• Steel and Composite Structures
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• v.34 no.4
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• pp.615-623
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• 2020

In this paper, free vibration analysis of a functionally graded cylindrical nanoshell resting on Pasternak foundation is presented based on the nonlocal elasticity theory. A two-dimensional formulation along the axial and radial directions is presented based on the first-order shear deformation shell theory. Hamilton's principle is employed for derivation of the governing equations of motion. The solution to formulated boundary value problem is obtained based on a harmonic solution and trigonometric functions for various boundary conditions. The numerical results show influence of significant parameters such as small scale parameter, stiffness of Pasternak foundation, mode number, various boundary conditions, and selected dimensionless geometric parameters on natural frequencies of nanoshell.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.595-601
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• 2014

For analysis of the plates and membranes by numerical or analytical methods, the question of choice of the system of functions satisfying the different boundary conditions remains a major challenge to address. It is to this issue that is dedicated this work based on an approach of choice of combinations of trigonometric functions, which are shape functions of a bended beam with the boundary conditions corresponding to the plate support mode. To do this, the shape functions of beam vibrations for strength analysis of the rectangular plates by Kantorovich-Vlasov's method is considered. Using the properties of quasi-orthogonality of those functions allowed assessing to differential equation for every member of the series. Therefore it's proposed some new forms of integration of the beam functions, in order to simplify the problem.

• Steel and Composite Structures
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• v.39 no.3
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• pp.291-306
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• 2021

Based on Reissner's mixed variational theorem (RMVT), the authors develop a semi-analytical finite element (FE) method for a three-dimensional (3D) bending analysis of nonhomogeneous orthotropic, complete and incomplete toroidal shells subjected to uniformly-distributed loads. In this formulation, the toroidal shell is divided into several finite annular prisms (FAPs) with quadrilateral cross-sections, where trigonometric functions and serendipity polynomials are used to interpolate the circumferential direction and meridian-radial surface variations in the primary field variables of each individual prism, respectively. The material properties of the toroidal shell are considered to be nonhomogeneous orthotropic over the meridianradial surface, such that homogeneous isotropic toroidal shells, laminated cross-ply toroidal shells, and single- and bi-directional functionally graded toroidal shells can be included as special cases in this work. Implementation of the current FAP methods shows that their solutions converge rapidly, and the convergent FAP solutions closely agree with the 3D elasticity solutions available in the literature.

• Journal of The Korean Association of Information Education
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• v.21 no.2
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• pp.199-208
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• 2017

The present study investigates the potential of an educational programming game as a strategy for enhancing effective domains of mathematics curriculum, which has been criticized as a problem of education in Korea. The process of programming Fortress, an educational game, in conjunction with the lesson on the trigonometric function as part of the middle school mathematics curriculum, was designed for instruction and learning, and its effectiveness was tested. The study was conducted using a nonequivalent pretest-posttest experimental design. Research procedures included the following steps: (1) both the experimental and the comparison groups participated in four classes to understand and apply the concept of the trigonometric function, and (2) the experimental group participated in Fortress game programming activities using Scratch, which was designed in this study, while the comparison group participated in solving a real-life trigonometric problem - calculating the height of a building using the concept of trigonometry. The results of the t-test showed that students' interest and perceived value of the mathematics curriculum were significantly higher in the experimental group than in the comparison group. However, the results of analysis of covariance (ANCOVA) using pretest scores of the interest and perceived value showed the influence of pretest scores on posttest scores for the interest level, although the effect of the experiment on the perceived value of the mathematics curriculum was more significant.

• Journal of Veterinary Clinics
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• v.22 no.2
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• pp.79-83
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• 2005

Six dogs including 4 dogs living in different geographic locations of Kangwon province and 2 client-owned dogs were used to determine the periodicity of microfilariae of D. immitis using a trigonometric model. The calculated periodicity index was ranged from 25.6 to $95.5\%$ with mean of $57.6\%$, and the estimated hour of peak was approximately 21:00 hrs (range, 20:04-21:29 hrs) and minimum counts at 09:00 hrs (range, 08:04 - 09:29 hrs). Correlation coefficient between the observed and the expected count from the model varies depending on dogs, ranging from 6.4 to $49.2\%$. Based on this study, the periodicity of microfilariae of D. immitis was considered as nocturnally sub-periodic for all dogs employed. This result is in consistent with previous report in peak hour but different in minimal hour, indicating that further studies on the periodicity need to be performed to better understanding the dynamics of the periodicity and to help practitioners in the choice of the time for examination of the dogs.

• School Mathematics
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• v.17 no.2
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• pp.309-329
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• 2015

This study is to provide didactical implications for teaching and learning of radian through a analysis of investigation result about pre-service teachers' understanding of radian. The results of this study are as follows. First, pre-service teachers understood the radian as ${\frac{180^{\circ}}{\pi}}$, rather than as the definition. Secondly, the definition style of radian affected the problem solving strategy for the measurement of the angle. Thirdly, pre-service teachers had insufficient content knowledge about properties of measurement as a pure number of radian. Lastly, They failed to describe the usefulness of circular measure. We suggested the definition of radian in textbooks should be changed from ${\frac{180^{\circ}}{\pi}}$ to mathematical definition of radian. And the general angle should be stated as the reason why the domain of trigonometric function is real numbers.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.391-402
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• 2017

In this paper, a new nonlocal trigonometric shear deformation theory is proposed for thermal buckling response of nanosize functionally graded (FG) nano-plates resting on two-parameter elastic foundation under various types of thermal environments. This theory uses for the first time, undetermined integral variables and it contains only four unknowns, that is even less than the first shear deformation theory (FSDT). It is considered that the FG nano-plate is exposed to uniform, linear and sinusoidal temperature rises. Mori-Tanaka model is utilized to define the gradually variation of material properties along the plate thickness. Nonlocal elasticity theory of Eringen is employed to capture the size influences. Through the stationary potential energy the governing equations are derived for a refined nonlocal four-variable shear deformation plate theory and then solved analytically. A variety of examples is proposed to demonstrate the importance of elastic foundation parameters, various temperature fields, nonlocality, material composition, aspect and side-to-thickness ratios on critical stability temperatures of FG nano-plate.

• The Korean Journal of Applied Statistics
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• v.29 no.1
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• pp.193-203
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• 2016

This paper forecasts electricity demand as a critical element of a demand management system in Smart Grid environment. We present a prediction method of using a combination of predictive values by time series clustering. Periodogram-based normalized clustering, predictive analysis clustering and dynamic time warping (DTW) clustering are proposed for time series clustering methods. Double Seasonal Holt-Winters (DSHW), Trigonometric, Box-Cox transform, ARMA errors, Trend and Seasonal components (TBATS), Fractional ARIMA (FARIMA) are used for demand forecasting based on clustering. Results show that the time series clustering method provides a better performances than the method using total amount of electricity demand in terms of the Mean Absolute Percentage Error (MAPE).

• Steel and Composite Structures
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• v.34 no.4
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• pp.511-524
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• 2020

In this research, a simple four-variable trigonometric integral shear deformation model is proposed for the static behavior of advanced functionally graded (AFG) ceramic-metal plates supported by a two-parameter elastic foundation and subjected to a nonlinear hygro-thermo-mechanical load. The elastic properties, including both the thermal expansion and moisture coefficients of the plate, are also supposed to be varied within thickness direction by following a power law distribution in terms of volume fractions of the components of the material. The interest of the current theory is seen in its kinematics that use only four independent unknowns, while first-order plate theory and other higher-order plate theories require at least five unknowns. The "in-plane displacement field" of the proposed theory utilizes cosine functions in terms of thickness coordinates to calculate out-of-plane shear deformations. The vertical displacement includes flexural and shear components. The elastic foundation is introduced in mathematical modeling as a two-parameter Winkler-Pasternak foundation. The virtual displacement principle is applied to obtain the basic equations and a Navier solution technique is used to determine an analytical solution. The numerical results predicted by the proposed formulation are compared with results already published in the literature to demonstrate the accuracy and efficiency of the proposed theory. The influences of "moisture concentration", temperature, stiffness of foundation, shear deformation, geometric ratios and volume fraction variation on the mechanical behavior of AFG plates are examined and discussed in detail.

• Steel and Composite Structures
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• v.47 no.5
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• pp.551-568
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• 2023

In this research, a new two-dimensional (2D) and quasi three-dimensional (quasi-3D) higher order shear deformation theory is devised to address the bending problem of functionally graded plates resting on an elastic foundation. The displacement field of the suggested theories takes into account a parabolic transverse shear deformation shape function and satisfies shear stress free boundary conditions on the plate surfaces. It is expressed as a combination of trigonometric and exponential shear shape functions. The Pasternak mathematical model is considered for the elastic foundation. The material properties vary constantly across the FG plate thickness using different distributions as power-law, exponential and Mori-Tanaka model. By using the virtual works principle and Navier's technique, the governing equations of FG plates exposed to sinusoidal and evenly distributed loads are developed. The effects of material composition, geometrical parameters, stretching effect and foundation parameters on deflection, axial displacements and stresses are discussed in detail in this work. The obtained results are compared with those reported in earlier works to show the precision and simplicity of the current formulations. A very good agreement is found between the predicted results and the available solutions of other higher order theories. Future mechanical analyses of three-dimensionally FG plate structures can use the study's findings as benchmarks.