• Proceedings of the KSME Conference
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• 2001.06c
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• pp.402-407
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• 2001

Sensitivity analysis scheme is developed in the elasto-plastic finite element method with explicit time integration using direct differentiation method. The direct differentiation is concerned with the time integration, constitutive relation, shell element with reduced integration and the contact scheme. Sensitivity analysis results are mainly examined with the highly nonlinear and quasi-static problem with the complicated contact condition. The result shows stable sensitivity especially in the sheet metal forming analysis.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.604-609
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• 2001

In the sheet metal forming process, the drawbead is used to control the flow of material during the forming process. The drawbead provides proper restraining force to the material and prevents defects such as wrinkling or breakage. For these reasons, many studies for designing the effective drawbead have been conducted. For the analysis, the numerical method called the static-explicit finite element method was used. The finite element analysis code for this method has been developed and applied to the drawbead process problems. In result, convergence problem and computation time due to large non-linearity in the existing numerical analysis methods were no longer a critical problem. Futhermore, this approach could treat the contact friction problem easily by applying very small time intervals. It is expected that various results from the numerical analysis will give very useful information for the design of tools in sheet metal forming process.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.2
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• pp.202-212
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• 1997

In this study, performance of the multi-stage explicit methods for numerical computation of the unsteady Navier-Stokes equations is investigated. Three methods under consideration are 1 st-, 2 nd-, and 4 th-order Runge-Kutta (R-K) methods. Compared in this estimation is stability, accuracy, and CPU time of each method. The computational codes developed are applied to the two-dimensional flow in a square cavity driven by an oscillating lid. It turned out that at Reynolds number 400, the 1 st-order R-K method is the best, while at 3200 the 2 nd-order R-K is recommended. At higher Reynolds numbers, it is conjectured that the 4 th-order R-K method will be the best algorithm among three due to its highest stability.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.2
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• pp.380-390
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• 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.

• Journal of Mechanical Science and Technology
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• v.17 no.4
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• pp.538-544
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• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.6
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• pp.164-170
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• 2003

The finite element analysis of tires has been conventionally performed by either neglecting tread pattern or modeling only circumferential grooves. Besides, the tire analysis has been mainly limited to static or steady state rolling analysis. In this paper, a transient dynamic analysis of a patterned tire rolling over a cleat with an explicit finite element program is presented. The patterned tire with detailed tread blocks is modeled by a systematic mesh generation procedure, in which tire body and tread pattern meshes are separately generated in the beginning and then both meshes are combined by the tie constraint method. The cleat impact analysis is conducted by using both the patterned tire and the smooth tire models to predict the cleat enveloping characteristics. It is seen that the analysis results of the patterned tire model are in a good agreement with the experimental results.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.2
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• pp.116-121
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• 2004

In rigid-plastic finite element method, there is a heavy computation time and convergence problem. In this study, static-explicit rigid-plastic finite element method will be introduced. This method is the way that restrict the convergence interval. It is expected that various results from the numerical analysis will give very useful information for the design of tools in sheet metal forming process.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.435-450
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• 2009

On page 366 of his lost notebook [15], Ramanujan recorded a cubic continued fraction and several theorems analogous to Rogers-Ramanujan's continued fractions. In this paper, we derive several general formulas for explicit evaluations of Ramanujan's cubic continued fraction, several reciprocity theorems, two formulas connecting V (q) and V ($q^3$) and also establish some explicit evaluations using the values of remarkable product of theta-function.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.2
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• pp.193-200
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• 2000

In the sheet metal forming process, the drawbead is used to control the flow of material during the forming process. The drawbead provides proper restraining force to the material and prevents defects such as wrinkling or breakage. For these reasons, many studies for designing the effective drawbead have been conducted. In this paper, the influence of the number of drawbead during the blank forming process will be introduced. For the analysis, the numerical method called the static-explicit finite element method was used. The finite element analysis code for this method has been developed and applied to the drawbead process problems. It is expected that this static-explicit finite element method could overcome heavy computation time and convergence problem due to the increase of drawbeads.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1438-1445
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• 2000

To determine dynamic characteristics of materials, a program was developed under base of stress wave propagation theory for SHPB with explicit finite element method. Through the program, all kinds of quasi-static stress-strain curves can be directly converted to dynamic stress-strain curves at any strain rate. This simulation results were compared with experimental results in the references and they are in a good agreement with each other.