• East Asian mathematical journal
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• v.26 no.5
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• pp.615-626
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• 2010

In this paper, we analyze discontinuous Galerkin methods with penalty terms, namly symmetric interior penalty Galerkin methods, to solve nonlinear parabolic equations. We construct finite element spaces on which we develop fully discrete approximations using extrapolated Crank-Nicolson method. We adopt an appropriate elliptic-type projection, which leads to optimal ${\ell}^{\infty}$ ($L^2$) error estimates of discontinuous Galerkin approximations in both spatial direction and temporal direction.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2002.05a
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• pp.108-113
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• 2002

This paper presents a multi-step structural design optimization method fur machine tool structures using a genetic algorithm with dynamic penalty. The first step is a sectional topology optimization, which is to determine the best sectional construction that minimize the structural weight and the compliance responses subjected to some constraints. The second step is a static design optimization, in which the weight and the static compliance response are minimized under some dimensional and safety constraints. The third step is a dynamic design optimization, where the weight static compliance, and dynamic compliance of the structure are minimized under the same constraints. The proposed design method was examined on the 10-bar truss problem of topology and sizing optimization. And the results showed that our solution is better than or just about the same as the best one of the previous researches. Furthermore, we applied this method to the topology and sizing optimization of a crossbeam slider for a high-speed machining center. The topology optimization result gives the best desirable cross-section shape whose weight was reduced by 38.8% than the original configuration. The subsequent static and dynamic design optimization reduced the weight, static and dynamic compliances by 5.7 %, 2.1% and 19.1% respectively from the topology-optimized model. The examples demonstrated the feasibility of the suggested design optimization method.

• Transactions of Materials Processing
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• v.12 no.1
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• pp.34-42
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• 2003

This paper presents a rigid-plastic finite element method to handle the frictional contact problem between two deformable bodies experiencing large deformation. The variational formulation combined with incremental quasi-static model is employed for treating the contact boundary condition. The frictional behavior of the model obeys Coulomb's law of friction. The proposed contact algorithms are classified into two categories, one for searching contacting nodes and the other for calculating contact forces at the contact surface. A slave node and master contact segment are defined using the geometric condition of finite elements on the contact interface. The penalty parameter is used to limit the penetration between contacting bodies, and the finite elements are coupled with contact boundary elements.us gates and cavity thicknesses. Through this study we have observed that the jetting is related to the die swell of material. This means that the jotting is strongly affected by the elastic flow property rather than the viscous flow property in viscoelastic characteristics of molten polymer. Different resins have different elastic properties, and elastic flow behavior depends on the shear rate of flow, i.e. injection speed. Large die swell would eliminate jetting however, the retardation of die swell would stimulate jetting. In the point of mole design, reducing the thickness ratio of cavity to gate can reduce or eliminate jetting regardless of amount of elasticity of polymer melt.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.3
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• pp.303-309
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• 2007

For the propagation of elastic waves in unbounded domains, absorbing boundary conditions at the fictitious numerical boundaries have been proposed. In this paper we focus on both first and second order paraxial boundary conditions(PBCs) in the framework of variational approximations which are based on paraxial approximations of the scalar and elastic wave equations. We propose a penalty function method for the treatment of PBCs and apply these into finite element analysis. The numerical verification of the efficiency is carried out through comparing PBCs with Lysmer-Kuhlemeyer's boundary conditions.

• Structural Engineering and Mechanics
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• v.82 no.1
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• pp.41-53
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• 2022

We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

• Transactions of Materials Processing
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• v.4 no.4
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• pp.365-374
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• 1995

Numerical simulation of blade forming is carried out as stretch forming by an elasto-plastic finite element method. The method adopts a Lagrangian formulation, which incorporates large deformation and rotation, with a penalty method to treat the contact boundary condition. Numerical integration is done with a directional reduced integration scheme to avoid shear locking. The numerical results demonstrates various final shapes of blades which depend on the variation of the stretching force. The strain distributions in deformed blades are also obtained with the variation of the stretching force.

• Transactions of Materials Processing
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• v.9 no.3
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• pp.274-283
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• 2000

A dynamic explicit finite element code for simulating sheet forming processes has been developed. The code utilizes the discrete Kirchhoff shell element and contact force is treated by a conventional penalty method. In order to reduce the computational cost, a new and robust contact searching algorithm has been developed and implemented into the code. In the method, a hierarchical structure of tool segments is built for each tool at the initial stage of the analysis. hierarchical structure is built in a way to divide a box to 8 sub-boxes, 2 in each direction, until the lowest level of the hierarchical structure contains exactly one segment of the tool or empty. Then at each time step, contact is checked from the box to sub-boxes hierarchically for each node. Comparisons of computational results of various examples with the existing ones show the validity of the method.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1996.10a
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• pp.20-28
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• 1996

An Eulerian finite element method for the analysis of steady state rolling/extrusion of sintered powder metals is presented. Initial guess of the porosity distribution in an Eulerian mesh is obtained from the velocity and scaled pressure field computed by the Consistent Penalty finite element formulations-the standard one and the consistent penalty type one-are invoked for the analysis of strain hardening, dilatant viscoplastic deformation of porous metals. Comparisons of the predicted distributions of porosity to those by a Lagrangian finite element method and by experiments reported in the articles prove the effectiveness and validity of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.6
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• pp.988-995
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• 2001

Functionally graded materials(FGMs) are highlighted to be suitable for high temperature engineering due to their continuous distribution of material properties. In this paper, an optimal design is executed for determining the optimal material volume distribution pattern that minimizes the steady-state thermal stress of FGM heat-resisting composites. The interior penalty function method and the golden section method are employed as optimization techniques while the finite element method is used for thermal stress analysis. Through numerical simulations we suggest the volume fraction distributions that considerably improve initial thermal stress distributions.

• International Journal of Korean Welding Society
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• v.1 no.2
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• pp.1-6
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• 2001

A weld quality assessment method is proposed in this work, which can be applied to the short-circuit mode in GMAW. Information about the welding signal trajectory, distribution of the signal duration at each sub-regions and short-circuit frequency is used to evaluate the weld quality. The weighted penalty, which is determined experimentally, is imposed for each abnormal signal. Performance of the proposed method is compared with the Simpson's method under the conditions of shielding gas reduction, workpiece surface contamination and joint gap in the butt and fillet welds. Although the proposed method predicts the weld quality with reasonable accuracy, further modification and extension to other metal transfer modes are needed as a further study.