• 한국수학교육학회지시리즈B:순수및응용수학
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• 제26권3호
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• pp.157-175
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• 2019

In this paper we define higher-order Stieltjes derivatives, and using Schaefer's fixed point theorem we investigate the existence of solutions for a class of differential equations involving second-order Stieltjes derivatives with two-point boundary conditions. The equations include ordinary and impulsive differential equations, and difference equations.

• 한국전산구조공학회논문집
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• 제21권4호
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• pp.391-399
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• 2008

본 논문에서는 다중 균열 구조물에서의 균열 진전에 따른 에너지 해방을 및 고차 미분값을 구할 수 있는 가상균열 진전법을 제시한다. 이 방법은 다중 균열 체계의 에너지 해방율과 고차 미분값이 단 한번의 해석으로 수행될 수 있는 장점이 있다. 예제에서 얻어진 해의 최대 오차는 에너지 해방율 0.2%, 일차 미분값 $2\sim3%$, 이차 미분값 $5\sim10%$이다 이 방법으로 구한 에너지 해방률의 미분값들은 파괴 확률을 구하거나, sire effect law에 적용될 수 있다.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권1호
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• pp.1-19
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• 2017

In this paper we obtain some integral inequalities by using Stieltjes derivatives, and we apply our results to the study of asymptotic behavior of a certain second-order integro-differential equation.

• 한국공작기계학회논문집
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• 제15권3호
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• pp.8-16
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• 2006

This paper discusses design sensitivity analysis and its application to a structural dynamics modification. Eigenvalue derivatives are determined with respect to the element parameters, which include intrinsic property parameters such as Young's modulus, density of the material, diameter of a beam element, thickness of a plate element, and shape parameters. Derivatives of stiffness and mass matrices are directly calculated by derivatives of element matrices. The first and the second order derivatives of the eigenvalues are then mathematically derived from a dynamic equation of motion of FEM model. The calculation of the second order eigenvalue derivative requires the sensitivity of its corresponding eigenvector, which are developed by Nelson's direct approach. The modified eigenvalue of the structure is then evaluated by the Taylor series expansion with the first and the second derivatives of eigenvalue. Numerical examples for simple beam and plate are presented. First, eigenvalues of the structural system are numerically calculated. Second, the sensitivities of eigenvalues are then evaluated with respect to the element intrinsic parameters. The most effective parameter is determined by comparing sensitivities. Finally, we predict the modified eigenvalue by Taylor series expansion with the derivatives of eigenvalue for single parameter or multi parameters. The examples illustrate the effectiveness of the eigenvalue sensitivity analysis for the optimization of the structures.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.721-726
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• 2004

A simplified method for the computation of first second and higher order derivatives of eigenvalues and eigenvectors derivatives associated with repeated eigenvalues is presented. Adjacent eigenvectors and orthonormal conditions are used to compose an algebraic equation whose order is (n+m)x(n+m), where n is the number of coordinates and m is the number of multiplicity of the repeated eigenvalues. The algebraic equation developed can be used to compute derivatives of both eigenvalues and eigenvectors simultaneously. Since the coefficient matrix in the proposed algebraic equation is non-singular, symmetric and based on N-space it is numerically stable and very efficient compared to previous methods. This method can be consistently applied to structural systems with structural design parameters and mechanical systems with lumped design parameters. To verify the effectiveness of the proposed method, the finite element model of the cantilever beam is considered.

• 한국수학교육학회지시리즈A:수학교육
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• 제53권1호
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• pp.25-40
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• 2014

Mathematical concept exists in the structural form, not in the independent form. The purpose of this study is to consider the network which students actually have for the mathematical concept structure related to the properties of derivatives. First, we analyzed the properties of derivatives in 'Mathematics II' and showed the mathematical concept structure of the relations among derivatives, functions, and primitive functions as a network. Also, we investigated the understanding of high school students for the mathematical concept structure between derivatives and functions, and the structure between functions and second order derivatives when the functional formula is not given, and only the graph is given. The results showed that students mainly focus on the relation of 'function-derivatives', the thinking process for direction of derivative and the thinking style for algebra. On this basis, we suggest the educational implication that is necessary for students to build the network properly.

• Journal of Hydrospace Technology
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• 제1권1호
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• pp.66-74
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• 1995

Unknown parameters can be determined by system identification techniques. Extended Kalman filter method was introduced as a real time estimator of hydrodynamic derivatives but it has the problem named the coefficient drift. In this study, 2nd order filter estimates hydrodynamic derivatives in Abkowitz model In order to reduce the coefficient drift, parallel processing is used. The measured state and ship trajectory are compared with the estimated values. Parallel processing of 2nd order filter gives very similar results to parallel processing of extended Kalman filter. Parallel processing cannot not remove the coefficient drift perfectly, but it reduces the estimation error.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1996년도 춘계 학술대회논문집
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• pp.46-51
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• 1996

The flow field around a three dimensional minivan-like body has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system using second-order accurate schemes for the time derivatives, and third/second-order scheme for the spatial derivatives. The Marker-and-Cell concept is applied to efficiently solve continuity equation. The fourth -order artificial damping is added to the continuity equation for numerical stability. A H-H type multi-block grid system is generated around a three dimensional minivan-like body. Turbulent flows have been modeled by the Baldwin-Lomax turbulent model. The simulation shows three dimensional vortex-pair just behind body. And the flow separation is also observed the rear of the body. It has concluded that the results of present study properly agree with physical flow phenomena.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 1997년도 추계 학술대회논문집
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• pp.86-91
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• 1997

This paper describes analysis of complex flow around Car-like body using Chimera grid technique. As a computational algorithm, Pullboat and Chaussee's Diagonal algorithm is selected to reduce computational time. Introducing hole points flag to this Diagonal algorithm, an algorithm for Chimera grid is generated easily. This study solves 3-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system using second-order accurate schemes for the time derivatives, and third/second-order scheme for the spatial derivatives. The Marker-and-Cell concept is applied to efficiently solve continuity equation. The fourth-order artificial damping is added to the continuity equation for numerical stability, It has concluded that the results of present study properly agree with physical flow phenomena.

• 충청수학회지
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• 제27권1호
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• pp.133-143
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• 2014

A new three-step quadraparametric family of eighth-order iterative methods free from second derivatives are proposed in this paper to find a simple root of a nonlinear equation. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.