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Volume 10, Number 2, June 2021

An analytical method based on the compatibility of deformations and equilibrium of forces is investigated to predict the reinforcement plate area in concrete beams strengthened with Functionally Graded (FG) plates bonded to the tension face of the beams. The models are given for beams having rectangular and T-crosssections. The effect of porosity that can happen inside FGM materials during their manufacture is also shown. New rules of the mixture that take into account different distribution rates of porosity in FG plates have been developed in this study. A parametric study is conducted to investigate the effect of several parameters such as the ultimate moment, plate stiffness, the distribution rate of the porosity, and compressive strength of the concrete. The results obtained show a significant gain in the reinforcement plate area of the RC beam strengthened with an FG plate relative to another reinforced with FRP plate, which makes it possible to reduce the interfacial stresses and prevents detachment of the reinforcing plate.

Key Words
RC beam; reinforcement; FGM plate; porosity

(1) Laboratory of Geomatics and sustainable development, University of Tiaret, Algeria;
(2) Department of Civil Engineering, Ibn Khaldoun University of Tiaret, Algeria.

The slope design under geological and hydraulic conditions has always been a different geotechnics problem. There have been potential main landslide and an undisturbed thin layer of saturated clays soil under the slopes in urban construction development area of Miliana city province of Algeria; its terrain is mountains. The landslide was framed by gravity creeping of thin layer of alluvium and mares cracks along steep clays. The favorable sliding surface larger than 2500 m2 had destroyed the foundation of the building. In order to learn from the comparison between stabilized and non-stabilized slopes with different improvement, the authors also investigated the slopes reinforced by retaining wall with prestressed anchor and discussed their behavior parameters. Based on finite element method, the analysis of slope stability under natural conditions is discussed first, then the support structure of retaining wall and anchor reinforced and their effect of slope stability are analyzed, and also the slope stability of each case is able to be compared. The results show that the stability of slope was significantly improved after reinforcement, and anchor reinforced with retaining wall has obvious reverse anchoring effect on soil. By comparing the factor of safety, stress level and displacement field before and after slope reinforcement, it is found that better reinforcement results can be achieved if strong reinforcement is applied upon the regions with high sliding surface. Furthermore, the increase in stress level at the zone dangerous is more favorable of improving the safety of the critical region.

Key Words
slopes; prestressed anchor; retaining wall; factor of safety; Plaxis

(1) Nouri Said:
Laboratory of Structures, Geotechnical and Risks (LSGR), University of Hassiba Benbouali, BP 78 C, Ouled Fares Chlef, 02180, Algeria;
(2) Nechnech Amar:
Laboratory of Environment, Water Geomechanics and works (LEWGW), University for Science and Technology, BP 32 El Alia16111 Bab Ezzouar Algiers, Algeria.

In this paper hyperbolic shear deformation plate theory is presented for bending and the free vibration of functionally graded plates with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Four different porosity types are used for functionally graded plates. Equations of motion are derived from Hamilton's principle. In the solution of the governing equations, the Navier procedure is implemented. In the numerical examples, the effects of the porosity parameters, porosity types and geometry parameters on the bending and free vibration of the functionally graded plates are investigated. It was found that the distribution form of porosity significantly influence the mechanical behavior of FG plates, in terms of deflection, normal, shear stress and frequency.

Key Words
bending; free vibration; functionally graded materials; porosity; Hamilton's principle

(1) Lazreg Hadji:
Department of Mechanical Engineering, University of Tiaret, BP 78 Zaaroura, Tiaret (14000), Algeria;
(2) Lazreg Hadji:
Laboratory of Geomatics and Sustainable Development, University of Tiaret, Algeria;
(3) Fabrice Bernard:
University of Rennes, INSA Rennes, Laboratory of Civil Engineering and Mechanical Engineering, France;
(4) Abdelkader Safa:
Department of Civil Engineering, Ahmed Zabana University Centre, Relizane, 48000, Algeria;
(5) Abdelouahed Tounsi:
Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes, Algeria;
(6) Abdelouahed Tounsi:
YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea;
(7) Abdelouahed Tounsi:
Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals, 31261 Dhahran, Eastern Province, Saudi Arabia.

The prime objective of the present study is to exploit a user friendly, inexpensive all solid state super capacitor using a suitable electrolyte and electrodes. A gel polymer electrolyte (GPE) consisted with polyvinylidene fluoride-co-hexafluopropylene (PVdF), ethylene carbonate (EC), propylene carbonate (PC) and zinc trifluoromethane sulfonate (Zn(CF3SO3)2-ZnTF) was prepared using solvent casting method and its properties were optimized by varying the composition. The composition of 16 PVdF : 22 ZnTF : 31 EC : 31 PC (weight %) exhibits the optimum room temperature conductivity of 3.09 × 10-3 Scm-1. It is purely an ionic conductor having a negligible electronic conductivity. In addition, it was possible to obtain a thin, mechanically stable film. The electrodes were prepared using Sri Lankan natural graphite (NG) with a polymer binder. Eventhough there are reports about natural graphite based super capacitors, Sri Lankan natural graphite has not been considered for super capacitors at a large scale. The main reason for turning towards natural graphite is to reap the benefits of low cost as well as the safety. In order to optimize the electrode properties, the ratio between graphite and polymer binder (in weight basis) was changed. The polymer binder used was polytetrafluoroethylene (PTFE). Super capacitor fabricated with the electrode of the composition, NG : PTFE = 90:10 shows the maximum single electrode specific capacitance (2.58 Fg-1). The fabricated device retains for continuous charge discharge operation with a minimum performance reduction.

Key Words
gel polymer electrolytes; natural graphite; super capacitors; binders; PTFE; specific capacitance

(1) Buddhika P. Gunasekara, K. Vignarooban:
Department of Physics, University of Jaffna, Jaffna, Sri Lanka;
(2) Kumudu S. Perera, Kamal P. Vidanapathirana:
Department of Electronics, Wayamba University of Sri Lanka, Kuliyapitiya, Sri Lanka.

The present paper is concerned with fracture analysis of an inhomogeneous beam with three longitudinal vertical parallel cracks. The three cracks are located symmetrically with respect to the mid-span. A notch is cut-out in the lateral surface of the beam in the mid-span. Only half of the beam is considered due to the symmetry. The material is continuously inhomogeneous in the width direction of the beam. Besides, the material exhibits nonlinear elastic mechanical behavior. The three cracks are located arbitrary in the width direction so as the cross-sections of the four crack arms have different width. The longitudinal fracture behavior is studied in terms of the strain energy release rate. Three solutions to the strain energy release rate are derived by differentiating the complementary strain energy with respect to the areas of the three cracks. The strain energy release rate is determined also by analyzing the balance of the energy for verification. Further verifications are carried-out by applying the J-integral approach. The influences of the locations of the three cracks, the material inhomogeneity and the beam geometry on the longitudinal fracture behavior are appraised. Results of analyses of a beam that is continuously inhomogeneous in both width and length directions are also presented.

Key Words
longitudinal vertical crack; continuously inhomogeneous material; non-linear elastic beam; bending; analytical investigation

Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 . Sofia, Bulgaria.

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