• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.53-59
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• 1998

A new algorithm using meshless particle method for the analysis of crack propagation problems is presented. The meshless particle method requires only a set of nodes and the description of boundaries in its formulation. The method is particulary useful for crack propagation problems due to the absence of any predefined element connectivity. Formulation procedures for the construction of displacement and shape functions are described. A numerical integration scheme and a strategy for the consideration of crack propagation are also described. Numerical examples show that the proposed method is very convenient and efficient in modeling crack problems and can guarantee the accuracy of solution in crack propagation analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.04a
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• pp.53-60
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• 2001

Meshfree methods have been attracting issue as computational methods during past a few years. Nowadays, various meshfree methods such as EFGM, RKPM h-p cloud method and etc. were developed and applied in engineering problems. But, most of them were not truly meshless method because background mesh of cell was required for the spatial integration of a weak form. A nodal integration is required for truly meshless methods but it is known that this method gives a little unstable and incorrect solutions. In this paper, an improvement scheme of the existed nodal integration which the weak form can be simply integrated without any stabilization term is proposed. Numerical tests show that the proposed method is more convenient and gives more correct solutions than the previous method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.16-23
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• 1997

The Reproducing Kernel Particle Method (RKPM), one of the popular meshless methods, is developed and applied to stress concentration problems. Since the meshless methods require only a set of particles (or nodes) and the description of boundaries in their formulation, the adaptivity can be implemented with much more ease than finite element method. In addition, due to its intrinsic property of multiresolution, the shape function of RKPM provides us a new criterion for adaptivity. Recently, this multiple scale Reproducing Kernel Particle Method and its adaptive procedure have been formulated for large deformation problems by the authors. They are also under development for damage materials and localization problems. In this paper the multiple scale RKPM for linear elasticity is presented and the adaptive procedure is applied to stress concentration problems. Therefore, this work may be regarded as the edition of linear elasticity in the complete framework of multiple scale RKPM and the associated adaptivity.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.8 no.3
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• pp.21-26
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• 2009

The finite element analysis of metal forming processes often fails because of severe mesh distortion at large deformation. As the concept of meshless methods, only nodal point data are used for modeling and solving. As the main feature of these methods, the domain of the problem is represented by a set of nodes, and a finite element mesh is unnecessary. This computational methods reduces time-consuming model generation and refinement effort. It provides a higher rate of convergence than the conventional finite element methods. The displacement shape functions are constructed by the reproducing kernel approximation that satisfies consistency conditions. In this research, A meshless method approach based on the reproducing kernel particle method (RKPM) is applied with metal forming analysis. Numerical examples are analyzed to verify the performance of meshless method for metal forming analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.25 no.10
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• pp.653-659
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• 2015

A new formulation of the non-dimensional dynamic influence function method, which is a type of the meshless method, is introduced to extract highly accurate eigenvalues of clamped plates with arbitrary shape. Originally, the final system matrix equation of the method, which was introduced by the author in 1999, does not have a form of algebraic eigenvalue problem unlike FEM. As the result, the non-dimensional dynamic influence function method requires an inefficient process to extract eigenvalues. To overcome this weak point, a new approach for clamped plates is proposed in the paper and the validity and accuracy is shown in verification examples.

• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.511-533
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• 2010

As a truly meshfree method, meshless equilibrium on line method (MELM), for 2D elasticity problems is presented. In MELM, the problem domain is represented by a set of distributed nodes, and equilibrium is satisfied on lines for any node within this domain. In contrary to conventional meshfree methods, test domains are lines in this method, and all integrals can be easily evaluated over straight lines along x and y directions. Proposed weak formulation has the same concept as the equilibrium on line method which was previously used by the authors for enforcement of the Neumann boundary conditions in the strong-form meshless methods. In this paper, the idea of the equilibrium on line method is developed to use as the weak forms of the governing equations at inner nodes of the problem domain. The moving least squares (MLS) approximation is used to interpolate solution variables in this paper. Numerical studies have shown that this method is simple to implement, while leading to accurate results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.1 no.1
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• pp.1-34
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• 1997

In this study, various available meshless methods are briefly reviewed and the connection among them is investigated. The objective of meshless methods is to eliminate some difficulties which are originated from reliance on a mesh by constructing the approximation entirely in terms of nodes. Especially, focusing on Element Free Galerkin Method(EFGM) based on moving least square interpolants(MLSI), a new implementation is developed based on a variational principle with penalty function method were used to enforce the essential boundary condition. In addition, the weighted orthogonal basis functions are constructed to overcome disadvantage of MLSI.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.18 no.6
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• pp.674-680
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• 2008

A new meshless method for obtaining natural frequencies of arbitrarily shaped plates with the free boundary condition is introduced in the paper. In order to improve the characteristics of convergence and accuracy of the method, a special local polar coordinates system is devised and located for each of nodes distributed along the boundary of the plate of interest. In addition, a new way of decreasing the size of the system matrix that gives natural frequencies of the plate is employed to reduce the amount of numerical calculations, which is needed for computing the determinant of the system matrix. Finally the excellence of the characteristics of convergence and accuracy of the method is shown in several case studies, which indicate that natural frequencies by the proposed method are very accurate and converged swiftly to exact values as the number of boundary nodes increases.

• Structural Engineering and Mechanics
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• v.89 no.2
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• pp.135-153
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• 2024

In this study, the impact response of a nanobeam with a moving nanoparticle is investigated. Timoshenko beam theory is used to model the nanobeam behavior and nonlocal elasticity theory is used to consider the effects of small dimensions. The interaction between the nanoparticle and nanobeam has been described using Lennard-Jones potential theory and the equations are discretized by the radial basis meshless method and a mathematical model is presented for the nanobeam-nanoparticle system. Validation of the proposed model is achieved by comparing the obtained natural frequencies with reference values, demonstrating good agreement. Dimensionless frequency analysis reveals a decrease with increasing nonlocal parameter, pointing out a toughening effect in nanobeam. The dynamic response of the nanobeam and nanoparticle is obtained by time integration of equations of motion using Newmark and Wilson-𝜃 methods. A comparative analysis of the two methods is conducted to determine the most suitable approach for this study. As a distinctive aspect in this study, the analysis incorporates the deformation of the nanobeam resulting from the nanoparticle-nanobeam interaction when calculating the Lennard-Jones force in the nanobeam-nanoparticle system. The numerical findings explore the impact of various factors, including the nonlocal parameter, initial velocity, nanoparticle mass, and boundary conditions.

• The KSFM Journal of Fluid Machinery
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• v.12 no.3
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• pp.79-83
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• 2009