• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.501-507
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• 2007

In the first part of this study, the moving least squares finite difference method for solving solid mechanics problems was formulated. This second part verified the accuracy, robustness and effectiveness of the developed method through several numerical examples. It was shown that the method gives excellent convergence rate for elasticity problem. The solution process of elastic crack problems showed the easiness in discontinuity modeling and demonstrates the accuracy and efficiency in finding singular stress solution based on adaptive node distribution. The applicability to the engineering problem with abrupt change in displacement and stresses gradient fields is verified through a localization band problem. The developed method is expected to be extended to the various special engineering problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.493-499
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• 2007

The Taylor expansion expresses a differentiable function and its coefficients provide good approximations for the given function and its derivatives. In this study, m-th order Taylor Polynomial is constructed and the coefficients are computed by the Moving Least Squares method. The coefficients are applied to the governing partial differential equation for solid problems including crack problems. The discrete system of difference equations are set up based on the concept of point collocation. The developed method effectively overcomes the shortcomings of the finite difference method which is dependent of the grid structure and has no approximation function, and the Galerkin-based meshfree method which involves time-consuming integration of weak form and differentiation of the shape function and cumbersome treatment of essential boundary.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.1
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• pp.17-26
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• 2014

This paper presents a dynamic crack propagation algorithm based on the Moving Least Squares(MLS) difference method. The derivative approximation for the MLS difference method is derived by Taylor expansion and moving least squares procedure. The method can analyze dynamic crack problems using only node model, which is completely free from the constraint of grid or mesh structure. The dynamic equilibrium equation is integrated by the Newmark method. When a crack propagates, the MLS difference method does not need the reconstruction of mode model at every time step, instead, partial revision of nodal arrangement near the new crack tip is carried out. A crack is modeled by the visibility criterion and dynamic energy release rate is evaluated to decide the onset of crack growth together with the corresponding growth angle. Mode I and mixed mode crack propagation problems are numerically simulated and the accuracy and stability of the proposed algorithm are successfully verified through the comparison with the analytical solutions and the Element-Free Galerkin method results.

• Journal of the Korea Computer Graphics Society
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• v.23 no.4
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• pp.1-9
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• 2017

We propose an efficient method to determine the position of blueprint by using a vector field with optimized MLS(Moving Least Squares). Typically, a professional architectural design office takes a long time to work as well as a high processing cost because the designer manually determines the location to place the buildings in a specific area. In order to solve this inefficient problem, we propose a method to automatically determine the location of the blueprint based on the optimized MLS method. In the proposed framework, the designer selects the desired region in the actual city data and calculates the flow of the vector based on the region. Use the optimized MLS method to extract the vector field and determine the amount of rotation of the drawing based on this field. The location of the blueprint determined by the proposed method is very similar to the flow seen when the actual building is located. As a result, the efficiency of the overall architectural design process is further improved by reducing the designer's inefficient workforce.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.5A
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• pp.457-465
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• 2009

This study presents a moving least squares (MLS) finite difference method for solving elastic crack problems with stress singularity at the crack tip. Near-tip functions are intrinsically employed in the MLS approximation to model near-tip field inducing singularity in stress field. employment of the functions does not lose the merit of the MLS Taylor polynomial approximation which approximates the derivatives of a function without actual differentiating process. In the formulation of crack problem, computational efficiency is considerably improved by taking the strong formulation instead of weak formulation involving time consuming numerical quadrature Difference equations are constructed on the nodes distributed in computational domain. Numerical experiments for crack problems show that the intrinsically enriched MLS finite difference method can sharply capture the singular behavior of near-tip stress and accurately evaluate stress intensity factors.

• Journal of computational fluids engineering
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• v.13 no.1
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• pp.49-56
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• 2008

Chimera grid methods have been widely used in Computational Fluid Dynamics due to its simplicity in constructing grid systems over complex bodies, and suitability for unsteady flow computations with bodies in relative motion. However, the interpolation procedure for ensuring the continuity of the solution over overlapped regions fails when the so-called orphan cells are present. We have adopted the MLS(Moving Least Squares) method to replace commonly used linear interpolations in order to alleviate the difficulty associated with the orphan cells. MLS is one of the interpolation methods used in mesh-less methods. A number of examples with MLS are presented to show the validity and the accuracy of the method.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.17-22
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• 2007

Chimera grid Method is widely used in Computational Fluid Dynamics due to its simplicity in constructing grid system over complex bodies. Especially, Chimera grid method is suitable for unsteady flow computations with bodies in relative motions. However, interpolation procedure for ensuring continuity of solution over overlapped region fails when so-call orphan cells are present. We have adopted MLS(Moving Least Squares) method to replace commonly used linear interpolations in order to alleviate the difficulty associated with orphan cells. MSL is one of interpolation methods used in mesh-less methods. A number of examples with MLS are presented to show the validity and the accuracy of the method.

• The Transactions of the Korean Institute of Power Electronics
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• v.13 no.6
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• pp.487-491
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• 2008

Tuning of the speed controller in the linear servo applications needs the accurate information of a mover mass including a load mass. Therefore this paper proposes the mass estimation method of a permanent magnet linear synchronous motor(PMLSM) applied at the vertical axis by using the recursive Least-Squares estimation algorithm. First, this paper derives the deterministic autoregressive moving average(DARMA) model of the mechanical dynamic system used at the vertical axis. The application of the Least-Squares algorithm to the derived DARMA model gives the mass estimation method. Matlab/Simulink-based simulation and experimental results show that the total mover mass of a PMLSM applied at the vertical axis can be accurately estimated at both no-load and load conditions.

• Journal of KIISE:Computer Systems and Theory
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• v.32 no.8
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• pp.411-417
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• 2005

We present a method to reconstruct a canal surface from a point cloud (a set of unorganized points). A canal surface is defined as a swept surface of a moving sphere with varying radii. By using the shrinking and moving least-squares methods, we reduce a point cloud to a thin curve-like point set which can be approximated to the spine curve of a canal surface. The distance between a point in the thin point cloud and a corresponding point in the original point set represents the radius of the canal surface.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.36 no.1
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• pp.67-74
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• 2023

A meshless technique using the geometric conservation least-squares method (GC-LSM) was devised to discretize the governing equation of linear elasticity. Although the finite-element method is widely used for structural analysis, a meshless method was developed because of its advantages in a moving grid system. This work is the preliminary phase for developing a fully meshless-based fluid-structure interaction solver. In this study, Cauchy's momentum equation was discretized in strong form using GC-LSM for the structural domain, and the Newmark beta method was used for time integration. The solver was validated in 1D, 2D, and 3D benchmarking problems. Static and dynamic results were obtained. The results are more accurate than those of analytic solutions.