Search results for: Isotropic materials

Authors: J. Hroudova, J. Zach

Abstract:

The majority of contemporary insulation materials commonly used in the building industry is made from non-renewable raw materials; furthermore, their production often brings high energy costs. A long-term trend as far as sustainable development is concerned has been the reduction of energy and material demands of building material production. One of the solutions is the possibility of using easily renewable natural raw material sources which are considerably more ecological and their production is mostly less energy-consuming compared to the production of normal insulations (mineral wool, polystyrene). The paper describes the results of research focused on the development of thermal and acoustic insulation materials based on natural fibres intended for floor constructions. Given the characteristic open porosity of natural fibre materials, the hygrothermal behaviour of the developed materials was studied. Especially the influence of relative humidity and temperature on thermal insulation properties was observed.

Keywords: Green thermal and acoustic insulating materials, natural fibres, technical hemp, flax, floor construction.

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Authors: Mukuna P. Mubiayi, Esther T. Akinlabi

Abstract:

Friction Stir Welding is a solid state welding technique which can be used to produce sound welds between similar and dissimilar materials. Dissimilar welds which include welds between the different series of aluminium alloys, aluminium to magnesium, steel and titanium has been successfully produced by many researchers. This review covers the work conducted in the above mentioned materials and further concludes by showing the need to fully understand the FSW process in order to expand the latter industrially.

Keywords: aluminium, dissimilar materials, FSW, hardness, magnesium, microstructure, steel, tensile test, titanium

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Authors: Juan Blas, Alfonso Bahillo, Santiago Mazuelas, David Bullido, Patricia Fernandez, Ruben M. Lorenzo, Evaristo J. Abril

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This paper presents a low cost automatic system for sampling the electric field in a limited area. The scanning area is a flat surface parallel to the ground at a selected height. We discuss in detail the hardware, software and all the arrangements involved in the system operation. In order to show the system performance we include a campaign of narrow band measurements with 6017 sample points in the surroundings of a cellular base station. A commercial isotropic antenna with three orthogonal axes was used as sampling device. The results are analyzed in terms of its space average, standard deviation and statistical distribution.

Keywords: measurement device, propagation, spatial sampling.

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Authors: Csaba Tóth, Éva Lakatos, László Pethő, Seoyoung Cho

Abstract:

The temperature effect on asphalt pavement structure is a crucial factor at the design stage. In this paper, by applying the German guidelines for temperature along the asphalt depth is estimated. The aim is to consider temperature profiles in different seasons in numerical modelling. The model is built with an elastic and isotropic solid element with 19 subdivisions of asphalt layers to reflect the temperature variation. Comparison with the simple three-layer pavement system (asphalt layers, base, and subgrade layers) will be followed to see the difference in result without temperature variation along with the depth. Finally, the fatigue life calculation was checked to prove the validity of the methodology of considering the temperature in the numerical modelling.

Keywords: Temperature profile, flexible pavement modelling, finite element method, temperature modelling.

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Authors: B. S. Jayashankarbabu, Karisiddappa

Abstract:

The finite element method is used to obtain the elastic buckling load factor for square isotropic plate containing circular, square and rectangular cutouts. ANSYS commercial finite element software had been used in the study. The applied inplane loads considered are uniaxial and biaxial compressions. In all the cases the load is distributed uniformly along the plate outer edges. The effects of the size and shape of concentric cutouts with different plate thickness ratios and the influence of plate edge conditions, such as SSSS, CCCC and mixed boundary condition SCSC on the plate buckling strength have been considered in the analysis.

Keywords: Concentric cutout, Elastic buckling, Finite element method, Inplane loads, Thickness ratio.

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Authors: Sittichai Kaewkuekool, Vanchai Laemlaksakul

Abstract:

At the present, auto part industries have become higher challenge in strategy market. As this consequence, manufacturers need to have better response to customers in terms of quality, cost, and delivery time. Moreover, they need to have a good management in factory to comply with international standard maximum capacity and lower cost. This would lead companies to have to order standard part from aboard and become the major cost of inventory. The development of auto part research by recycling materials experiment is to compare the auto parts from recycle materials to international auto parts (CKD). Factors studied in this research were the recycle material ratios of PU-foam, felt, and fabric. Results of recycling materials were considered in terms of qualities and properties on the parameters such as weight, sound absorption, water absorption, tensile strength, elongation, and heat resistance with the CKD. The results were showed that recycling materials would be used to replace for the CKD.

Keywords: International auto parts, recycling materials.

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Authors: Mourad Makhlouf, Omar Bouchher, Messabih Sidi Mohamed, Benrachedi Khaled

Abstract:

The objective of this study was to investigate the removal of two organic pollutants; 4-hydroxybenzoic acid (p-hydroxybenzoic acid) and phenol from synthetic wastewater by the adsorption on mesoporous materials. In this context, the aim of this work is to study the adsorption of organic compounds phenol and 4AHB on MCM-41 and FSM-16 non-grafted (NG) and other grafted (G) by trimethylchlorosilane (TMCS). The results of phenol and 4AHB adsorption in aqueous solution show that the adsorption capacity tends to increase after grafting in relation to the increase in hydrophobicity. The materials are distinguished by a higher adsorption capacity to the other NG materials. The difference in the phenol is 14.43% (MCM-41), 14.55% (FSM-16), and 16.72% (MCM-41), 13.57% (FSM-16) in the 4AHB. Our adsorption results show that the grafted materials by TMCS are good adsorbent at 25 °C.

Keywords: MCM-41, FSM-16, TMCS, phenol, 4AHB.

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Authors: Bogdan Il. Bogdanov, Dimitar R.Rusev, Yancho H. Hristov, Irena G. Markovska, Dimitar P.Georgiev

Abstract:

New design of a grid for preparation of high density granules with enhanced mechanical strength by granulation of dispersed materials is suggested. A method for hydrodynamic dimensioning of the grid depending on granulation conditions, hydrodynamic regime of the operation, dispersity and physicochemical characteristics of the materials to be granulated was suggested. The aim of the grid design is to solve the problems arising by the granulation of disperse materials.

Keywords: fluidized bed reactor, granulation, porous silicatematerials.

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Authors: Nwakaego C. Onyenokporo

Abstract:

Cement is the most extensively used construction material due to its strength and versatility of use. However, the production of Portland cement has become unsustainable because of high energy usage, reduction of natural non-renewable resources and emissions of greenhouse gases. Production of cement contributes to anthropogenic greenhouse gases emissions annually. The growing concerns for the environment resulting from this constant and excessive use of cement has therefore raised the need for more green materials and technology. The use of supplementary cementitious materials (SCMs) is considered as one of the many alternatives suited to address this issue and serve as a sustainable partial replacement for cement in construction. This paper will examine the reuse of these waste materials to partially replace Portland cement. It provides a critical review of literature analysing various supplementary cementitious materials which are applicable in the building industry as either partial replacement for cement or aggregates. These materials have been grouped based on source into industrial wastes, domestic/general wastes, and agricultural wastes. The reuse of these waste materials could potentially reduce the negative effects of cement production and reduce landfills which constitute an environmental nuisance. This paper seeks to inform building industry professionals and researchers in the field on the applicability of these waste materials in construction.

Keywords: cement, greenhouse gases, landfills, sustainable, waste materials

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Authors: Nwakaego C. Onyenokporo

Abstract:

Cement is the most extensively used construction material due to its strength and versatility of use. However, the production of Portland cement has become unsustainable because of high energy usage, reduction of natural non-renewable resources and emissions of greenhouse gases. Production of cement contributes to anthropogenic greenhouse gases emissions annually. The growing concerns for the environment resulting from this constant and excessive use of cement has therefore raised the need for more green materials and technology. The use of supplementary cementitious materials (SCMs) is considered as one of the many alternatives suited to address this issue and serve as a sustainable partial replacement for cement in construction. This paper will examine the reuse of these waste materials to partially replace Portland cement. It provides a critical review of literature analysing various supplementary cementitious materials which are applicable in the building industry as either partial replacement for cement or aggregates. These materials have been grouped based on source into industrial wastes, domestic/general wastes, and agricultural wastes. The reuse of these waste materials could potentially reduce the negative effects of cement production and reduce landfills which constitute an environmental nuisance. This paper seeks to inform building industry professionals and researchers in the field on the applicability of these waste materials in construction.

Keywords: Cement, greenhouse gases, landfills, sustainable, waste materials.

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Authors: M. Karami Khorramabadi, P. Khazaeinejad

Abstract:

The static stability analysis of stiffened functionally graded cylindrical shells by isotropic rings and stringers subjected to axial compression is presented in this paper. The Young's modulus of the shell is taken to be function of the thickness coordinate. The fundamental relations, the equilibrium and stability equations are derived using the Sander's assumption. Resulting equations are employed to obtain the closed-form solution for the critical axial loads. The effects of material properties, geometric size and different material coefficient on the critical axial loads are examined. The analytical results are compared and validated using the finite element model.

Keywords: Functionally graded material, Stability, Stiffened cylindrical shell, Finite element analysis

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Authors: S. I. Durowaye, O. P. Gbenebor, B. O. Bolasodun, I. O. Rufai, V. O. Durowaye

Abstract:

Particles are the most common and cheapest reinforcement producing discontinuous reinforced composites with isotropic properties. Conventional fabrication methods can be used to produce a wide range of product forms, making them relatively inexpensive. Optimising composite development must include consideration of all the fundamental aspect of particles including their size, shape, volume fraction, distribution and mechanical properties. Research has shown that the challenges of low fracture toughness, poor crack growth resistance and low thermal stability can be overcome by reinforcement with particles. The unique properties exhibited by micro particles reinforced ceramic composites have made them to be highly attractive in a vast array of applications.

Keywords: Ceramic composites, Mechanical properties, Microparticles, Thermal stability.

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Authors: F. Pourhasanzade, S. H. Sabzpoushan

Abstract:

Computer modeling has played a unique role in understanding electrocardiography. Modeling and simulating cardiac action potential propagation is suitable for studying normal and pathological cardiac activation. This paper presents a 2-D Cellular Automata model for simulating action potential propagation in cardiac tissue. We demonstrate a novel algorithm in order to use minimum neighbors. This algorithm uses the summation of the excitability attributes of excited neighboring cells. We try to eliminate flat edges in the result patterns by inserting probability to the model. We also preserve the real shape of action potential by using linear curve fitting of one well known electrophysiological model.

Keywords: Cellular Automata, Action Potential Propagation, cardiac tissue, Isotropic Pattern, accurate shape of cardiac actionpotential.

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Authors: E. Çetin, A. Kurşun, Ş. Aksoy, M. Tunay Çetin

Abstract:

The closed form study deals with elastic stress analysis of annular bi-material discs with variable thickness subjected to the mechanical and thermomechanical loads. Those discs have many applications in the aerospace industry, such as gas turbines and gears. Those discs normally work under thermal and mechanical loads. Their life cycle can increase when stress components are minimized. Each material property is assumed to be isotropic. The results show that material combinations and thickness of profiles play an important role in determining the responses of bi-material discs and an optimal design of those structures. Stress distribution is investigated and results are shown as graphs.

Keywords: Bi-material discs, elastic stress analysis, mechanical loads, rotating discs.

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Authors: A. Tavangari, N. Salehzadeh

Abstract:

In the crack growth analysis, the Stress Intensity Factor (SIF) is a fundamental prerequisite. In the present study, the mode I stress intensity factor (SIF) of three-dimensional penny- Shaped crack is obtained in an isotropic elastic cylindrical medium with arbitrary dimensions under arbitrary loading at the top of the cylinder, by the semi-analytical method based on the Rayleigh-Ritz method. This method that is based on minimizing the potential energy amount of the whole of the system, gives a very close results to the previous studies. Defining the displacements (elastic fields) by hypothetical functions in a defined coordinate system is the base of this research. So for creating the singularity conditions at the tip of the crack the appropriate terms should be found.

Keywords: Penny-shaped crack, Stress intensity factor, Fracture mechanics, Ritz method.

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Authors: Siu Hua Chang, Ayub Md Som, Jagannathan Krishnan

Abstract:

The kinetics of Cu(II) transport through a bulk liquid membrane with different membrane materials was investigated in this work. Three types of membrane materials were used: fresh cooking oil, waste cooking oil and kerosene, each of which was mixed with di-2-ethylhexylphosphoric acid (carrier) and tributylphosphate (modifier). Kinetic models derived from the kinetic laws of two consecutive irreversible first-order reactions were used to study the facilitated transport of Cu(II) across the source, membrane and receiving phases of bulk liquid membrane. It was found that the transport kinetics of Cu(II) across the source phase was not affected by different types of membrane materials but decreased considerably when the membrane materials changed from kerosene, waste cooking oil to fresh cooking oil. The rate constants of Cu(II) removal and recovery processes through the bulk liquid membrane were also determined.

Keywords: Transport kinetics, Cu(II), bulk liquid membrane, waste cooking oil.

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Authors: S. Larbi, R. Bensaada, S. Djebali, A. Bilek

Abstract:

The manufacture of composite parts is a major issue in many industrial domains. Polymer composite materials are ideal for structural applications where high strength-to-weight and stiffness-to-weight ratios are required. However, exposition to extreme environment conditions (temperature, humidity) affects mechanical properties of organic composite materials and lead to an undesirable degradation. Aging mechanisms in organic matrix are very diverse and vary according to the polymer and the aging conditions such as temperature, humidity etc. This paper studies the hygrothermal aging effect on the mechanical properties of fiber reinforced plastics laminates at 40 °C in different environment exposure. Two composite materials are used to conduct the study (carbon fiber/epoxy and glass fiber/vinyl ester with two stratifications for both the materials [904/04] and [454/04]). The experimental procedure includes a mechanical characterization of the materials in a virgin state and exposition of specimens to two environments (seawater and demineralized water). Absorption kinetics for the two materials and both the stratifications are determined. Three-point bending test is performed on the aged materials in order to determine the hygrothermal effect on the mechanical properties of the materials.

Keywords: FRP laminates, hygrothermal aging, mechanical properties, theory of laminates.

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Authors: Mohsin T. Mohammed, Zahid A. Khan, Arshad N. Siddiquee

Abstract:

The field of biomedical materials plays an imperative requisite and a critical role in manufacturing a variety of biological artificial replacements in a modern world. Recently, titanium (Ti) materials are being used as biomaterials because of their superior corrosion resistance and tremendous specific strength, free- allergic problems and the greatest biocompatibility compared to other competing biomaterials such as stainless steel, Co-Cr alloys, ceramics, polymers, and composite materials. However, regardless of these excellent performance properties, Implantable Ti materials have poor shear strength and wear resistance which limited their applications as biomaterials. Even though the wear properties of Ti alloys has revealed some improvements, the crucial effectiveness of biomedical Ti alloys as wear components requires a comprehensive deep understanding of the wear reasons, mechanisms, and techniques that can be used to improve wear behavior. This review examines current information on the effect of thermal and thermomechanical processing of implantable Ti materials on the long-term prosthetic requirement which related with wear behavior. This paper focuses mainly on the evolution, evaluation and development of effective microstructural features that can improve wear properties of bio grade Ti materials using thermal and thermomechanical treatments.

Keywords: Wear Resistance, Heat Treatment, Thermomechanical Processing, Biomedical Titanium Materials.

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Authors: M. Benachour, N. Benachour, M. Benguediab

Abstract:

In this paper fatigue crack initiation and propagation in notched plate under constant amplitude loading through tensile residual stress field of 2024 T351 Al-alloy plate were investigated. Residual stress field was generated by plastic deformation using finite element method (FEM) where isotropic hardening in Von Mises model was applied. Simulation of fatigue behavior was made on AFGROW code. It was shown that the fatigue crack initiation and propagation were affected by level of residual stress filed. In this investigation, the presence of tensile residual stresses at notch (hole) reduces considerably the total fatigue life. It was shown that the decreasing in stress reduces the fatigue crack growth rates.

Keywords: Residual stress, fatigue crack initiation, fatigue crack growth, Al-alloy.

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Authors: I-Ling Chang, Jer-An Chen

Abstract:

The elastic properties and fracture of two-dimensional graphene were calculated purely from the atomic bonding (stretching and bending) based on molecular mechanics method. Considering the representative unit cell of graphene under various loading conditions, the deformations of carbon bonds and the variations of the interlayer distance could be realized numerically under the geometry constraints and minimum energy assumption. In elastic region, it was found that graphene was in-plane isotropic. Meanwhile, the in-plane deformation of the representative unit cell is not uniform along armchair direction due to the discrete and non-uniform distributions of the atoms. The fracture of graphene could be predicted using fracture criteria based on the critical bond length, over which the bond would break. It was noticed that the fracture behavior were directional dependent, which was consistent with molecular dynamics simulation results.

Keywords: Energy minimization, fracture, graphene, molecular mechanics.

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Authors: Maysam Saidi, Reza Maddahian, Bijan Farhanieh

Abstract:

Hydrocyclones flow field study is conducted by performing a parametric study. Effect of cone angle on deoiling hydrocyclones flow behaviour is studied in this research. Flow field of hydrocyclone is obtained by three-dimensional simulations with OpenFOAM code. Because of anisotropic behaviour of flow inside hydrocyclones LES is a suitable method to predict the flow field since it resolves large scales and model isotropic small scales. Large eddy simulation is used to predict the flow behavior of three different cone angles. Differences in tangential velocity and pressure distribution are reported in some figures.

Keywords: Deoiling hydrocyclones, Flow field, Hydrocyclone cone angle, Large Eddy Simulation, Pressure distribution

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Authors: A. Uchaipichat

Abstract:

The hydro-mechanical model for unsaturated soils has been presented based on the effective stress principle taking into account effects of drying-wetting process. The elasto-plastic constitutive equations for stress-strain relations of the soil skeleton have been established. A plasticity model is modified from modified Cam-Clay model. The hardening rule has been established by considering the isotropic consolidation paths. The effect of dryingwetting process is introduced through the ¤ç parameter. All model coefficients are identified in terms of measurable parameters. The simulations from the proposed model are compared with the experimental results. The model calibration was performed to extract the model parameter from the experimental results. Good agreement between the results predicted using proposed model and the experimental results was obtained.

Keywords: Drying-wetting process, Effective stress, Elastoplasticmodel, Unsaturated soils

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Authors: I. V. Kuzminov

Abstract:

The alternative hypothesis of the physics of gravitation is put forward in this paper. The hypothesis is constructed on the laws of classical physics. The process of expansion of the Universe explains the physics of gravity. The expansion of the Universe induces the resistance of gyroscopic forces of electron’s rotation. The second component of gravity forces is the resistance arising from the second derivative of linear expansion. This hypothesis does not reject the existing foundation of settlement, particularly as it is empirically constructed. The forces of gravitation and inertia share a common nature, which has been recognized before. The presented hypothesis does not criticize existing theories of gravitation; rather, it explores a separate theme. It is important to acknowledge that the expansion of the Universe exhibits isotropic characteristics. The proposed hypothesis provides a fundamental direction for further research. It is worth noting that this article does not aim to encompass all possible aspects of future investigations.

Keywords: Gyroscopic forces, the unity of the micro- and macrocosm, the expansion of the universe, the second derivative of expansion.

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Authors: Syhalath Xaphakdy, Toshio Nagata, Saykham Phommathat, Pavy Souwannavong, Vilayvanh Srithilat, Phoxay Sengdala, Bounaom Phetarnousone, Boualay Siharath, Xaya Chemcheng

Abstract:

The National University of Laos (NUOL) invited a group of volunteers from the Japan International Cooperation Agency (JICA) to revise the physics experiments to utilize the materials that were already available to students. The intension was to review and revise the materials regularly utilized in physics class. The project had access to limited materials and a small budget for the class in the unit; however, by developing experimental textbooks related to mechanics, electricity, and wave and vibration, the group found a way to apply them in the classroom and enhance the students teaching activities. The aim was to introduce a way to incorporate the materials and practices in the classroom to enhance the students learning and teaching skills, particularly when they graduate and begin working as high school teachers.

Keywords: NUOL, JICA, physics experiment materials, small budget, mechanics, electricity.

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Authors: M. Qwamizadeh, K. Zhou, Z. Zhang, YW. Zhang

Abstract:

Typical load-bearing biological materials like bone, mineralized tendon and shell, are biocomposites made from both organic (collagen) and inorganic (biomineral) materials. This amazing class of materials with intrinsic internally designed hierarchical structures show superior mechanical properties with regard to their weak components from which they are formed. Extensive investigations concentrating on static loading conditions have been done to study the biological materials failure. However, most of the damage and failure mechanisms in load-bearing biological materials will occur whenever their structures are exposed to dynamic loading conditions. The main question needed to be answered here is: What is the relation between the layout and architecture of the load-bearing biological materials and their dynamic behavior? In this work, a staggered model has been developed based on the structure of natural materials at nanoscale and Finite Element Analysis (FEA) has been used to study the dynamic behavior of the structure of load-bearing biological materials to answer why the staggered arrangement has been selected by nature to make the nanocomposite structure of most of the biological materials. The results showed that the staggered structures will efficiently attenuate the stress wave rather than the layered structure. Furthermore, such staggered architecture is effectively in charge of utilizing the capacity of the biostructure to resist both normal and shear loads. In this work, the geometrical parameters of the model like the thickness and aspect ratio of the mineral inclusions selected from the typical range of the experimentally observed feature sizes and layout dimensions of the biological materials such as bone and mineralized tendon. Furthermore, the numerical results validated with existing theoretical solutions. Findings of the present work emphasize on the significant effects of dynamic behavior on the natural evolution of load-bearing biological materials and can help scientists to design bioinspired materials in the laboratories.

Keywords: Load-bearing biological materials, nanostructure, staggered structure, stress wave decay.

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Authors: Moses F. Oduori, Enoch K. Musyoka, Thomas O. Mbuya

Abstract:

The selection of materials is an essential task in mechanical design processes. This paper sets out to demonstrate the application of analytical decision making during mechanical design and, particularly, in selecting a suitable material for a given application. Equations for the mechanical design of a manual winch rope drum are used to derive quantitative material performance indicators, which are then used in a multiple attribute decision making (MADM) model to rank the candidate materials. Thus, the processing of mechanical design considerations and material properties data into information that is suitable for use in a quantitative materials selection process is demonstrated for the case of a rope drum design. Moreover, Microsoft Excel^®, a commonly available computer package, is used in the selection process. The results of the materials selection process are in agreement with current industry practice in rope drum design. The procedure that is demonstrated here should be adaptable to other design situations in which a need arises for the selection of engineering materials, and other engineering entities.

Keywords: Design Decisions, Materials Selection, Mechanical Design, Rope Drum Design.

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Authors: Moudar H. A. Zgoul, Amin Al Zamer

Abstract:

Adhesive materials and adhesion have been the focal point of multiple research works related to numerous applications, particularly, aerospace, and aviation industries. To enhance the properties of conventional adhesive materials, additives have been introduced to the mix in order to enhance their mechanical and physical properties by creating a hybrid adhesive material. The evaluation of the mechanical properties of such hybrid adhesive materials is thus of an essential requirement for the purpose of properly modeling their behavior accurately. This paper presents an approach/tool to simulate the behavior such hybrid adhesives in a way that will allow researchers to better understand their behavior while in service.

Keywords: Adhesive materials, analysis, hybrid adhesives, mechanical properties, simulation.

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Authors: Tatheer Zahra

Abstract:

Auxetic materials have counteractive properties due to re-entrant geometry that enables them to possess Negative Poisson’s Ratio (NPR). These materials have better energy absorbing and shock resistance capabilities as compared to conventional positive Poisson’s ratio materials. The re-entrant geometry can be created through 3D printing for convenient application of these materials. This paper investigates the mechanical properties of 3D printed chiral auxetic geometries of various sizes. Small scale samples were printed using an ordinary 3D printer and were tested under compression and tension to ascertain their strength and deformation characteristics. A maximum NPR of -9 was obtained under compression and tension. The re-entrant chiral cell size has been shown to affect the mechanical properties of the re-entrant chiral auxetics.

Keywords: Auxetic materials, 3D printing, Negative Poisson’s Ratio, re-entrant chiral auxetics.

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Authors: J. Hodna, B. Dohnalkova, V. Petranek, R. Drochytka

Abstract:

The paper is focused on the identification of limiting environmental factors of individual industrial floors on which newly developed polymer protection and repair systems with the use of secondary raw materials will be used. These mainly include floors with extreme stresses and special requirements for materials used. In relation to the environment of a particular industrial floor, it is necessary to ensure, for example, chemical stability, resistance to higher temperatures, resistance to higher mechanical stress, etc. for developed materials, which is reflected in the demands for the developed material systems. The paper describes individual environments and, in relation to them, also requirements for individual components of the developed materials and for the developed materials as a whole.

Keywords: Limits, environment, polymer, industrial floors, recycling, secondary raw material, protective system.

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Authors: E. Jomehzadeh, A.R. Saidi

Abstract:

In the present article, nonlinear vibration analysis of single layer graphene sheets is presented and the effect of small length scale is investigated. Using the Hamilton's principle, the three coupled nonlinear equations of motion are obtained based on the von Karman geometrical model and Eringen theory of nonlocal continuum. The solutions of Free nonlinear vibration, based on a one term mode shape, are found for both simply supported and clamped graphene sheets. A complete analysis of graphene sheets with movable as well as immovable in-plane conditions is also carried out. The results obtained herein are compared with those available in the literature for classical isotropic rectangular plates and excellent agreement is seen. Also, the nonlinear effects are presented as functions of geometric properties and small scale parameter.

Keywords: Small scale, Nonlinear vibration, Graphene sheet, Nonlocal continuum

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