A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding

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

doi:10.1016/j.enganabound.2014.09.011

Cited by 42 publications

(27 citation statements)

References 17 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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“…In order to overcome the inversion of the tangent stiffness matrix at each time step, we adopt an homotopy technique used in the previous work of the same authors [8]. Its consists to introduce an arbitrary invertible matrix and apply an homotopy transformation which acts both on quadratic term and on the right hand side as follows [8,15,28,9,13] :…”

Section: The Homotopy Transformationsmentioning

confidence: 99%

“…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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“…The overwhelming majority of the theoretical works is concerned with simulations of the welding process and velocity and temperature field distributions around the rotated FSW tool [17][18][19][20][21], including the microstructural evolution during the process [22,23]. Investigations dealing with modelling the mechanical loading of metal pieces butted together by the FSW technique are few in number and have been performed for the most part with the use of essentially idealized macroscopic models [18,[24][25][26][27], even though they were based on a multiscale methodology [28]. The welded joint zone as a rule is idealized and represents a regularly shaped region with plane interfaces, whereas the material inside the weld region is homogeneous.…”

Section: Introductionmentioning

confidence: 99%

A mesomechanical analysis of the stress–strain localisation in friction stir welds of polycrystalline aluminium alloys

et al. 2015

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A numerical analysis is presented of the microstructural effects on the deformation and fracture of friction stir welds in aluminium alloys. A dynamic boundary-value problem in a plane strain formulation is solved numerically by the finite-difference method. Experimental polycrystalline microstructures inherent in different weld zones-base material, weld nugget, and thermo-mechanically affected zones-were accounted for explicitly in the calculations. To simulate the mechanical response of individual grains, use was made of an elastic-plastic formulation of the problem accounting for isotropic strain hardening, including the Hall-Petch effect, and of a fracture model allowing for crack initiation and growth in the regions of maximum equivalent plastic strains. Plastic strain and fracture localisation is shown to depend on the strength of welded materials.

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A new algorithm based on Moving Least Square method to simulate material mixing in friction stir welding

Cited by 42 publications

References 17 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

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

A mesomechanical analysis of the stress–strain localisation in friction stir welds of polycrystalline aluminium alloys

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