• Journal of the Korean School Mathematics Society
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• v.12 no.2
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• pp.151-170
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• 2009

The purpose of the study is to analyze the sixth graders' understanding of concepts and operation about fraction. The test was administered and analyzed to 707 sixth graders' performance on fractions after the fraction instructions in elementary schools in Seoul, Korea. The participants are asked to answer two sets of questions for 40 minutes. First, they are asked to answer to 16 problems about the concepts of fraction with respect to part-whole, ratio, operator, measure, quotient, equivalent, and operations. Second, specially, to investigate sixth graders' ability of drawing and describing the situation of division including fraction, the descriptive problem asked students (1) to describe $3\;{\div}\;\frac{1}{2}$ into pictorial representation and (2) to write the solving process. The participants of this study didn't show deep understandings about the concepts and operation of fraction. The degree of understanding of subconstructs of fraction shows that their knowledge of ratio concept with respect to fraction was highest while their understanding of measure with respect to fraction was lowest. Considering their wrong answers, about 59% of participants showed misconception to the question of naming one fraction that appears between $\frac{1}{5}$ and $\frac{1}{6}$. Further, they didn't explain their understanding with drawing about the division of fraction ($3\;{\div}\;\frac{1}{2}$).

• Advances in nano research
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• v.10 no.2
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• pp.129-138
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• 2021

In present article, utilizing the Love shell theory with volume fraction laws for the cylindrical shells vibrations provides a governing equation for the distribution of material composition of material. Isotopic materials are the constituents of these rings. The position of a ring support has been taken along the radial direction. The Rayleigh-Ritz method with three different fraction laws gives birth to the shell frequency equation. Moreover, the effect of height- and length-to-radius ratio and angular speed is investigated. The results are depicted for circumferential wave number, length- and height-radius ratios with three laws. It is found that the backward and forward frequencies of exponential fraction law are sandwich between polynomial and trigonometric laws. It is examined that the backward and forward frequencies increase and decrease on increasing the ratio of height- and length-to-radius ratio. As the position of ring is enhanced for clamped simply supported and simply supported-simply supported boundary conditions, the frequencies go up. At mid-point, all the frequencies are higher and after that the frequencies decreases. The frequencies are same at initial and final stage and rust itself a bell shape. The shell is stabilized by ring supports to increase the stiffness and strength. Comparison is made for non-rotating and rotating cylindrical shell for the efficiency of the model. The results generated by computer software MATLAB.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1891-1897
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• 2006

In this study, a new model to predict the effective elastic constants of composites with spherical fillers is proposed. The original Eshelby model is extended to a finite filler volume fraction without using Mori-Tanaka's mean field approach. When single filler is embedded in the matrix, the effective elastic constants of the composite are computed. The composite is in turn considered as a new matrix, where new single filler is again embedded in the matrix. The predicted results by the present model with a series of embedding procedures are compared with those by Mori-Tanaka, self-consistent, and generalized self-consistent models. It is revealed through parametric studies such as stiffness ratio of the filler to the matrix and filler volume fraction that the present model gives more accurate predictions than Mori-Tanaka model without using the complicated numerical scheme used in self-consistent and generalized self-consistent models.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.6 no.3
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• pp.58-64
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• 1997

A micromechanics model to describe the elastic behavior of fiber or whisker reinforced metal matrix composites was developed and the stress concentrations between reinforcements were investigated using the modified shear lag model with the comparison of finite element analysis (FEA). The rationale is based on the replacement of the matrix between fiber ends with the fictitious fiber to maintain the compatibility of displacement and traction. It was found that the new model gives a good agreement with FEA results in the small fiber aspect ratio regime as well as that in the large fiber aspect ratio regime. By the calculation of the present model, stress concentration factor in the matrix and the composite elastic modulus were predicted accurately. Some important factors affecting stress concentrations, such as fiber volume fraction, fiber aspect ratio, end gap size, and modulus ratio, were also discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.318-324
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• 2005

Theoretical efforts are performed to extend the formulation of NSLT(New Shear Lag Theory) for the prediction of the elastic modulus in short fiber composite. The formulation is based on the elastic stress transfer considering the stress concentration effects influenced by elastic modulus ratio between fiber and matrix. The composite modulus, thus far, is calculated by changing the fiber aspect ratio and volume fraction. It is found that the comparison with FEA(Finite Element Analysis) results gives a good agreement with the present theory (NSLT). It is also found that the NSLT is more accurate than the SLT(Shear Lag Theory) in short fiber regime when compared by FEA results. However, The modulus predicted by NSLT becomes similar values that of SLT when the fiber aspect ratio increases. Finally, It is shown that the present model has the capability to predict the composite modulus correctly in elastic regime.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.06a
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• pp.1812-1818
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• 2005

Even though SMA actuators have high power to volume ratio, there exist disadvantages such as hysteresis and saturation. So the model identification for SMA actuators is very difficult. For the qualitative model identification, we described the behavior of SMA actuators using a so-called diagonal model, which can readily expect the turning point of an incomplete phase transformation. For the quantitative model identification, we developed the general dynamics of SMA actuators using the modified Liang's model. Using this dynamics we can describe the hysteresis and the saturation very well. It is also very important to notice that the modified Liang's model maintains a continuous martensite fraction at the change of the phase transformation but the original model cannot.

• Journal of the Korean Society for Precision Engineering
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• v.27 no.9
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• pp.52-57
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• 2010

The analysis of a crack in a bone-like material is performed numerically. The bone-like material is hierarchically structured and each hierarchy is structured by mineral platelets and protein matrix through staggered arrangement. Mechanical behavior of the composite can be analyzed using tension shear chain model. The Dugdale model is adopted to evaluate the fracture energy of Bone-like material. The fracture energy dissipation is assumed to concentrate within a strip near the crack tip along the prospective crack path. Fracture criterion of the bone-like material is estimated by using J integral. Effects of hierarchical level, ratio of elastic modulus of mineral to protein, aspect ratio of mineral platelet and volume fraction on J integral are investigated. It is found that the J integral decreases as elastic modulus ratio and hierarchy level increase. It is also shown that the J integral increases as the volume fraction and aspect ratio decrease.

• Transactions of Materials Processing
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• v.8 no.4
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• pp.374-383
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• 1999

To determine the flow stress of semi-solid materials, a new combined method has been studied by experimental and analytic technique in the current approach. Using backward extrusion experiment and its numerical analysis, the characterization scheme of semi-solid materials according to the change of initial solid volume fraction has been proposed. Because that solid volume fraction is sensitive to temperature change, it is required to precisely control the temperature setting. Model materials can guarantee the establishment of material characterization technique from the noise due to temperature change. Thus, clay mixed with bonded abrasives was used for experiment and the change of initial solid fraction was copied out through the variation of mixing ratio. Upper bound method was adapted to increase in efficiency of the calculation in numerical analysis and new kinematically admissible velocity field was employed to improve the accuracy of numerical solution. It is thought that the material characterization scheme proposed in this study can be applied to not only semi-solid materials, but also other materials that is difficult to obtain the simple stress state.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.102-105
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• 2008

To investigate the evolution of deformation texture during cold rolling deformation, cold rolling process on a commercial Al-5% Mg sheet was carried out at different rolling reduction ratio. The evolution of annealing texture in cold-rolled Al-5% Mg sheet was also investigated. The evolution of recrystallization texture during annealing process strongly depends on the rolling reduction ratio before heat treatment. Visco-plastic self-consistent (VPSC) polycrystal model was used to predict r-value anisotropy of the cold-rolled and annealed Al-5% Mg sheets. The change of volume fraction for the major texture components was also analyzed.

• Structural Engineering and Mechanics
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• v.61 no.5
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• pp.605-615
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• 2017

Shear failure of reinforced concrete (RC) beams is a major concern for structural engineers. It has been shown through various studies that the shear strength and ductility of RC beams can be improved by adding steel fibers to the concrete. An accurate model predicting the shear strength of steel fiber reinforced concrete (SFRC) beams will help SFRC to become widely used. An artificial neural network (ANN) model consisting of an input layer, a hidden layer of six neurons and an output layer was developed to predict the shear strength of SFRC slender beams without stirrups, where the input parameters are concrete compressive strength, tensile reinforcement ratio, shear span-to-depth ratio, effective depth, volume fraction of fibers, aspect ratio of fibers and fiber bond factor, and the output is an estimate of shear strength. It is shown that the model is superior to fourteen equations proposed by various researchers in predicting the shear strength of SFRC beams considered in this study and it is verified through a parametric study that the model has a good generalization capability.