• 대한수학회논문집
• /
• 제38권1호
• /
• pp.281-298
• /
• 2023

A class of systems of Caputo fractional differential equations with integral boundary conditions is considered. A numerical method based on a finite difference scheme on a uniform mesh is proposed. Supremum norm is used to derive an error estimate which is of order κ − 1, 1 < κ < 2. Numerical examples are given which validate our theoretical results.

• 한국자동차공학회논문집
• /
• 제4권5호
• /
• pp.16-25
• /
• 1996

In the present work a rigid-plastic finite element formulation using dynamic explicit time integration scheme is proposed for numerical analysis of auto-body panel stamping processes. The rigid-plastic finite element method based on membrane elements has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM(abbreviated from Bending Energy Augmented Membrane) elements are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and the direct trial-and-error method. Computations are carried out for analysis of complicated auto-body panel stamping processes such as forming of an oilpan, a fuel tank and a front fender. The numerical results of explicit analysis are compared with the implicit results with good agreements and it is shown that the explicit scheme requires much shorter computational time, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigid-plastic finite element method enables an effective computation for complicated autobody panel stamping processes.

• Journal of applied mathematics & informatics
• /
• 제40권3_4호
• /
• pp.603-618
• /
• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• International Journal of Reliability and Applications
• /
• 제11권1호
• /
• pp.17-22
• /
• 2010

It is desired to estimate the reliability of a system that has two subsystems connected in series where each subsystem has two components connected in parallel. A batch sequential sampling scheme is introduced. It is shown that the batch sequential sampling scheme is asymptotically optimal as the total number of units goes to infinity. Numerical comparisons indicate that the batch sequential sampling scheme performs better than the balanced sampling scheme and is nearly optimal.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제20권3호
• /
• pp.243-259
• /
• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• 한국지반공학회지:지반
• /
• 제14권4호
• /
• pp.129-140
• /
• 1998

탄소성 유한 요소 해석은 기지의 변형률 증분에 대한 응력 적분을 필요로 하며, 탄소성 구성 모델의 경우 특별한 경우를 제외하고는 해석적인 응력 적분이 불가능하고 수치적인 방법을 필요로 한다. 이때 응력 수치 적분의 정확도가 비선형 유한요소해의 전체적인 정확도에 상당히 큰 영향을 미치게 된다. 본 연구에서는 탄소성 구성 관계의 응력 적분을 위하여 외연적 방법중의 하나로서 Sloan이 제안한 단계분할 절차를 보완하여 안정적이고 정착한 응력 수치 적분법을 제시하고자 한다. 수정 오일러 절차에 따른 오차 조절의 기본 개념은 그대로 사용하고 오차를 평가하는 기준에 응력 수준이 영향을 미치는 단점을 보완하여 응력 수준에 관계없는 안정적이고 정확한 수치 적분법을 제시하였으며, 그 결과의 신뢰성을 삼축시험모사를 이용하여 검증하였다.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 추계학술대회
• /
• pp.453-458
• /
• 2004

This study proposes a new two-level condensation scheme for the construction of a reduced system. In the first step, the candidate area is selected for the construction of the reduced system by energy estimation in element-level. In the second step, primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements. Numerical examples demonstrate that the proposed method saves the computational cost effectively and provides a reduced system which predicts the eigenvalues accurately. Moreover, the well-constructed reduced system can present the reliable behavior of the structure under arbitrary dynamic loads comparing to that of global system. Time integration in a reduced system can save the computing time remarkably. Through a few numerical examples, the efficiency and reliability of the proposed scheme are verified.

• 대한기계학회논문집A
• /
• 제22권2호
• /
• pp.380-390
• /
• 1998

In the present work a finite element formulation using dynamic explicit time integration scheme is used for numerical analysis of auto-body panel stamping processes. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and direct trial-and-error method. In this work, for economic analysis the faster punch velocity and the mass scaling method are introduced. To investigate the effects of punch velocity and mass scaling, the various values of punch velocity and the various mass scalings are used for numerical analysis. Computations are carried out for analysis of complicated auto-body panel stamping processes such as forming of an oil pan and a fuel tank.

• 한국정밀공학회지
• /
• 제8권4호
• /
• pp.23-32
• /
• 1991

The paper discusses the problem of the flow over the backward facing step and the offset jet, which are calculated numerically. Standard k- .epsilon. model and its LPS modification are used as turbulence models. Hybrid central/upwind scheme and skew- upwind scheme are used as numerical schemes. The numerical scheme has a strong influence on the offset jet rather than the flow over backward facing step. The skew-upwind scheme gives good results in both cases. However, the k- .epsilon. model with LPS modification yields no remarkable improvements in the predictions of both flows. The skew-upwind scheme improves the prediction of reattachment length in the offset jet.

• Journal of Mechanical Science and Technology
• /
• 제15권11호
• /
• pp.1580-1587
• /
• 2001

In Part I, we extended the capability of the Goore Scheme for application to multi-dimensional problems and improved convergence performance. In this paper, we apply the improved Goore Scheme to th e control of turbulence for drag reduction. Direct numerical simulations combined with the control scheme are carried out to simulate a controlled turbulent channel flow at low Reynolds number. The wall blowing and suction is applied through the Goore algorithm using the total drag as feedback. An optimum distribution of the wall blowing and suction in terms of the wall-shear stresses in the spanwise and streamwise directions is sought. The best case reduces drag by more than 20 %.