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ON THE SYMMETRIES OF THE Sol<sub>3</sub> LIE GROUP
Belarbi, Lakehal Korean Mathematical Society 2020 대한수학회지 Vol.57 No.2
In this work we consider the Sol<sub>3</sub> Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.
ON TRANSLATION SURFACES WITH ZERO GAUSSIAN CURVATURE IN LORENTZIAN SOL<sub>3</sub> SPACE
BELARBI, LAKEHAL,ZOUBIR, HANIFI The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6
In this work we classified translation invariant surfaces with zero Gaussian curvature in the 3-dimensional Sol Lie group endowed with Lorentzian metric.
Belarbi, Abdeldjelil,Prakash, Suriya,You, Young-Min Techno-Press 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.33 No.2
This paper investigates the behavior of reinforced concrete (RC) circular columns under combined loading including torsion. The main variables considered in this study are the ratio of torsional moment to bending moment (T/M) and the level of detailing for moderate and high seismicity (low and high transverse reinforcement/spiral ratio). This paper presents the results of tests on seven columns subjected to cyclic bending and shear, cyclic torsion, and various levels of combined cyclic bending, shear, and torsion. Columns under combined loading were tested at T/M ratios of 0.2 and 0.4. These columns were reinforced with two spiral reinforcement ratios of 0.73% and 1.32%. Similarly, the columns subjected to pure torsion were tested with two spiral reinforcement ratios of 0.73% and 1.32%. This study examined the significance of proper detailing, and spiral reinforcement ratio and its effect on the torsional resistance under combined loading. The test results demonstrate that both the flexural and torsional capacities are decreased due to the effect of combined loading. Furthermore, they show a significant change in the failure mode and deformation characteristics depending on the spiral reinforcement ratio. The increase in spiral reinforcement ratio also led to significant improvement in strength and ductility.
Abdeldjelil Belarbi,Suriya Prakash,Young-Min You 국제구조공학회 2009 Structural Engineering and Mechanics, An Int'l Jou Vol.33 No.2
This paper investigates the behavior of reinforced concrete (RC) circular columns under combined loading including torsion. The main variables considered in this study are the ratio of torsional moment to bending moment (T/M) and the level of detailing for moderate and high seismicity (low and high transverse reinforcement/spiral ratio). This paper presents the results of tests on seven columns subjected to cyclic bending and shear, cyclic torsion, and various levels of combined cyclic bending, shear, and torsion. Columns under combined loading were tested at T/M ratios of 0.2 and 0.4. These columns were reinforced with two spiral reinforcement ratios of 0.73% and 1.32%. Similarly, the columns subjected to pure torsion were tested with two spiral reinforcement ratios of 0.73% and 1.32%. This study examined the significance of proper detailing, and spiral reinforcement ratio and its effect on the torsional resistance under combined loading. The test results demonstrate that both the flexural and torsional capacities are decreased due to the effect of combined loading. Furthermore, they show a significant change in the failure mode and deformation characteristics depending on the spiral reinforcement ratio. The increase in spiral reinforcement ratio also led to significant improvement in strength and ductility.
On the symmetries of the $Sol_{3}$ Lie group
Lakehal Belarbi 대한수학회 2020 대한수학회지 Vol.57 No.2
In this work we consider the $Sol_{3}$ Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations.
Karima Belarbi,Fawzia Atik-Bekkara,Imad Abdelhamid El Haci,Ilhem Bensaid,Fawzia Beddou,Chahrazed Bekhechi 경희대학교 융합한의과학연구소 2017 Oriental Pharmacy and Experimental Medicine Vol.17 No.2
Teucrium pseudo-Scorodonia Desf., is one of many Mediterranean plants widely used in Algerian folk medicine for their medicinal properties. This study represents the first antioxidant investigation of Teucrium pseudo-Scorodonia with different analytical methods. Total phenolic, flavonoid, and condensed tannin contents were determined using spectrophotometric techniques. In vitro antioxidant and radical scavenging profiling was determined through total antioxidant capacity (TAC), DPPH radical-scavenging, ferric reducing antioxidant power (FRAP), and β-carotene bleaching assays. Leaf extracts exhibited high total phenolics (266.36 ± 0.14 mg GAE/g DW), flavonoids (161.23 ± 0.18 mg CE/g DW) and condensed tannins (5.00 ± 0.08 mg CE/g DW) contents. The greatest antioxidant activity was founding in the butanolic fraction of leaves (IC50.DPPH = 0.05 ± 0.00 mg/ml) followed by crude methanolic extract and ethyl acetate fraction. These values were to some extent high in comparison to the positive control (0.07 ± 0.01 mg/ml). The same tendency was observed with ferric reducing power. A strong correlation of IC50 values of antioxidant assays with total phenolics and total flavonoids content of T. pseudo-Scorodonia was exhibited in this study. Thin layer chromatographic (TLC) screening using DPPH radical, AlCl3 and FeCl3 as detection reagents led to the identification of potent antioxidant compounds: methylated flavonoids or hydroxyflavonols. These results indicate that flavonoids and phenolics can be the major contributors to the antioxidant activity observed for the T. pseudo-Scorodonia leaf extracts. Further study is necessary for isolation and characterization of the active antioxidants, which may serve as a potential source of natural antioxidants.
Strength buckling predictions of cold-formed steel built-up columns
A. Belarbi,A. Megnounif,M. Djafour,D. Kerdal 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.4
The aim of this paper is to propose a design procedure for predicting the buckling strength of built-up, cold-formed steel columns based on the two well known methods; the effective width method and the Direct Strength Method. Several design approaches, based on different elastic buckling solutions, were considered in this investigation. Traditional hand methods, without interaction effects between the different modes, and a new numerical spline finite strip method were used to predict the buckling stresses. All of the proposed methods were compared with experimental data on plain and lipped, built-up columns. Results have shown that the effective width approaches are more accurate than the Direct Strength Method. However, both methods can be investigated using more experimental data to assess a practical design method for built-up columns.
Mohamed-Ouejdi Belarbi,Abdelouahab Tati,Houdayfa Ounis,Adel Benchabane 국제구조공학회 2016 Structural Engineering and Mechanics, An Int'l Jou Vol.57 No.3
The aim of this work is the development of a 2D quadrilateral isoparametric finite element model, based on a layerwise approach, for the bending analysis of sandwich plates. The face sheets and the core are modeled individually using, respectively, the first order shear deformation theory and the third-order plate theory. The displacement continuity condition at the interfaces „face sheets-core‟ is satisfied. The assumed natural strains method is introduced to avoid an eventual shear locking phenomenon. The developed element is a four-nodded isoparametric element with fifty two degrees-of-freedom (52 DOF). Each face sheet has only two rotational DOF per node and the core has nine DOF per node: six rotational degrees and three translation components which are common for the all sandwich layers. The performance of the proposed element model is assessed by six examples, considering symmetric/unsymmetric composite sandwich plates with different aspect ratios, loadings and boundary conditions. The numerical results obtained are compared with the analytical solutions and the numerical results obtained by other authors. The results indicate that the proposed element model is promising in terms of the accuracy and the convergence speed for both thin and thick plates.
Mohamed-Ouejdi Belarbi,Sattar Jedari Salami,Aman Garg,Hicham Hirane,Daikh Ahmed Amine,Mohammed Sid Ahmed Houari 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.44 No.4
In the present paper, the static bending and buckling responses of functionally graded carbon nanotubes-reinforced composite (FG-CNTRC) beam under various boundary conditions are investigated within the framework of higher shear deformation theory. The significant feature of the proposed theory is that it provides an accurate parabolic distribution of transverse shear stress through the thickness satisfying the traction-free boundary conditions needless of any shear correction factor. Uniform (UD) and four graded distributions of CNTs which are FG-O, FG-X, FG- and FG-V are selected here for the analysis. The effective material properties of FG-CNTRC beams are estimated according to the rule of mixture. To model the FG-CNTRC beam realistically, an efficient Hermite–Lagrangian finite element formulation is successfully developed. The accuracy and efficiency of the present model are demonstrated by comparison with published benchmark results. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, and length-to-thickness ratio on the bending and buckling responses of FGCNTRC beam. Several new referential results are also reported for the first time which will serve as a benchmark for future studies in a similar direction. It is concluded that the FG-X-CNTRC beam is the strongest beam that carries the lowest central deflection and is followed by the UD, V, Λ, and FG-O-CNTRC beam. Besides, the critical buckling load belonging to the FG-XCNTRC beam is the highest, followed by UD and FG-O.
$F$-Biharmonic curves in three-dimensional generalized symmetric spaces
Yasmine Bahous,Lakehal Belarbi,Mansour Belarbi,Hichem Elhendi 한국전산응용수학회 2024 Journal of applied mathematics & informatics Vol.42 No.1
In this work we give the necessary and sufficient conditions for $f$-biharmonic curves in three-dimensional generalized symmetric spaces.