• 대한수학회지
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• 제61권4호
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• pp.621-657
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• 2024

In this study, the numerical solution of a space-fractional Burgers' equation with initial and boundary conditions is considered. This equation is the simplest nonlinear model for diffusive waves in fluid dynamics. It occurs in a variety of physical phenomena, including viscous sound waves, waves in fluid-filled viscous elastic pipes, magneto-hydrodynamic waves in a medium with finite electrical conductivity, and one-dimensional turbulence. The proposed QBS/CNG technique consists of the Galerkin method with a function basis of quadratic B-splines for the spatial discretization of the space-fractional Burgers' equation. This is then followed by the Crank-Nicolson approach for time-stepping. A linearized scheme is fully constructed to reduce computational costs. Stability analysis, error estimates, and convergence rates are studied. Finally, some test problems are used to confirm the theoretical results and the proposed method's effectiveness, with the results displayed in tables, 2D, and 3D graphs.

• Steel and Composite Structures
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• 제44권4호
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• pp.531-543
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• 2022

An exact dynamic analytical method for free vibrations of continuous partial-interaction composite beams is proposed based on the Timoshenko beam theory. The main advantage of this method is that the independent shear deformations and rotary inertia of sub-beams are considered, which is more in line with the reality. Therefore, the accuracy of eigenfrequencies obtained by this method is significantly improved, especially for higher order modes, compared to the existing methods where the rotary angles of both sub-beams are assumed to be equal irrespective of the differences in the shear stiffness of each sub-beam. Furthermore, the solutions obtained by the proposed method are exact owing to no introduction of approximated displacement and force fields in the derivation. In addition, an exact analytical solution for the case of simply supported is obtained. Based on this, an approximate expression for the fundamental frequency of continuous partial-interaction composite beams is also proposed, which is useful for practical engineering applications. Finally, the practicability and effectiveness of the proposed method and the approximate expression are explored using numerical and experimental examples; The influence factors including the interfacial interaction, shear modulus ratio, span-to-depth ratio, and side-to-main span length ratio on the eigenfrequencies are presented and discussed in detail.

• Structural Engineering and Mechanics
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• 제34권1호
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• pp.139-142
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• 2010

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2003년도 The Fifth Asian Computational Fluid Dynamics Conference
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• pp.33-34
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• 2003

• 비파괴검사학회지
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• 제24권6호
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• pp.559-565
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• 2004

원주형 기공(SDH: side-drilled hole)의 초음파 산란장 해석을 두 가지 방법으로 수행하였다. 근사해석법인 Kirchhoff 근사법과 변수분리에 의한 엄밀해법으로 구한 원거리 산란진폭 식을 제시하고 시간영역에서 그 결과를 서로 비교하였다. 수직횡파(SV)의 SDH 입사를 고려하였으며, 원거리 산란 진폭을 주파수와 시간영역에서 각각 구하였다. 엄밀해법은 직접 산란파뿐만 아니라 잠행성 파를 나타내었으며, Kirchhoff 근사법은 잠행성 파를 예측하지 못하는 젓을 제외하고 엄밀해의 결과와 잘 일치하였다. 수침, 펄스-에코 시험법에서 SDH의 수신 신호 응답을 예측할 수 있는 두 가지 측정모델을 소개하였고, 수직 횡파가 45도로 입사할 때 지름 1mm SDH의 수신신호를 계산하고 그 결과를 실험과 비교하였다.

• Steel and Composite Structures
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• 제26권4호
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• pp.453-461
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• 2018

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.

• 한국정보통신학회:학술대회논문집
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• 한국정보통신학회 2012년도 추계학술대회
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• pp.590-593
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• 2012

매설강관에 대한 전파상수는 대지도전율에 의한 매질 영향을 받기 때문에 대기중에서의 해석과 같지 않고 복잡한 초월식을 풀어야 하는 어려움이 있다. 이러한 매설관에 대한 전파상수 해석에 관하여는 Wait의 논문에서 연구되어 있고 이것을 근간으로 일본과 미국에서 각각 전송선 이론에 의한 초월식을 실용적으로 수립하여 제시하고 있다. 본 논문에서는 매설 강관에 대한 몇 가지 다른 형태의 전파상수 계산식에 대하여 시뮬레이션을 통한 값을 다루어 보고 유도전압에 대하여 적절한 산출 적용이 되는 지 검토하여 본 바 정학한 계의 해석에 의한 것과 Wait 근간의 일본 방식에 의한 계산값이 유사한 것으로 도출되었다.

• Steel and Composite Structures
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• 제45권4호
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• pp.547-554
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• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• 한국소음진동공학회논문집
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• 제14권1호
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• pp.56-63
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• 2004

Exact solutions are presented for the free vibration and buckling of rectangular plates haying two opposite edges ( x=0 and a) simply supported and the other two ( y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress $\sigma$$_{x}$=- $N_{0}$[1-a(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement ( w) to vary as sin(m$\pi$x/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients. for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and byields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters a= 0, 0.5, 1, 1.5. 2, for which a=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for a= 0, 1, 2 obtained by the method of integration of the differential equation (a=0) or the method of energy (a=1, 2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b =0.5, 1, 2 when a=2, with load intensities $N_{0}$ / $N_{cr}$ =0, 0.5, 0.8, 0.95, 1. where $N_{cr}$ is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes ate also shown.shown.

• 복합신소재구조학회 논문집
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• 제4권1호
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• pp.1-8
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• 2013

The finite element analysis (FEA) is a numerical technique to find solutions of field problems. A field problem is approximated by differential equations or integral expressions. In a finite element, the field quantity is allowed to have a simple spatial variation in terms of linear or polynomial functions. This paper represents a review and an accuracy-study of the finite element method comparing the FEA results with the exact solution. The exact solutions were calculated by solid mechanics and FEA using matrix stiffness method. For this study, simple bar and cantilever models were considered to evaluate four types of basic elements - constant strain triangle (CST), linear strain triangle (LST), bi-linear-rectangle(Q4),and quadratic-rectangle(Q8). The bar model was subjected to uniaxial loading whereas in case of the cantilever model moment loading was used. In the uniaxial loading case, all basic element results of the displacement and stress in x-direction agreed well with the exact solutions. In the moment loading case, the displacement in y-direction using LST and Q8 elements were acceptable compared to the exact solution, but CST and Q4 elements had to be improved by the mesh refinement.