• International Journal of Reliability and Applications
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• 제4권1호
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• pp.1-12
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• 2003

Many software reliability growth models (SRGM's) based on a nonhomogeneous Poisson process (NHPP) have been proposed by many researchers. Most of the SRGM's which have been proposed up to the present treat the event of software fault-detection in the testing and operational phases as a counting process. However, if the size of the software system is large, the number of software faults detected during the testing phase becomes large, and the change of the number of faults which are detected and removed through debugging activities becomes sufficiently small compared with the initial fault content at the beginning of the testing phase. Therefore, in such a situation, we can model the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose a new software reliability growth model describing the fault-detection process by applying a mathematical technique of stochastic differential equations of an Ito type. We also compare our model with the existing SRGM's in terms of goodness-of-fit for actual data sets.

• 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.

• 한국자동차공학회논문집
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• 제5권5호
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• pp.9-19
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• 1997

In this paper, the modeling and analysis of dynamic characteristics has been carried out for friction clutches and brakes in an automatic transmission. From the operating oil pressure generated by the valve-body, time delay by check valve and the movement of piston has been examined. Also torque capacity and torque transferred at the clutch is studied. Heat capacity and temperature distribution at the reaction plate of clutch are codeled by time-dependent, nonhomogeneous partial differential equation, and brake torque, brake time, and the amount of heat generated are investigated. It is found that the time delay at the check valve is very short but dominant at the spool.

• Steel and Composite Structures
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• 제21권4호
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• pp.791-803
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• 2016

In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.

• 호남수학학술지
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• 제40권4호
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• pp.785-794
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• 2018

In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.

• 한국항공우주학회지
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• 제33권8호
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• pp.75-83
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• 2005

확대형 채널 내의 정상 천음속 희박 예혼합 연소에 대해 점근해석을 이용하여 연구하였다. 이 모델은 근음속의 유동 속도와 일직선 채널로부터 벗어난 작은 형상변화 그리고 1단 1차 Arrhenius 화학 반응율에 의한 적은 열 방출 사이에서 일어나는 비선형 상호작용에 대하여 탐구하였다. 반응유체 유동은 연소 가스의 질량 분율을 계산하는 상미분 방정식과 연계된 비균질 천음속 미교란 방정식(TSD)을 사용하여 묘사하였다. 또한 점근해석으로부터 반응유체 유동 문제를 지배하는 상사 파라미터들을 유도하였다. 수치 결과들은 대류와 화학반응 그리고 형상효과 사이에 일어나는 복잡한 비선형 상호작용과 유동에 미치는 이것의 영향 등이 잘 나타나 있다.

• Advances in aircraft and spacecraft science
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• 제11권1호
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• pp.55-81
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• 2024

This paper presents the exact solutions and closed forms for of nonlinear stability and vibration behaviors of straight and curved beams with nonlinear viscoelastic boundary conditions, for the first time. The mathematical formulations of the beam are expressed based on Euler-Bernoulli beam theory with the von Karman nonlinearity to include the mid-plane stretching. The classical boundary conditions are replaced by nonlinear viscoelastic boundary conditions on both sides, that are presented by three elements (i.e., linear spring, nonlinear spring, and nonlinear damper). The nonlinear integro-differential equation of buckling problem subjected to nonlinear nonhomogeneous boundary conditions is derived and exactly solved to compute nonlinear static response and critical buckling load. The vibration problem is converted to nonlinear eigenvalue problem and solved analytically to calculate the natural frequencies and to predict the corresponding mode shapes. Parametric studies are carried out to depict the effects of nonlinear boundary conditions and amplitude of initial curvature on nonlinear static response and vibration behaviors of curved beam. Numerical results show that the nonlinear boundary conditions have significant effects on the critical buckling load, nonlinear buckling response and natural frequencies of the curved beam. The proposed model can be exploited in analysis of macrosystem (airfoil, flappers and wings) and microsystem (MEMS, nanosensor and nanoactuators).

• 대한토목학회논문집
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• 제43권2호
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• pp.187-193
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• 2023

이 논문은 말뚝체의 자중을 고려한 말뚝의 좌굴거동에 관한 연구이다. 비균질 지반에 설치된 부분매립 말뚝의 좌굴을 지배하는 미분방정식과 경계조건을 유도하였다. Runge-Kutta법과 Regula-Falsi법을 결합한 수치해석법을 적용하여 말뚝의 좌굴하중과 좌굴형을 산정하였다. 계산된 좌굴하중의 수치해와 문헌값은 잘 일치하였고, 수치예를 통해 말뚝의 자중, 매립비, 세장비, 경계조건 및 지반의 반력형상비, 지반강성비가 말뚝의 좌굴특성에 미치는 영향을 분석하였다. 분석결과, 말뚝의 자중은 말뚝의 좌굴하중을 감소시켰으며 이러한 자중효과의 무시는 부분매립 말뚝의 좌굴하중을 과대평가할 수 있음을 확인하였다.