• Transactions of Materials Processing
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• v.11 no.6
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• pp.513-518
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• 2002

The equivalent boundary conditions have been applied to the front door panel forming process, in order to demonstrate its reliability and validity. The elongation in the bead forming process is applied to the binder wrap process as the equivalent displacement boundary condition and the restraining force in the drawing process is applied to stamping process as the equivalent force boundary condition. The result calculated with the equivalent boundary conditions shows closer coincidence with the experimental result than simulation with different boundary conditions. The numerical result fully demonstrates that drawbead forming simulation for calculation of equivalent boundary conditions is necessary and effective.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.11
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• pp.720-728
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• 2000

This paper describes the calculation of the equivalent circuit parameters and the characteristic analysis of a capacitor-run type single-phase induction motor by means of the finite element method in coupled with the conventional equivalent circuit model. The circuit parameters of the stator are calculated form the lumped parameter and the slot leakage reactance of the rotor with the closed slot can be obtained by the use of slot pitch boundary condition. From the analysis result this combined equivalent circuit and finite element method which is used slot pitch boundary condition is compared with the experimental results, the validity of the method is proved.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2005.05a
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• pp.130-133
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• 2005

Efficient finite element method has been introduced for metallic sandwich plates subject to 3-point bending. A full model 3-point bending FE-analysis shows that plastic behavior of inner structures appears only at the load point. So, Unit structures of sandwich plates are defined to numerically calculate the bending stiffness with recurrent boundary condition of pure bending. And then equivalent models with same bending stiffness and strength of full models are designed analytically. It is demonstrated that results of both models are almost same and FE analysis method with equivalent models can reduce analysis time effectively.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 1998.04a
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• pp.120-127
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• 1998

It is very difficult to execute the vibration analysis of a huge strucutre, which takes up much time and expense. In this paper we intend to make the equivalent system of a local vibration system of a huge structure with a view to improving the dynamic characteristics and reducing time and expense. First of all, upper deck structure model is maded. And we perform the vibration analysis by the Substructure Synthesis Method and execute the exciting test for the upper deck structure model, and observe the coincidences of two results to confirm the reliability of the analyzing tools used. To make the equivalent system, we give boundary condition to sub-structure that want to be modified and execute the Sensitivity Analysis Method and the Optimum Structural Modification Method. And we execute the structural modification of the equivalent system.. The following can be found from this study. 1. The analytical results are generally coincident with each other. 2. The equivalent system of the superstructure model can be easily obtained using the sensitivity analysis metho and the optimum structural modification method. 3. The structural modification using the equivalent system can be obtained good results above 90% of object value.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.937-948
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• 2011

The method of Asymptotic Inner Boundary Condition for Singularly Perturbed Two-Point Boundary value Problems is presented. By using a terminal point, the original second order problem is divided in to two problems namely inner region and outer region problems. The original problem is replaced by an asymptotically equivalent first order problem and using the stretching transformation, the asymptotic inner condition in implicit form at the terminal point is determined from the reduced equation of the original second order problem. The modified inner region problem, using the transformation with implicit boundary conditions is solved and produces a condition for the outer region problem. We used Chawla's fourth order method to solve both the inner and outer region problems. The proposed method is iterative on the terminal point. Some numerical examples are solved to demonstrate the applicability of the method.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.71-111
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• 2021

We consider the boundary value problem for the deflection of a finite beam on an elastic foundation subject to vertical loading. We construct a one-to-one correspondence �� from the set of equivalent well-posed two-point boundary conditions to gl(4, ℂ). Using ��, we derive eigenconditions for the integral operator ��M for each well-posed two-point boundary condition represented by M ∈ gl(4, 8, ℂ). Special features of our eigenconditions include; (1) they isolate the effect of the boundary condition M on Spec ��M, (2) they connect Spec ��M to Spec ����,α,k whose structure has been well understood. Using our eigenconditions, we show that, for each nonzero real λ ∉ Spec ����,α,k, there exists a real well-posed boundary condition M such that λ ∈ Spec ��M. This in particular shows that the integral operators ��M, arising from well-posed boundary conditions, may not be positive nor contractive in general, as opposed to ����,α,k.

• Transactions of Materials Processing
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• v.11 no.6
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• pp.503-512
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• 2002

The drawbead is used to control material flow into the die during the binder wrap process and the stamping process in the sheet metal forming process. Since the dimension of drawbead is relatively small in comparison with the typical dimensions, it is difficult to include drawbeads in finite element analysis of the sheet metal forming process. It is because the mesh system has to be fine enough to describe the drawbead and the computation time is drastically increased. In this paper, simulation of drawbead forming has been carried out to obtain the equivalent boundary conditions in the binder wrap process and the stamping process. In order to investigate the effect of various die geometries, parameter studies are performed with the variation of parameters such as the blank length, the drawbead depth, the drawbead radius, the inclination of die and the friction coefficient.

• Transactions of Materials Processing
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• v.14 no.8 s.80
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• pp.718-724
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• 2005

An efficient finite element method has been introduced for analysis of metallic sandwich plates subject to bending moment. A full model 3-point bending FE-analysis shows that the plastic behavior of inner structures appears only at the load point. The unit structures of sandwich plates are defined to numerically calculate the bending stiffness and strength utilizing the recurrent boundary condition for pure bending analysis. The equivalent models with the same bending stiffness and strength of full models are then designed analytically. It is demonstrated that the results of both models are almost the same and the FE-analysis method incorporating the equivalent models can reduce the computation time effectively. The dominant collapse modes are face buckling and face yielding. Since the inner dimpled structures prevent face buckling, sandwich plates with inner dimpled shell structure can absorb more energy than other types of sandwich plates during the bending behavior.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.4
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• pp.305-316
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• 2014

The Hodge-Helmholtz decomposition splits a vector field into the unique sum of a divergence-free vector field (solenoidal part) and a gradient field (irrotational part). In a bounded domain, a boundary condition needs to be supplied to the decomposition. The decomposition with the non-penetration boundary condition is equivalent to solving the Poisson equation with the Neumann boundary condition. The Gibou-Min method is an application of the Poisson solver by Purvis and Burkhalter to the decomposition. Using the $L^2$-orthogonality between the error vector and the consistency, the convergence for approximating the divergence-free vector field was recently proved to be $O(h^{1.5})$ with step size h. In this work, we analyze the convergence of the irrotattional in the decomposition. To the end, we introduce a discrete version of the Poincare inequality, which leads to a proof of the O(h) convergence for the scalar variable of the gradient field in a domain with general intersection property.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.404-409
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• 2001

An account of second-order fractional-step methods and boundary conditions for the incompressible Navier-Stokes equations is presented. The present work has aimed at (i) identification and analysis of all possible splitting methods of second-order splitting accuracy; and (ii) determination of consistent boundary conditions that yield second-order accurate solutions. It has been found that only three types (D, P and M) of splitting methods called the canonical methods are non-degenerate so that all other second-order splitting schemes are either degenerate or equivalent to them. Investigation of the properties of the canonical methods indicates that a method of type D is recommended for computations in which the zero divergence is preferred, while a method of type P is better suited to the cases when highly-accurate pressure is more desirable. The consistent boundary conditions on the tentative velocity and pressure have been determined by a procedure that consists of approximation of the split equations and the boundary limit of the result. The pressure boundary condition is independent of the type of fractional-step methods. The consistent boundary conditions on the tentative velocity were determined in terms of the natural boundary condition and derivatives of quantities available at the current timestep (to be evaluated by extrapolation). Second-order fractional-step methods that admit the zero pressure-gradient boundary condition have been derived. The boundary condition on the new tentative velocity becomes greatly simplified due to improved accuracy built in the transformation.