A 2D mechanical–thermal coupled model to simulate material mixing observed in friction stir welding process

Mesmoudi, Said; Timesli, Abdelaziz; Braikat, Bouazza; Lahmam, Hassane; Zahrouni, Hamid

doi:10.1007/s00366-017-0504-3

Cited by 37 publications

(22 citation statements)

References 19 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%

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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%

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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“…The choice of these proposed homotopy transformations leads to strong reduction of stiffness matrix triangulations. This high-order implicit algorithm was applied successfully to solving instationary nonlinear problems [15,28,18] and to structural nonlinear dynamic problems [8,9]. Two numerical examples of forced nonlinear dynamic problems of thin-walled beams with open cross section subjected to external arbitrary dynamic loads are analyzed to access the efficiency and the reliability of the developed high-order implicit algorithm by considering new homotopy transformations.…”

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confidence: 99%

Efficient high-order implicit solvers for the dynamic of thin-walled beams with open cross section under external arbitrary loadings

Kaimbillah¹,

Bourihane²,

Braikat³

et al. 2019

Discrete &Amp; Continuous Dynamical Systems - S

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This paper aims to investigate, in large displacement and torsion context, the nonlinear dynamic behavior of thin-walled beams with open cross section subjected to various loadings by high-order implicit solvers. These homotopy transformations consist to modify the nonlinear discretized dynamic problem by introducing an arbitrary invertible pre-conditioner [K ] and an arbitrary path following parameter. The nonlinear strongly coupled equations of these structures are derived by using a 3D nonlinear dynamic model which accounts for large displacements and large torsion without any assumption on torsion angle amplitude. Coupling complex structural phenomena such that warping, bending-bending, and flexural-torsion are taken into account. Two examples of great practical interest of nonlinear dynamic problems of various thin-walled beams with open section are presented to validate the Key words and phrases. Thin-walled beam, open cross section, large displacement, large torsion, forced nonlinear dynamic, finite element, homotopy, power series expansion, Asymptotic Numerical Method (ANM).

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A 2D mechanical–thermal coupled model to simulate material mixing observed in friction stir welding process

Cited by 37 publications

References 19 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

Efficient high-order implicit solvers for the dynamic of thin-walled beams with open cross section under external arbitrary loadings

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