Belaidi Idir

Publications

1 Applying Element Free Galerkin Method on Beam and Plate

Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: Numerical computation, Meshless Methods, element-free Galerkin, moving least squares

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Abstracts

2 Applying Element Free Galerkin Method on Beam and Plate

Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: Numerical computation, Meshless Methods, element-free Galerkin (EFG), moving least squares (MLS)

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1 The Consequences of Vibrations in Machining

Authors: Belaidi Idir, Boughedaoui Rachid, Ouali Mohamed

Abstract:

The formatting by removal of material remains an indispensable means for obtaining different forms of pieces. The objective of this work is to study the influence of parameters of the vibratory regime of the system PTM 'Piece-Tool-Machine, in the case of the machining of the thin pieces on the surface finish. As a first step, an analytical study of essential dynamic models 2D slice will be presented. The stability lobes will be thus obtained. In a second step, a characterization of PTM system will be realized. This system will be instrumented with accelerometric sensors but also a laser vibrometer so as to have the information closer to the cutting area. Dynamometers three components will be used for the analysis of cutting forces. Surface states will be measured and the condition of the cutting edge will be visualized thanks to a binocular microscope coupled to a data acquisition system. This information will allow quantifying the influence of chatter on the dimensional quality of the parts. From lobes stabilities previously determined experimental validation allow for the development a method for detecting of the phenomenon of chatter and so an approach will be proposed.

Keywords: Dynamic, Milling, chatter, lobe stability

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