• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1075-1083
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• 2000

The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method. The prediction of the inelastic behavior of the structure is an essential part of reliability assessment procedure, because most of the failures are induced by the inelastic deformation, such as creep and plastic deformation. During decades, there has been much progress in understanding of the inelastic behavior of the materials and a lot of inelastic constitutive equations have been developed. These equations consist of the definition of inelastic strain and the evolution of the state variables introduced to quantify the irreversible processes occurred in the material. With respect to the definition of the inelastic strain, the inelastic constitutive models can be categorized into elastoplastic model, unified viscoplastic model and separated viscoplastic model and the different integration methods have been applied to each category. In the present investigation, the generalized integration method applicable for various types of constitutive equations is developed and implemented into ABAQUS by means of UMAT subroutine. The solution of the non-linear system of algebraic equations arising from time discretization with the generalized midpoint rule is determined using line-search technique in combination with Newton method. The strategy to control the time increment for the improvement of the accuracy of the numerical integration is proposed. Several numerical examples are considered to demonstrate the efficiency and applicability of the present method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.413-420
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• 2012

In this study, the Kernel integration scheme for 2D linear elastic direct boundary element method has been discussed on the basis of subparametric element. Usually, the isoparametric based boundary element uses same polynomial order in the both basis function and mapping function. On the other hand, the order of mapping function is lower than the order of basis function to define displacement field when the subparametric concept is used. While the logarithmic numerical integration is generally used to calculate Kernel integration as well as Cauchy principal value approach, new formulation has been derived to improve the accuracy of numerical solution by algebraic modification. The subparametric based direct boundary element has been applied to 2D elliptical partial differential equation, especially for plane stress/strain problems, to demonstrate whether the proposed algebraic expression for integration of singular Kernel function is robust and accurate. The problems including cantilever beam and square plate with a cutout have been tested since those are typical examples of simple connected and multi connected region cases. It is noted that the number of DOFs has been drastically reduced to keep same degree of accuracy in comparison with the conventional isoparametric based BEM. It is expected that the subparametric based BEM associated with singular Kernel function integration scheme may be extended to not only subparametric high order boundary element but also subparametric high order dual boundary element.

• Communications of Mathematical Education
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• v.23 no.1
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• pp.109-128
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• 2009

This study aimed to investigate students' learning process by examining their perception process of problem structure and mathematization, and further to suggest an effective teaching and learning of mathematics to improve students' problem-solving ability. Using the qualitative research method, the researcher observed the collaborative learning of two middle school students by providing problem-posing activities of five lessons and interviewed the students during their performance. The results indicated the student with a high achievement tended to make a similar problem and a new problem where a problem structure should be found first, had a flexible approach in changing its variability of the problem because he had advanced algebraic thinking of quantitative reasoning and reversibility in dealing with making a formula, which related to developing creativity. In conclusion, it was observed that the process of problem posing required accurate understanding of problem structures, providing students an opportunity to understand elements and principles of the problem to find the relation of the problem. Teachers may use a strategy of simplifying external structure of the problem and analyzing algebraical thinking necessary to internal structure according to students' level so that students are able to recognize the problem.

• Journal of the Korea institute for structural maintenance and inspection
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• v.22 no.5
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• pp.13-22
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• 2018

In this study, a governing differential equation for the bending problem of orthotropic rectangular plate is drived. It's exact solution for various boundary conditions is presented. This solution follows traditional method like Navier's solution or Levy's solution that transforms the governing differential equation into an algebraic equation by using trigonometric series. To obtain a solution by Levy's method, it is required that two opposite edges of the plate be simply supported. And the boundary conditions, for which the Navier's method is applicable, are simply supported edge at all edges. In this study, it overcomes the limitations of the previous Navier's and Levy's methods.This solution is applicable for any combination of boundary conditions with simply supported edge and clamped edge in x, y direction. The plate could be subjected to uniform, partially uniform, and line loads. The advantage of the solution is that it is the exact solution as well as it overcomes the limitations of the previous Navier's and Levy's methods. Calculations are presented for orthotropic plates with nonsymmetric boundary conditions. Comparisons between the result of this paper and the result of Navier, Levy and Szilard solutions are made for the isotropic plates. The deflections were in excellent agreement.

• School Mathematics
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• v.18 no.3
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• pp.589-609
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• 2016

In this study, researchers have modernly reinterpreted geometric solving of cubic equations presented by an arabic mathematician, Omar Khayyam in medieval age, and have considered the pedagogical significance of geometric solving of the cubic equations using two conic sections in terms of analytic geometry. These efforts allow to analyze educational application of mathematics instruction and provide useful pedagogical implications in school mathematics such as 'connecting algebra-geometry', 'induction-generalization' and 'connecting analogous problems via analogy' for the geometric approaches of cubic equations: $x^3+4x=32$, $x^3+ax=b$, $x^3=4x+32$ and $x^3=ax+b$. It could be possible to reciprocally convert between algebraic representations of cubic equations and geometric representations of conic sections, while geometrically approaching the cubic equations from a perspective of connecting algebra and geometry. Also, it could be treated how to generalize solution of cubic equation containing variables from geometric solution in which coefficients and constant terms are given under a perspective of induction-generalization. Finally, it could enable to provide students with some opportunities to adapt similar solving procedures or methods into the newly-given cubic equation with a perspective of connecting analogous problems via analogy.

• Journal of Korean Society of Steel Construction
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• v.10 no.4 s.37
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• pp.657-666
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• 1998

This study presents an effective dual algorithm for the optimal design of steel structures with displacement constraints. The dual method can replace a primary optimization problem with a sequence of approximate explicit subproblems with a simple algebraic structure. Since being convex and separable, each subproblem can be solved efficiently by the dual method. Specifically, this study uses the principle of virtual work to obtain the displacement constraint equations with an explicit form and adds the linear regression equation expressing the relationships between the cross-section properties to the dual algorithm to reduce the number of design variables. Furthermore, this study deals with the discrete optimization problem to select members with the standard steel sections. Through numerical analyses, the proposed method will be compared with the conventional optimality criteria method.

• Tunnel and Underground Space
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• v.14 no.6 s.53
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• pp.391-398
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• 2004

An algebraic algorithm for predicting the joint trace distribution on the cut-face of rock slope based on the orientations and the locations of joints investigated in the borehole has been developed. Joint trace prediction is manipulated by utilizing the three dimensional plane equations of both joint planes and projection face, and the extent of trace within the projection area is calculated by considering the persistence of each joint plane. Joint trace prediction method is efficiently applied for analyzing the stability and the adequacy of support design of Gimhae Naesam cut-slope, which is structurally unstable due to slumping. Structural characteristics of rock mass is investigated by performing DOM drilling and the potential rock mass sliding inside slope face is analyzed by examining the orientations of joint planes which can induce the slope failure. Also, the efficiency of anchor support design is evaluated by considering the joint trace distribution on the anchor installation area and its sliding potential.

• Wind and Structures
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• v.23 no.6
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• pp.505-521
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• 2016

The objective of this study is to investigate numerically the effect of building roof shaps on wind flow and pollutant dispersion in a street canyon with one row of trees of pore volume, $P_{vol}=96%$. A three-dimensional computational fluid dynamics (CFD) model is used to evaluate air flow and pollutant dispersion within an urban street canyon using Reynolds-averaged Navier-Stokes (RANS) equations and the Explicit Algebraic Reynolds Stress Models (EARSM) based on k-${\varepsilon}$ turbulence model to close the equation system. The numerical model is performed with ANSYS-CFX code. Vehicle emissions were simulated as double line sources along the street. The numerical model was validated by the wind tunnel experiment results. Having established this, the wind flow and pollutant dispersion in urban street canyons (with six roof shapes buildings) are simulated. The numerical simulation results agree reasonably with the wind tunnel data. The results obtained in this work, indicate that the flow in 3D domain is more complicated; this complexity is increased with the presence of trees and variability of the roof shapes. The results also indicated that the largest pollutant concentration level for two walls (leeward and windward wall) is observed with the upwind wedge-shaped roof. But the smallest pollutant concentration level is observed with the dome roof-shaped.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.9
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• pp.88-93
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• 2003

This Paper described the simulation program development for helicopter. In the design of flight control system to accomplish some special missions like UAV, it is important to minimize the execution time obtaining a linear model from nonlinear model that is used for design of controller. The first step for this kind of purpose is to complete a nonlinear model that contains full dynamic characteristics. The second step is to get the trim values that are obtained from the nonlinear model by solving an algebraic equation. And then stability and control derivatives are derived through hovering to forward flight by numerical perturbation that will be used for linear model for a specified flight condition. The software program(HeliSim) is developed by using MATLAB GUI and will provide easy modeling procedure. The suggested method in this paper is much more simpler than any other method like a fully scale helicopter model. The advantage of our suggested method will reduce the computational time due to simple formula to extract a linear model from nonlinear model that will be beneficially used for flight control system of unmanned helicopter by some reduction of computational load.