Search results for: theory of laminates.

Authors: Hireni R. Mankodi, D. J. Chudasama

Abstract:

The textile preforms play a key role in providing the mechanical properties and gives the idea about selection parameter of preforms to improve the quality and performance of laminates. The main objectives of this work are to study the effect of non-crimp fabric preform structure in final properties of laminates. It has been observed that the multi-axial preform give better mechanical properties of laminates as compared to woven and biaxial fabrics. This study investigated the effect of different non-crimp glass preform structure on tensile strength, bending and compression properties of glass laminates. The different woven, bi-axial and multi-axial fabrics with similar GSM used to manufacture the laminates using polyester resin. The structural and mechanical properties of preform and laminates were studied using standard methods. It has been observed that the glass fabric geometry, including type of weaves, warps and filling density and number of layer plays significant role in deciding mechanical properties of laminates.

Keywords: Preform, non-crimp, laminates, bi-axial, multiaxial.

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Authors: Jeongho Choi, Krishna Shankar, Alan Fien, Andrew Neely

Abstract:

Corrugated wire mesh laminates (CWML) are a class of engineered open cell structures that have potential for applications in many areas including aerospace and biomedical engineering. Two different methods of fabricating corrugated wire mesh laminates from stainless steel, one using a high temperature Lithobraze alloy and the other using a low temperature Eutectic solder for joining the corrugated wire meshes are described herein. Their implementation is demonstrated by manufacturing CWML samples of 304 and 316 stainless steel (SST). It is seen that due to the facility of employing wire meshes of different densities and wire diameters, it is possible to create CWML laminates with a wide range of effective densities. The fabricated laminates are tested under uniaxial compression. The variation of the compressive yield strength with relative density of the CWML is compared to the theory developed by Gibson and Ashby for open cell structures [22]. It is shown that the compressive strength of the corrugated wire mesh laminates can be described using the same equations by using an appropriate value for the linear coefficient in the Gibson-Ashby model.

Keywords: cellular solids, corrugation, foam, open-cell, metal mesh, laminate, stainless steel

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Authors: M. R. Ghasemi, A. Ehsani

Abstract:

In this paper, the optimum weight and cost of a laminated composite plate is seeked, while it undergoes the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill theory is used as the failure criterion. The theory of analysis was based on the Classical Lamination Theory (CLT). A newly type of Genetic Algorithm (GA) as an optimization technique with a direct use of real variables was employed. Yet, since the optimization via GAs is a long process, and the major time is consumed through the analysis, Radial Basis Function Neural Networks (RBFNN) was employed in predicting the output from the analysis. Thus, the process of optimization will be carried out through a hybrid neuro-GA environment, and the procedure will be carried out until a predicted optimum solution is achieved.

Keywords: Composite Laminates, GA, Multi-objectiveOptimisation, Neural Networks, RBFNN.

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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: Shaher Bano, Samia Fida, Asif Israr

Abstract:

The synergistic effect of properties of metals and fibers reinforced laminates has diverted attention of the world towards use of robust composite materials known as fiber-metal laminates in many high performance applications. In this study, modification of an adhesively bonded joint as a single lap joint of carbon fibers based CARALL FML has done to increase interlaminar shear strength of the joint. The effect of different configurations of joint designs such as spews, stepped and modification in adhesive by addition of nano-fillers was studied. Both experimental and simulation results showed that modified joint design have superior properties as maximum force experienced stepped joint was 1.5 times more than the simple lap joint. Addition of carbon nano-tubes as nano-fillers in the adhesive joint increased the maximum force due to crack deflection mechanism.

Keywords: Adhesive joint, carbon reinforced aluminium laminate, CARALL, fiber metal laminates, spews.

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Authors: S.C. Chin, N. Shafiq, M.F. Nuruddin

Abstract:

This paper presents the study of strengthening R/C beams with large circular and square opening located at flexure zone by Carbon Fiber Reinforced Polymer (CFRP) laminates. A total of five beams were tested to failure under four point loading to investigate the structural behavior including crack patterns, failure mode, ultimate load and load deflection behaviour. Test results show that large opening at flexure reduces the beam capacity and stiffness; and increases cracking and deflection. A strengthening configuration was designed for each un-strengthened beams based on their respective crack patterns. CFRP laminates remarkably restore the beam capacity of beam with large circular opening at flexure location while 10% re-gain of beam capacity with square opening. The use of CFRP laminates with the designed strengthening configuration could significantly reduce excessive cracking and deflection and increase the ultimate capacity and stiffness of beam.

Keywords: CFRP, large opening, R/C beam, strengthening

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Authors: Tao Qu, Chandra Prakash, Vikas Tomar

Abstract:

The interfaces between organic and inorganic phases in natural materials have been shown to be a key factor contributing to their high performance. This work analyzes crack propagation in a 2-ply laminate subjected to uniaxial tensile mode-I crack propagation loading that has laminate properties derived based on biological material constituents (marine exoskeleton- chitin and calcite). Interfaces in such laminates are explicitly modeled based on earlier molecular simulations performed by authors. Extended finite element method and cohesive zone modeling based simulations coupled with theoretical analysis are used to analyze crack propagation. Analyses explicitly quantify the effect that interface mechanical property variation has on the delamination as well as the transverse crack propagation in examined 2-ply laminates.

Keywords: Chitin, composites, interfaces, fracture.

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Authors: Jayden Levy, Garth M. K. Pearce

Abstract:

An automated fibre placement method has been developed to build through-thickness reinforcement into carbon fibre reinforced plastic laminates during their production, with the goal of increasing delamination fracture toughness while circumventing the additional costs and defects imposed by post-layup stitching and z-pinning. Termed ‘inter-weaving’, the method uses custom placement sequences of thermoset prepreg tows to distribute regular fibre link regions in traditionally clean ply interfaces. Inter-weaving’s impact on mode I delamination fracture toughness was evaluated experimentally through double cantilever beam tests (ASTM standard D5528-13) on [±15°]9 laminates made from Park Electrochemical Corp. E-752-LT 1/4” carbon fibre prepreg tape. Unwoven and inter-woven automated fibre placement samples were compared to those of traditional laminates produced from standard uni-directional plies of the same material system. Unwoven automated fibre placement laminates were found to suffer a mostly constant 3.5% decrease in mode I delamination fracture toughness compared to flat uni-directional plies. Inter-weaving caused significant local fracture toughness increases (up to 50%), though these were offset by a matching overall reduction. These positive and negative behaviours of inter-woven laminates were respectively found to be caused by fibre breakage and matrix deformation at inter-weave sites, and the 3D layering of inter-woven ply interfaces providing numerous paths of least resistance for crack propagation.

Keywords: AFP, automated fibre placement, delamination, fracture toughness, inter-weaving.

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Authors: Jean François Chatelain, Imed Zaghbani, Joseph Monier

Abstract:

The machining of Carbon Fiber Reinforced Plastics has come to constitute a significant challenge for many fields of industry. The resulting surface finish of machined parts is of primary concern for several reasons, including contact quality and impact on the assembly. Therefore, the characterization and prediction of roughness based on machining parameters are crucial for costeffective operations. In this study, a PCD tool comprised of two straight flutes was used to trim 32-ply carbon fiber laminates in a bid to analyze the effects of the feed rate and the cutting speed on the surface roughness. The results show that while the speed has but a slight impact on the surface finish, the feed rate for its part affects it strongly. A detailed study was also conducted on the effect of fiber orientation on surface roughness, for quasi-isotropic laminates used in aerospace. The resulting roughness profiles for the four-ply orientation lay-up were compared, and it was found that fiber angle is a critical parameter relating to surface roughness. One of the four orientations studied led to very poor surface finishes, and characteristic roughness profiles were identified and found to only relate to the ply orientations of multilayer carbon fiber laminates.

Keywords: Roughness, Detouring, Composites, Aerospace

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Authors: P. Chockalingam, C. K. Kok, T. R. Vijayaram

Abstract:

A study on grindability of chopped strand mat glass fiber reinforced polymer laminates (CSM GFRP) have been carried out to evaluate the significant parameters on wheel performance. Performance of Aluminum oxide and c-BN wheels during grinding of CSM GFRP laminate was evaluated in terms of grinding force and surface roughness during grinding. The cubic Boron Nitride wheel experiences higher tangential grinding forces components and lower normal force component than Aluminum oxide grinding wheels. In case of surface finish, Aluminum oxide grinding wheels outdo the cubic Boron Nitride grinding wheels.

Keywords: Grinding, glass fiber reinforced polymer laminates, grinding force, surface finish.

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Authors: P. Chockalingam, C. K. Kok, T. R. Vijayaram

Abstract:

Glass fiber reinforced polymer (GFRP) laminates have been widely used because of their unique mechanical and physical properties such as high specific strength, stiffness and corrosive resistance. Accordingly, the demand for precise grinding of composites has been increasing enormously. Grinding is the one of the obligatory methods for fabricating products with composite materials and it is usually the final operation in the assembly of structural laminates. In this experimental study, an attempt has been made to develop an empirical model to predict the surface roughness of ground GFRP composite laminate with respect to the influencing grinding parameters by factorial design approach of design of experiments (DOE). The significance of grinding parameters and their three factor interaction effects on grinding of GFRP composite have been analyzed in detail. An empirical equation has been developed to attain minimum surface roughness in GFRP laminate grinding.

Keywords: GFRP Laminates, Grinding, Surface Roughness, Factorial Design.

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Authors: Jean François Chatelain, Imed Zaghbani, Gilbert Lebrun, Kaml Hasni

Abstract:

Severe damages may occur during the drilling of carbon fiber reinforced plastics (CFRP). In practice, this damage is limited by adding a backup support to the drilled parts. For some aeronautical parts with curvatures, backing up parts is a demanding process. In order to simplify the operation, this research studies the effect of using a configurable setup to support parts on the resulting quality of drilled holes. The test coupons referenced in this study are twenty four-plies unidirectional laminates made of carbon fibers and epoxy resin. Different signals were measured during the drilling process for these laminates, including the thrust force, the displacement and the acceleration. The processing of these signals demonstrated that the damage is due to the combination of two main factors: the spring-back of the thin part and the thrust force. The results found were confirmed for different feeds and speeds. When the distance between supports is increased, it is observed that the spring-back increases but the thrust force decreases. The study proves the feasibility of unsupported drilling of thin CFRP laminates without creating any observable damage.

Keywords: CFRP, Damage, Drilling, Flexible setup.

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Authors: P Chockalingam, K Kok, R Vijayaram

Abstract:

This paper presents a comparative study on dry and wet grinding through experimental investigation in the grinding of CSM glass fibre reinforced polymer laminates using a pink aluminium oxide wheel. Different sets of experiments were performed to study the effects of the independent grinding parameters such as grinding wheel speed, feed and depth of cut on dependent performance criteria such as cutting forces and surface finish. Experimental conditions were laid out using design of experiment central composite design. An effective coolant was sought in this study to minimise cutting forces and surface roughness for GFRP laminates grinding. Test results showed that the use of coolants reduces surface roughness, although not necessarily the cutting forces. These research findings provide useful economic machining solution in terms of optimized grinding conditions for grinding CSM GFRP.

Keywords: Chopped Strand Mat GFRP laminates, Dry and Wet Grinding, Cutting Forces, Surface Finish.

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Authors: M.kayhani, M.Nourouzi, A. Amiri Delooei

Abstract:

This study presents an exact general solution for steady-state conductive heat transfer in cylindrical composite laminates. Appropriate Fourier transformation has been obtained using Sturm-Liouville theorem. Series coefficients are achieved by solving a set of equations that related to thermal boundary conditions at inner and outer of the cylinder, also related to temperature continuity and heat flux continuity between each layer. The solution of this set of equations are obtained using Thomas algorithm. In this paper, the effect of fibers- angle on temperature distribution of composite laminate is investigated under general boundary conditions. Here, we show that the temperature distribution for any composite laminates is between temperature distribution for laminates with θ = 0° and θ = 90° .

Keywords: exact solution, composite laminate, heat conduction, cylinder, Fourier transformation.

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Authors: Pavel Y. Tabakov

Abstract:

An accurate optimal design of laminated composite structures may present considerable difficulties due to the complexity and multi-modality of the functional design space. The Big Bang – Big Crunch (BB-BC) optimization method is a relatively new technique and has already proved to be a valuable tool for structural optimization. In the present study the exceptional efficiency of the method is demonstrated by an example of the lay-up optimization of multilayered anisotropic cylinders based on a three-dimensional elasticity solution. It is shown that, due to its simplicity and speed, the BB-BC is much more efficient for this class of problems when compared to the genetic algorithms.

Keywords: Big Bang – Big Crunch method, optimization, composite laminates, pressure vessel.

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Authors: Mohammad Reza Ghasemi, Ali Ehsani

Abstract:

In this paper, the optimum weight and cost of a laminated composite plate is seeked, while it undergoes the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill theory is used as the failure criterion. The theory of analysis was based on the Classical Lamination Theory (CLT). A newly type of Genetic Algorithm (GA) as an optimization technique with a direct use of real variables was employed. Yet, since the optimization via GAs is a long process, and the major time is consumed through the analysis, Radial Basis Function Neural Networks (RBFNN) was employed in predicting the output from the analysis. Thus, the process of optimization will be carried out through a hybrid neuro-GA environment, and the procedure will be carried out until a predicted optimum solution is achieved.

Keywords: Composite Laminates, GA, Multi-objectiveOptimization, Neural Networks, RBFNN.

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Authors: Farhad Asgari Mehrabadi, Mohammad Reza Khoshravan

Abstract:

In the present study, fracture behavior of woven fabric-reinforced glass/epoxy composite laminates under mode III crack growth was experimentally investigated and numerically modeled. Two methods were used for the calculation of the strain energy release rate: the experimental compliance calibration (CC) method and the Virtual Crack Closure Technique (VCCT). To achieve this aim ECT (Edge Crack Torsion) was used to evaluate fracture toughness in mode III loading (out of plane-shear) at different crack lengths. Load–displacement and associated energy release rates were obtained for various case of interest. To calculate fracture toughness JIII, two criteria were considered including non-linearity and maximum points in load-displacement curve and it is observed that JIII increases with the crack length increase. Both the experimental compliance method and the virtual crack closure technique proved applicable for the interpretation of the fracture mechanics data of woven glass/epoxy laminates in mode III.

Keywords: Mode III, Fracture, Composite, Crack growth Finite Element.

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Authors: Vanchai Laemlaksakul, Sompoap Talabgaew

Abstract:

This research studied the appropriate factors and conditions for laminated bamboo bending by Design of Experiments (DOE). The interested factors affecting the spring back in laminates bamboo were (1) time, (2) thickness, and (3) frequency. This experiment tested the specimen by using high frequency machine and measured its spring back immediately and next 24 hours for comparing the spring back ratio. Results from the experiments showed that significant factors having major influence to bending of laminates bamboo were thickness and frequency. The appropriate conditions of thickness and frequency were 4 mm. and 1.5 respectively.

Keywords: Bamboo, bending, spring back, design of experiments.

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Authors: H. Achache, Y. Madani, A. Benzerdjeb

Abstract:

The present study is based on the three-dimensional digital analysis by the finite elements method of the mechanical loading effect on the delamination of unidirectional and multidirectional stratified composites. The aim of this work is the determination of the release energy rate G in mode I and the Von Mises equivalent constraint distribution along the damaged area under the influence of several parameters such as the applied load and the delamination size. The results obtained in this study show that the unidirectional composite laminates have better mechanical resistance one the loading line than the multidirectional composite laminates.

Keywords: Delamination, release energy rate, stratified composite, finite element method and ply.

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Authors: Sung-Hae Jun, Kyung-Whan Oh

Abstract:

Statistical learning theory was developed by Vapnik. It is a learning theory based on Vapnik-Chervonenkis dimension. It also has been used in learning models as good analytical tools. In general, a learning theory has had several problems. Some of them are local optima and over-fitting problems. As well, statistical learning theory has same problems because the kernel type, kernel parameters, and regularization constant C are determined subjectively by the art of researchers. So, we propose an evolutionary statistical learning theory to settle the problems of original statistical learning theory. Combining evolutionary computing into statistical learning theory, our theory is constructed. We verify improved performances of an evolutionary statistical learning theory using data sets from KDD cup.

Keywords: Evolutionary computing, Local optima, Over-fitting, Statistical learning theory

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Authors: H. Sezgin, O. B. Berkalp, R. Mishra, J. Militky

Abstract:

In the last few decades, due to their advanced properties, there has been an increasing interest in hybrid composite materials. In this study, the effect of different stacking sequences of jute and carbon fabric plies on dynamic mechanical properties of composite laminates were investigated. Vacuum bagging system was used to fabricate the composite samples. Each composite laminate was reinforced with two plies of jute fabric and two plies of carbon fabric by varying the position of layers. Dynamic mechanical analyzer (DMA) was used to examine the dynamic mechanical properties of composite laminates with increasing temperature. Results showed that the composite sample, which has carbon fabric at the outer layers, has the highest storage and loss modulus. Besides, it was observed that glass transition temperature (T_g) of samples are close to each other and at about 75 °C.

Keywords: Differential scanning calorimetry dynamic mechanical analysis, textile reinforced composites, thermogravimetric analysis.

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Authors: Nisrin R. Abdelal, Steven L. Donaldson

Abstract:

Composite materials are widely used in aviation industry due to their superior properties; however, they are susceptible to delamination. Through-thickness stitching is one of the techniques to alleviate delamination. Kevlar is one of the most common stitching materials; in contrast, it is expensive and presents stitching fabrication challenges. Therefore, this study compares the performance of Kevlar with an inexpensive and easy-to-use nylon fiber in stitching to alleviate delamination. Three laminates of unidirectional carbon fiber-epoxy composites were manufactured using vacuum assisted resin transfer molding process. One panel was stitched with Kevlar, one with nylon, and one unstitched. Mode I interlaminar fracture tests were carried out on specimens from the three composite laminates, and the results were compared. Fractographic analysis using optical and scanning electron microscope were conducted to reveal the differences between stitching with Kevlar and nylon on the internal microstructure of the composite with respect to the interlaminar fracture toughness values.

Keywords: Carbon, delamination, Kevlar, mode I, nylon, stitching.

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Authors: Amin Almasi

Abstract:

Composite laminates are relatively weak in out of plane loading, inter-laminar stress, stress concentration near the edge and stress singularities. This paper develops a new analytical formulation for laminated composite rotating disc fabricated from symmetric sequential quasi isotropic layers to predict three dimensional stress and deformation. This analysis is necessary to evaluate mechanical integrity of fiber reinforced multi-layer laminates used for high speed rotating applications such as high speed impellers. Three dimensional governing equations are written for rotating composite disc. Explicit solution is obtained with "Frobenius" expansion series. Based on analytical results, there are two separate zones of three dimensional stress fields in centre and edge of rotating disc. For thin discs, out of plane deformations and stresses are small in comparison with plane ones. For relatively thick discs deformation and stress fields are three dimensional.

Keywords: Composite Disc, Rotating Machine.

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Authors: Pauline E. Ngo-Henha

Abstract:

Existing turnover intention theories are reviewed in this paper. This review was conducted with the help of the search keyword “turnover intention theories” in Google Scholar during the month of July 2017. These theories include: The Theory of Organizational Equilibrium (TOE), Social Exchange Theory, Job Embeddedness Theory, Herzberg’s Two-Factor Theory, the Resource-Based View, Equity Theory, Human Capital Theory, and the Expectancy Theory. One of the limitations of this review paper is that data were only collected from Google Scholar where many papers were sometimes not freely accessible. However, this paper attempts to contribute to the research in clarifying the distinction between theories and models in the context of turnover intention.

Keywords: Job embeddedness theory, theory of organizational equilibrium (TOE), Herzberg’s two-factor theory, turnover intention theories, theories and models.

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Authors: R. Eslami-Farsani, S. M. S. Mousavi Bafrouyi

Abstract:

During past decades, increasing demand of modified Fiber Metal Laminates (FMLs) has stimulated a strong trend towards the development of these structures. FMLs contain several thin layers of metal bonded with composite materials. Characteristics of FMLs such as low specific mass, high bearing strength, impact resistance, corrosion resistance and high fatigue life are attractive. Nowadays, increasing development can be observed to promote the properties of polymer-based composites by nanofillers. By dispersing strong, nanofillers in polymer matrix, modified composites can be developed and tailored to individual applications. On the other hand, the synergic effects of nanoparticles such as graphene and carbon nanotube can significantly improve the mechanical, electrical and thermal properties of nanocomposites. In present paper, the modifying of FMLs by nanofillers and the dispersing of nanoparticles in the polymers matrix are discussed. The evaluations have revealed that this approach is acceptable. Finally, a prospect is presented. This paper will lead to further work on these modified FML species.

Keywords: Fiber metal laminate, nanofiller, polymer matrix, property modification.

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Authors: K. Krushnamurty, D. Rasmitha, I. Srikanth, K. Ramji, Ch. Subrahmanyam

Abstract:

E-glass-epoxy laminated composites having different fiber volume fractions (40, 50, 60 and 70) were fabricated with and without the addition of nanoclay. Flexural strength and tensile strength of the composite laminates were determined. It was observed that, with increasing the fiber volume fraction (V_f) of fiber from 40 to 60, the ability of nanoclay to enhance the tensile and flexural strength of E-glass-epoxy composites decreases significantly. At 70V_f, the tensile and flexural strength of the nanoclay reinforced E-glass-epoxy were found to be lowest when compared to the E-glass-epoxy composite made without the addition of nanoclay. Based on the obtained data and microstructure of the tested samples, plausible mechanism for the observed trends has been proposed. The enhanced mechanical properties for nanoclay reinforced E-glass-epoxy composites for 40-60 V_f, due to higher interface toughness coupled with strong interfilament bonding may have ensured the homogeneous load distribution across all the glass fibers. Results in the decrease in mechanical properties at 70V_f, may be due to the inability of the matrix to bind the nanoclay and glass-fibers.

Keywords: E-glass-epoxy composite laminates, fiber volume fraction, e-glass fiber, mechanical properties, delamination.

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Authors: Sh. Mirhosseini, Y. Haghighatfar, M. Sedighi

Abstract:

Forced vibration problem of a delaminated beam made of fiber metal laminates is studied in this paper. Firstly, a delamination is considered to divide the beam into four sections. The classic beam theory is assumed to dominate each section. The layers on two sides of the delamination are constrained to have the same deflection. This hypothesis approves the conditions of compatibility as well. Consequently, dynamic response of the beam is obtained by the means of differential transform method (DTM). In order to verify the correctness of the results, a model is constructed using commercial software ABAQUS 6.14. A linear spring with constant stiffness takes the effect of contact between delaminated layers into account. The attained semi-analytical outcomes are in great agreement with finite element analysis.

Keywords: Delamination, forced vibration, finite element modelling, natural frequency.

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Authors: Ajay Gupta, Arvind Bhardwaj, Arun Kanda

Abstract:

Dr Eliyahu Goldratt has done the pioneering work in the development of Theory of Constraints. Since then, many more researchers around the globe are working to enhance this body of knowledge. In this paper, an attempt has been made to compile the salient features of this theory from the work done by Goldratt and other researchers. This paper will provide a good starting point to the potential researchers interested to work in Theory of Constraints. The paper will also help the practicing managers by clarifying their concepts on the theory and will facilitate its successful implementation in their working areas.

Keywords: Drum-Buffer-Rope, Goldratt, ProductionScheduling, Theory of Constraints.

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Authors: Haiyan Wang

Abstract:

Constuctivism learning theory lays emphasis on the learners' active learning, such as learning initiative, sociality and context. By analyzing the relationship between constructivism learning theory and learner autonomy, this paper explores how to cultivate learners' learner autonomy under the guidance of constructivism learning theory.

Keywords: Constructivism learning theory, learner autonomy, relationship, cultivation.

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Authors: Serkan Narlı, Ahmet Z. Ozcelik

Abstract:

The theory of rough sets is generalized by using a filter. The filter is induced by binary relations and it is used to generalize the basic rough set concepts. The knowledge representations and processing of binary relations in the style of rough set theory are investigated.

Keywords: Rough set, fuzzy set, membership function, knowledge representation and processing, information theory

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