompressible fluid flows by a high‐order mesh‐free approach

A mesh-free approach for the simulation of incompressible flows

Bifurcation points and bifurcated branches in fluids mechanics by high‐order mesh‐free geometric progression algorithms

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