• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.1-1
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• 2003

In this talk, a reduced-order modeling methodology based on centroidal Voronoi tessellations (CVT's)is introduced. CVT's are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. The discrete data sets, CVT's are closely related to the h-means clustering techniques. Even with the use of good mesh generators, discretization schemes, and solution algorithms, the computational simulation of complex, turbulent, or chaotic systems still remains a formidable endeavor. For example, typical finite element codes may require many thousands of degrees of freedom for the accurate simulation of fluid flows. The situation is even worse for optimization problems for which multiple solutions of the complex state system are usually required or in feedback control problems for which real-time solutions of the complex state system are needed. There hava been many studies devoted to the development, testing, and use of reduced-order models for complex systems such as unsteady fluid flows. The types of reduced-ordered models that we study are those attempt to determine accurate approximate solutions of a complex system using very few degrees of freedom. To do so, such models have to use basis functions that are in some way intimately connected to the problem being approximated. Once a very low-dimensional reduced basis has been determined, one can employ it to solve the complex system by applying, e.g., a Galerkin method. In general, reduced bases are globally supported so that the discrete systems are dense; however, if the reduced basis is of very low dimension, one does not care about the lack of sparsity in the discrete system. A discussion of reduced-ordering modeling for complex systems such as fluid flows is given to provide a context for the application of reduced-order bases. Then, detailed descriptions of CVT-based reduced-order bases and how they can be constructed of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVT-based reduced-order bases. The CVT-based reduced-order modeling methodology is shown to be effective for these examples and is also shown to be inexpensive to apply compared to other reduced-order methods.

• The Journal of Engineering Geology
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• v.19 no.2
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• pp.205-215
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• 2009

The conventional numerical models to analyze flow in subsurface porous media under the transient state usually generate numerical oscillation and unstability due to local flux domain for critical cases such as infiltration into initially dry soil during rainfall period. In this case, it is required refined mesh and small time step, but it decrease efficiency of computation. In this study, numerical unstability in discontinuity domain is removed by applying particle tracking algorithm to simulate unsteady subsurface flow with inflow boundary condition. Finally the hybrid LE FEM improving numerical stability is proposed. The hypothetical domains with unsteady uniform and nonuniform flow field were used to demonstrated algorithm verification. In comparison with analytic solution, we obtained reasonable results and conducted simulation of hypothetical 3-D recharge/pumping area. The proposed algorithm can simulate saturated/unsaturated porous media with more practical problems and will greatly contribute to accuracy and stability of numerical computation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.263-270
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• 1996

Noise control of a plate structure with multiple disk shaped piezoelectric actuators is studied. The plate is excited by an acoustic pressure field produced by a noise source located below the plate. Finite element modeling is used for the plate structure that supports a combination of three dimensional solid, flat shell and transition elements. The objective function, in the optimization procedure, is to minimize the sound energy radiated onto a hemispherical surface of given radius and the design parameters are the locations and sizes of the piezoelectric actuators as well as the amplitudes of the voltages applied to them. Automatic mesh generation is addressed as part of the modeling procedure. Numerical results for both resonance and off resonance frequencies show remarkable noise reduction and the optimal locations of the actuators are found to be close to the edges of the plate structure. The optimized result is robust such that when the acoustic pressure pattern is changed, reduction of radiated sound is still maintained. The robustness of an optimally designed structure is also tested by changing the frequency of the noise source using only the actuator voltages as design parameters.

• Interaction and multiscale mechanics
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• v.2 no.2
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• pp.177-187
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• 2009

Machine or structural members subjected to fatigue loading will have a crack initiated during early part of their life. Therefore analysis of members with cracks and other discontinuities is very important. Finite element method has enjoyed widespread use in engineering, but it is not convenient for crack problems as the region very close to crack tip is to be discretized with very fine mesh. However, as the body force method (BFM), requires only the boundary of the discontinuity (crack or hole) to be discretized it is easy versatile technique to analyze such problems. In the present work fundamental solution for concentrated load x + iy acting in the semi-infinite plate at an arbitrary point $z_0=x_0+iy_0$ is considered. These fundamental solutions are in complex form ${\phi}(z)$ and ${\psi}(z)$ (England 1971). These potentials are known as Melan potentials (Ramakrishna 1994). A crack in the semi-infinite plate as shown in Fig. 1 is considered. This crack is divided into number of divisions. By applying pair of body forces on a division, the resultant forces on the remaining 'N'divisions are to be found for which ${\phi}_1(z)$ and ${\psi}_1(z)$ are derived. Body force method is applied to calculate stress intensity factor for crack in semi-infinite plate. Also for the case of crack emanating from circular hole in semi-infinite plate radial stress, hoop stress and shear stress are calculated around the hole and crack. Convergent results are obtained by body force method. These results are compared with FEM results.

• Journal of Environmental Science International
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• v.18 no.2
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• pp.221-230
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• 2009

In this study, a river basin with a lot of measured data such as water level, flow rate, current speed, and sediment rate from the past to now was selected and geometrical shape of a pier was re-analyzed, in order to study the effects of the flow around the pier area as well as the riverbed alternation characteristics. A finite element mesh of the entire river was prepared, and via parameter revision, the section that the pier has influence on was decided, to analyze the shape of the pier using RMA-2 and SED2D-WES models. With regards to the section that the pier has influence on, analysis was done on the four pier shapes, namely circle, square, rectangle, and octagon. The results showed that the shape with the least influence around the pier around is the octagon, followed by circle, rectangle, and square, showing the different geometrical effects that the shapes have on the pier. Furthermore, it was shown that the distribution of sediment concentration had effect from about (+) 110 m of the upstream to about (-) 130 m of the downstream, from the pier installation point. Also, it was shown after analyzing drag forces for different sediment particle distributions that the shape with the greatest drag is the octagon, followed by circle, square, and rectangle.

• Journal of the Korean Society of Propulsion Engineers
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• v.14 no.5
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• pp.32-44
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• 2010

A two-dimensional thermal response and ablation analysis code for predicting charring material ablation and shape change on solid rocket nozzle is presented. The thermogravimetric analysis (TGA) techniques have been used to characterize the thermal decomposition constants for Arrhenius parameters. Two heterogeneous reactions involving carbon and the oxidizing species of $H_2O$ and $CO_2$ are considered and determined by Zvyagin's ablation model and kinetic constants. The moving boundary problem and mesh moving are solved by remeshing-rezoning method in MSC-Marc-ATAS program. The difference between the calculated and experimental value of char and ablation thickness is up to 20%. For the performance prediction of thermal protection systems, this method will be integrated with a three-dimensional finite-element thermal and structure analysis code through the real time sensing of in-depth temperature and heat flux.

• Journal of the Korean Society for Precision Engineering
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• v.14 no.8
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• pp.29-39
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• 1997

The clamp, as the structure which is used for supporting the pipe in the atomic power plant, is produced with a certain degree of anticlastic curvature in the current manufacturing process. In this study, the structural analysis of the clamp and the pipe was performed using ABAQUS. And the finite element modelling for the analysis was made by an HyperMesh. The contact forces which are transferred between the clamp and the pipe for the external force are changed according to the binding force of bolts and keeps the clamp tightly and protects the slipping between the clamp and the pipe. The clamps with the anticlastic curvature and with the flat curvature are considered in order to invest the anticlastic effect. In this study, another case is suggested. The present case does not have the stiffness ring on the end of the clamp but the suggested case has the ring. For the present case, the results showed that the equivalent stress is higher in the anticlastic curvature case than in the flat curvature case and the equivalent stresses on the pipe are almost the same as the binding force increses. For the suggested case, the result showed that the equivalent stress in the anticlastic curvature case decreases until some binding force and increases as the binding forces increase and is lower in some range than in the flat curvature case. From this study, the clamp with the anticlastic curvature in the suggested method is better than the clamp with the flat curvature and the optimal binding force are given.

• The Journal of Engineering Geology
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• v.5 no.1
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• pp.31-44
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• 1995

The puppose of this study is to propose the numerical modelling criteria for underground opening, rock mass continuum is regarded as homogeneous rock behaved linear elastic. The results of this study are summarized as follows: - Boundaries of the finite element mesh should be located at least 6 radii away from the center of the opening. - For circular openings, tension only developed when $K_0$ was less than one-fourAs the ratio of initial horiwntal to vertical stress increased, the inward springline movement increased and the inward crown movement decreased. - The displacement patterns developing for opening I shaped horse-shoe and opening II shaped powerstation are similar to those for circular openings. For both type opening I and opening II, stress concentrations develop at the intersection of the wall and floor. Greater stress concentrations are found for the type opening II.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.4
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• pp.363-370
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• 2014

A new NURBS-based shape optimization method is proposed. Most shape optimization studies consider only control point positions as design variables. Some shape optimization processes present problems with mesh quality and convergence when control points are constrained to a limited space. If the weights of the control points are regarded as additional design variables, it should be possible to attain a better degree of shape control. In this study, positions and weights of NURBS control points are used as design variables, and a shape optimization algorithm incorporates position optimization and weight optimization steps. This method is applied to shape optimization benchmarking problems to verify its advantages.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.2
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• pp.139-148
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• 2012

The MLS(Moving Least Squares) Difference Method is a numerical scheme that combines the MLS method of Meshfree method and Taylor expansion involving not numerical quadrature or mesh structure but only nodes. This paper presents an dynamic algorithm of MLS difference method for solving transient solid mechanics problems. The developed algorithm performs time integration by using Newmark method and directly discretizes strong forms. It is very convenient to increase the order of Taylor polynomial because derivative approximations are obtained by the Taylor series expanded by MLS method without real differentiation. The accuracy and efficiency of the dynamic algorithm are verified through numerical experiments. Numerical results converge very well to the closed-form solutions and show less oscillation and periodic error than FEM(Finite Element Method).