• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.497-504
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• 2002

In meshless methods, the moving least squares approximation technique is widely used to approximate a solution space because of its useful numerical characters such as non-element approximation, easily controllable smoothness, and others. In this work, a generalized version of the moving least squares method Is introduced to enhance the approximation performance through the Information converning to the derivative of the field variable. The results of numerical tests for approximation verify the improved accuracy of the generalized meshless approximation procedure compared to the conventional moving least squares method. By using this generalized moving least squares method, meshless analysis of thin beam is carried out, and its performance is investigated.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.68 no.1
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• pp.83-89
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• 2019

In this paper, beam forming using moving least squares method (MLSM) is studied. In the previous research, the least squares method (LSM), one of the data interpolation methods, was used to determine the desired beam pattern and obtain a beam pattern that minimizes the square of the error with the desired beam pattern. However, LSM has a disadvantage in that the beam pattern can not be formed to satisfy the exact steering angle of the desired beam pattern and the peak sidelobe level (PSLL) condition. To overcome this drawback, MLSM is used for beam forming. In order to verify, the proposed method is applied in beam forming of Bezier platform array antenna which is one of conformal array antenna platform.

• Journal of Ocean Engineering and Technology
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• v.24 no.1
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• pp.20-33
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• 2010

The paper deals with strength design of a riser support installed on floating production storage and offloading (FPSO) vessel under various loading conditions - operation, extreme, damaged, one line failure case (OLFC) and installation. The design problem is formulated such that thickness sizing variables are determined by minimizing the weight of a riser support structure subject to stresses constraints. The initial design model is generated based on an actual FPSO riser support specification. The finite element analysis (FEA) is conducted using MSC/NASTRAN, and optimal solutions are obtained via moving least squares method (MLSM) in the context of response surface based approximate optimization. For the meta-modeling of inequality constraint functions of stresses, a constraint-feasible moving least squares method (CF-MLSM) is used in the present study. The method of CF-MLSM, compared to a conventional MLSM, has been shown to ensure the constraint feasibility in a case where the approximate optimization process is employed. The optimization results present improved design performances under various riser operating conditions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.315-322
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• 2009

This paper presents a novel numerical method based on the extended moving least squares finite difference method(MLS FDM) for solving 1-D Stefan problem. The MLS FDM is employed for easy numerical modelling of the moving boundary and Taylor polynomial is extended using wedge function for accurate capturing of interfacial singularity. Difference equations for the governing equations are constructed by implicit method which makes the numerical method stable. Numerical experiments prove that the extended MLS FDM show high accuracy and efficiency in solving semi-infinite melting, cylindrical solidification problems with moving interfacial boundary.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.10
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• pp.1605-1612
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• 2001

Least-squares meshfree method is presented. Conventional meshfree methods based on the Galerkin formulation suffer from inaccurate numerical integration. Least-squares formulation exhibits rather different integration-related characteristics. It is demonstrated through numerical examples that least-squares formulation is much more robust to integration errors than the Galerkin's. Therefore efficient meshfree methods can be devised by combining very simple integration algorithms and least-squares formulation.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.6
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• pp.779-787
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• 2007

This paper presents a highly efficient moving least squares finite difference method (MLS FDM) for a heat transfer problem of bi-material with interfacial boundary. The MLS FDM directly discretizes governing differential equations based on a node set without a grid structure. In the method, difference equations are constructed by the Taylor polynomial expanded by moving least squares method. The wedge function is designed on the concept of hyperplane function and is embedded in the derivative approximation formula on the moving least squares sense. Thus interfacial singular behavior like normal derivative jump is naturally modeled and the merit of MLS FDM in fast derivative computation is assured. Numerical experiments for heat transfer problem of bi-material with different heat conductivities show that the developed method achieves high efficiency as well as good accuracy in interface problems.

• Interaction and multiscale mechanics
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• v.3 no.2
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• pp.123-143
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• 2010

The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

• Structural Engineering and Mechanics
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• v.22 no.3
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• pp.331-349
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• 2006

The stresses and deflections in a laminated rectangular plate under thermal vibration are determined by using the moving least squares differential quadrature (MLSDQ) method based on the first order shear deformation theory. The weighting coefficients used in MLSDQ approximation are obtained through a fast computation of the MLS shape functions and their partial derivatives. By using this method, the governing differential equations are transformed into sets of linear homogeneous algebraic equations in terms of the displacement components at each discrete point. Boundary conditions are implemented through discrete grid points by constraining displacements, bending moments and rotations of the plate. Solving this set of algebraic equations yields the displacement components. Then substituting these displacements into the constitutive equation, we obtain the stresses. The approximate solutions for stress and deflection of laminated plate with cross layer under thermal load are obtained. Numerical results show that the MLSDQ method provides rapidly convergent and accurate solutions for calculating the stresses and deflections in a multi-layered plate of cross ply laminate subjected to thermal vibration of sinusoidal temperature including shear deformation with a few grid points.

• Journal of the Korea Computer Graphics Society
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• v.30 no.2
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• pp.1-9
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• 2024

In this paper, we propose a new method to visualize different vector field patterns from density data. We use moving least squares (MLS), which is used in physics-based simulations and geometric processing. However, typical MLS does not take into account the nature of density, as it is interpolated to a higher order through vector-based constraints. In this paper, we design an algorithm that incorporates Monte Carlo-based weights into the MLS to efficiently account for the density characteristics implicit in the input data, allowing the algorithm to represent different forms of white noise. As a result, we experimentally demonstrate detailed vector fields that are difficult to represent using existing techniques such as naive MLS and divergence-constrained MLS.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.5
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• pp.439-446
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• 2012

This paper presents an implicit moving least squares(MLS) difference method for improving the solution accuracy of 1-D free boundary problems, which implicitly updates the topology change of moving interface. The conventional MLS difference method explicitly updates the moving interface; it requires no iterative solution procedure but results in the loss of accuracy. However, the newly developed implicit scheme makes the total system nonlinear involving iterative solution procedure, but numerical verification show that it dramatically elevates the solution accuracy with moderate computation increase. Through numerical experiments for melting problems having moving singularity, it is verified that the proposed method can achieve the second order accuracy.