An Implicit Algorithm Based on Continuous Moving Least Square to Simulate Material Mixing in Friction Stir Welding Process

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

doi:10.1155/2013/716383

Cited by 12 publications

(8 citation statements)

References 22 publications

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“…The objective in the future is to apply this approach on other type of shells, such as FGM cylindrical Shells [15,19]. In addition, we will try to develop meshless models [20][21][22][23][24][25][26][27] based on TSDT theory for the analysis of FGM plates. Comparison of natural frequencies between a laminated P-FGM plate and a simple P-FGM plate using the power law.…”

Section: Discussionmentioning

confidence: 99%

TSDT theory for free vibration of functionally graded plates with various material properties

Allah¹,

Belaasilia²,

Timesli³

et al. 2021

Math. Model. Comput.

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In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

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Section: Discussionmentioning

confidence: 99%

TSDT theory for free vibration of functionally graded plates with various material properties

Allah¹,

Belaasilia²,

Timesli³

et al. 2021

Math. Model. Comput.

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“…It is noted that the critical parameters of the pulsation

{\omega}_c

and of the Strouhal number

S{t}_c

, for which a Hopf bifurcation point is detected by the indicator, are expressed by:

{\omega}_c=\omega \left({\eta}^h\approx 0\right);\kern1em S{t}_c=\frac{D{\omega}_c}{2\pi {u}_d}.

In these tests, we adopt the direct dynamic simulation by the high order mesh‐free algorithm proposed in References 35‐38 to confirm the results obtained by the presented indicator, as well as a comparison with those of references available in the literature in each case.…”

Section: Numerical Applicationmentioning

confidence: 99%

Mesh‐free model for Hopf's bifurcation points in incompressible fluid flows problems

Rammane

Mesmoudi

Tri

et al. 2022

Numerical Methods in Fluids

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In this article, a new numerical model is proposed to detect numerically the Hopf bifurcation point of incompressible fluid flows problems. The concept of this model consists to propose a Hopf bifurcation indicator which is solved by a high order mesh free algorithm (HO‐MFA) using the moving least squares (MLS) approximation. This numerical model is based on a strong formulation of Navier–Stokes equations. This procedure allowed us to recover the results of the literature in 3D$$ 3D $$ using only a 2D$$ 2D $$ modelization for low Reynolds number. This new model is tested on the classical flow around a cylindrical obstacle and the backward‐facing step flow to show the advantage and ability of the proposed model to detect the bifurcation points and to determinate the flow periodicity.

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“…It is shown in the next section that RLS algorithm which needs more computational power for the present problem benefits in terms of minimizing the MSE which drops from 152 to just over 1 for the testing data. There are certainly some emerging algorithms [30][31][32][33][34] and conventional techniques of algorithm manipulation [35,36] with varying degree of complexity which can lead to the potential expansions of this work.…”

Section: Computational Complexitymentioning

confidence: 99%

On Modelling and Comparative Study of LMS and RLS Algorithms for Synthesis of MSA

Hassan

Affandi

2016

Modelling and Simulation in Engineering

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This paper deals with analytical modelling of microstrip patch antenna (MSA) by means of artificial neural network (ANN) using least mean square (LMS) and recursive least square (RLS) algorithms. Our contribution in this work is twofold. We initially provide a tutorial-like exposition for the design aspects of MSA and for the analytical framework of the two algorithms while our second aim is to take advantage of high nonlinearity of MSA to compare the effectiveness of LMS and that of RLS algorithms. We investigate the two algorithms by using gradient decent optimization in the context of radial basis function (RBF) of ANN. The proposed analysis is based on both static and adaptive spread factor. We model the forward side or synthesis of MSA by means of worked examples and simulations. Contour plots, 3D depictions, and Tableau presentations provide a comprehensive comparison of the two algorithms. Our findings point to higher accuracies in approximation for synthesis of MSA using RLS algorithm as compared with that of LMS approach; however the computational complexity increases in the former case.

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An Implicit Algorithm Based on Continuous Moving Least Square to Simulate Material Mixing in Friction Stir Welding Process

Cited by 12 publications

References 22 publications

TSDT theory for free vibration of functionally graded plates with various material properties

TSDT theory for free vibration of functionally graded plates with various material properties

Mesh‐free model for Hopf's bifurcation points in incompressible fluid flows problems

On Modelling and Comparative Study of LMS and RLS Algorithms for Synthesis of MSA

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