• Smart Structures and Systems
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• v.22 no.3
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• pp.259-276
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• 2018

This paper studies the energies and energy release rate (ERR) for the initially rotationally symmetric compressed (or stretched) in the inward (outward) radial direction of the PZT/Elastic/PZT sandwich circular plate with interface penny-shaped cracks. The investigations are made by utilizing the so-called three-dimensional linearized field equations and relations of electro-elasticity for piezoelectric materials. The quantities related to the initial stress state are determined within the scope of the classical linear theory of piezoelectricity. Mathematical formulation of the corresponding problem and determination of the quantities related to the stress-strain state which appear as a result of the action of the uniformly normal additional opening forces acting on the penny-shaped crack's edges are made within the scope of the aforementioned three-dimensional linearized field equations solution which is obtained with the use of the FEM modelling. Numerical results of the energies and ERR and the influence of the problem parameters on these quantities are presented and discussed for the PZT- 5H/Al/PZT-5H, PZT-4/Al/PZT-4, $BaTiO_3/Al/BaTiO_3$ and PZT-5H/StPZT-5H sandwich plates. In particular, it is established that the magnitude of the influence of the piezoelectricity and initial loading on the ERR increases with crack radius length.

• Smart Structures and Systems
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• v.15 no.6
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• pp.1601-1623
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• 2015

Electroactive polymers have attracted considerable attention in recent years due to their sensing and actuating properties which make them a material of choice for a wide range of applications including sensors, biomimetic robots, and biomedical micro devices. This paper presents an effective modeling strategy for nonlinear large deformation (small strains and moderate rotations) dynamic analysis of polymer actuators. Considering that the complicated electro-chemo-mechanical dynamics of these actuators is a drawback for their application in functional devices, establishing a mathematical model which can effectively predict the actuator's dynamic behavior can be of paramount importance. To effectively predict the actuator's dynamic behavior, a comprehensive mathematical model is proposed correlating the input voltage and the output bending displacement of polymer actuators. The proposed model, which is based on the rigid finite element (RFE) method, consists of two parts, namely electrical and mechanical models. The former is comprised of a ladder network of discrete resistive-capacitive components similar to the network used to model transmission lines, while the latter describes the actuator as a system of rigid links connected by spring-damping elements (sdes). Both electrical and mechanical components are validated through experimental results.

• The Mathematical Education
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• v.56 no.1
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• pp.1-17
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• 2017

The purpose of this study is to analyze the differences between the cognitive load of mathematics textbooks based on storytelling and traditional mathematics textbooks that are presented to students. In order to verify this, we have selected two 4th grade classes in elementary school that were identified as a homogeneous group through prior testing, and thus were separated into experimental group and comparative group. Then, without the teacher's lessons, the experimental group learned from mathematics textbooks based on storytelling and the comparative group learned from traditional mathematics textbooks. Afterwards, the two groups' cognitive load was measured through a questionnaire, and the following results were obtained: In the 'mental effort' and 'self evaluation' categories, the students that learned from the mathematics textbook based on storytelling showed higher scores than the students that learned from the traditional mathematics textbook. also there was statistically significant difference in some items. However, no statistically significant difference was found in the remaining categories 'task difficulty', 'self evaluation', and 'material design'.

• Research in Mathematical Education
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• v.4 no.1
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• pp.45-55
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• 2000

The rapid proliferation of wireless networks provides a ubiquitous channel for delivering instructional materials at the convenience of the user. By delivering content through portable devices linked to the Internet, the full spectrum of multimedia capabilities is available for engaging the user's interest. This capability encompasses not only text but images, video, speech generation and voice recognition. Moreover, the incorporation of machine learning capabilities at the source provides the ability to tailor the material to the general level of expertise of the user as well as the immediate needs of the moment: for instance, a request for information regarding a particular city might be covered by a leisurely presentation if solicited from the home, but more tersely if the user happens to be driving a car. This paper presents system architecture to support mobile instruction in conjunction with knowledge-based tutoring capabilities. For concreteress, the general concepts are examined in the context of a system for mathematics education on the Web.

• The Mathematical Education
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• v.55 no.4
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• pp.417-445
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• 2016

The purpose of this research is to discover and analyze the stages of concern, level of use, innovation configurations and the analysis of their relationship to each other of storytelling-based math education among elementary teachers based on the concerns-based adoption model (CBAM). And then the researcher derives support strategies for the education by empirically examining at which levels and how actual elementary teachers perceive storytelling-based math education and also how they adopt it. In addition, the researcher lays the purpose of this study on seeking proper supporting strategies for helping elementary teachers implement storytelling-based math education and providing basic material for teaching activities by examining the correlation between stages of concern, levels of use and the innovation configuration, and grasping the relation between teachers concern and their educational practice regarding storytelling-based math education.

• Journal of the Korean Society for Precision Engineering
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• v.19 no.9
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• pp.157-165
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• 2002

The design of hydraulic & control system has been developed for the disc spinning machine. The hydraulic system has been designed in the overall system including the vertical & horizontal slide fur spinning works which are controlled by hydraulic servo valves in right & left side, and the clamping slide for holding & pressing blank material in center during spinning process. Based on the design concept of this hydraulic system, model test experiments for hydraulic servo control system is tested to conform confidence and applying possibility. The control system is introduced with the fuzzy-sliding mode controller for the hydraulic force control reacting force as a disturbance, because a fuzzy controller does not require an accurate mathematical model for the generation of nonlinear factors in the actual nonlinear plant with unknown disturbances and a sliding controller has the robustness & stability in mathematical control algorithm. We conform that the fuzzy-sliding mode controller has a good performance in force control for the plant with a strong disturbance. Also, we observe that a steady state error of the fuzzy-sliding mode controller can be reduced better than those of an another controllers.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.4
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• pp.367-380
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• 2019

A 1kW-class horizontal axis wind turbine (HAWT) rotor blade is taken into account to investigate elastic characteristics in 2-D. The elastic blade field is composed of symmetric cross-ply laminated composite material. Blade element momentum theory is applied to obtain the boundary conditions pressuring the blade, and the plane stress elasticity problem is formulated in terms of two displacement parameters with mixed boundary conditions. For the elastic characteristics a fair of differential equations are derived based on the elastic theory. The domain is divided by triangular and rectangular elements due to the complexity of the blade configuration, and a finite element method is developed for the governing equations to search approximate solutions. The results describe that the elastic behavior is deeply influenced by the layered angle of the middle laminate and the stability of the blade can be improved by controlling the layered angle of laminates, which can be evaluated by the mathematical approach.

• The Mathematical Education
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• v.55 no.3
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• pp.299-316
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• 2016

The abilities for 21st learners have recently changed and learners' engagement is emphasized. In flipped classroom, students learn the prerequisite concepts of the lecture online in advance and perform various types of activities based on interaction and engagement. As students in flipped classroom construct knowledge actively, students' engagement is very important. Therefore, I conducted a research of flipped mathematics class to help teachers to better understand students' engagement in flipped mathematics class. The flipped mathematics class was conducted for about 3 weeks with 29 middle school students and one teacher. Video and audio recordings, completed student worksheets and interview data were collected and analyzed using the qualitative method. The results of this study showed that students' engagement is influenced by diverse factors. Engagement factors were categorized by teacher factors, community factors, material factors, tasks and strategy factors, classroom culture factors. Each factor facilitates or suppresses behavioral, emotional, cognitive, agentic engagements, and sometimes several factors are related. The results of this study increase understanding of engagement through the example of a case study on flipped mathematics class.

• Journal of Biosystems Engineering
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• v.14 no.4
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• pp.242-250
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• 1989

The performance of a vertical type centrifugal distributor of granular materials was studied by means of mathematical models and experimental investigations. To develop the mathematical description of particle motion, some assumptions were made. The distribution process consisted of three stages: the entrance of a particle to the blade, the motion of the particle on the blade, and the motion of the particle in the air. The physical properties of fertilizer, which affected the particle motion, were investigated: bluk density, coefficient of friction, coefficient of restitution, and particle size distribution. The particle motion were simulated by using a computer. A prototype distributor was designed and constructed for experimental tests. The following conclusions were drawn from the computer simulation and experiment results. 1. The fertilizer may slide or roll at the point of contact when they impact on the blade and move along the blade. 2. The interaction among fertilizers may prevent them from bouncing. 3. When fertilizers roll on the blade, rolling resistance is one of the factors affecting the particle's motion. 4. The trajectory angle and position of fertilizers from a disc depend on the blade position and particle shape, but the rotating speed of the disc affected them only slightly.

• School Mathematics
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• v.5 no.2
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• pp.209-221
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• 2003

This study focuses on the necessity of developing the material for teachers who are involved in diagnosing and prescribing students' mathematical errors. And it also intends to stimulate the related research of this area. For this, it tries to suggest the fundamental components-(1)types and frequencies of errors, (2) diagnostic test kit, (3)causes of errors, (4)ideas for prevention, (5)ideas for correction, (6)practice for settlement, and (7) performance test kit and frame of the teaching guide book for the teachers according to the general procedure of diagnosis and prescription. Finally it provides the concrete research areas for the future study.