• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.5
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• pp.279-286
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• 2020

In this study, we investigate the accuracy of higher order derivatives in the moving least square (MLS) difference method. An interpolation function is constructed by employing a Taylor series expansion via MLS approximation. The function is then applied to the mixed variational theorem in which the displacement and stress resultants are treated as independent variables. The higher order derivatives are evaluated by solving simply supported beams and cantilevers. The results are compared with the analytical solutions in terms of the order of polynomials, support size of the weighting function, and number of nodes. The accuracy of the higher order derivatives improves with the employment of the mean value theorem, especially for very high-order derivatives (e.g., above fourth-order derivatives), which are important in a classical asymptotic analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.381-388
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• 2004

We propose a 2D 'crack' element for the simulation of propagating crack with minimal remeshing. A regular finite element containing the crack tip is replaced with this novel crack element, while the elements which the crack has passed are split into two transition elements. Singular elements can easily be implemented into this crack element to represent the crack-tip singularity without enrichment. Both crack element and transition element proposed in our formulation are mapped from corresponding master elements which are commonly built using the moving least-square (MLS) approximation only in the natural coordinate. In numerical examples, the accuracy of stress intensity factor K/sub I/ is demonstrated and the crack propagation in a plate is simulated.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1737-1751
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• 2013

An efficient and stable point collocation scheme based on a meshfree method is studied for the stationary incompressible Navier-Stokes equations. We describe the diffuse derivatives associated with the moving least square method. Using these diffuse derivatives, we propose a point collocation method to fit in solving the Navier-Stokes equations which improves the stability of the direct point collocation scheme. The convergence of the numerical solution is investigated from numerical examples. The driven cavity ow and the backward facing step ow are implemented for the reliability of the scheme. Also, the viscous ow on complicated geometry is successfully calculated such as the ow past a circular cylinder in duct.

• Structural Engineering and Mechanics
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• v.57 no.3
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• pp.441-456
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• 2016

This work reports wave propagation in the nanocomposite cylinders that reinforced by straight single-walled carbon nanotubes based on a mesh-free method. Moving least square shape functions have been used for approximation of displacement field in weak form of motion equation. The straight carbon nanotubes (CNTs) are assumed to be oriented in specific or random directions or locally aggregated into some clusters. In this simulation, an axisymmetric model is used and also the volume fractions of the CNTs and clusters are assumed to be functionally graded along the thickness. So, material properties of the carbon nanotube reinforced composite cylinders are variable and estimated based on the Eshelby-Mori-Tanaka approach. The effects of orientation, aggregation and volume fractions of the functionally graded clusters and CNTs on dynamic behavior of nanocomposite cylinders are studied. This study results show that orientation and aggregation of CNTs have significant effects on the effective stiffness and dynamic behaviors.

• Interaction and multiscale mechanics
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• v.1 no.3
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• pp.339-355
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• 2008

A Galerkin meshfree method is presented for analyzing shear deformable cylindrical panels. Based upon the analogy between the cylindrical panel and the curved beam a pure bending mode for cylindrical panel is rationally constructed. The meshfree approximation employed herein is characterized by an enhanced moving least square or reproducing kernel basis function that can exactly represent the pure bending mode and thus meets the requirement of Kirchhoff mode reproducing condition. The variational form is discretized using the efficient stabilized conforming nodal integration with a smoothed nodal gradient based curvature. The resulting meshfree formulation satisfies the integration constraint for bending exactness. Moreover, it is shown here that the smoothed gradient preserves several desired properties which are valid for the standard gradient obtained by direct differentiation, such as partition of nullity and reproduction of a constant strain field. The efficacy of the proposed approach is demonstrated by two benchmark cylindrical panel examples.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.335-341
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• 2009

In this paper, review of developed MLS-based finite elements and a proposal for their applications are described. The shape functions and their derivatives of MLS-based finite elements are constructed using Moving-Least Square approximation. In MLS-based finite element, using the adequate influence domain of weight function used in MLS approximation, kronecker delta condition could be satisfied at the element boundary. Moreover, because of the characteristics of MLS approximation, we could easily add extra nodes at an arbitrary position in MLS-based finite elements. For these reasons, until now, several variable-node elements(2D variable element for linear case and quadratic case and 3D variable-node elements) and finite crack elements are developed using MLS-based finite elements concept. MLS-based finite elements could be extended to 2D variable-node triangle element, 2D finite crack triangle element, variable-node shell element, finite crack shell element, and 3D polyhedron element. In this paper, we showed the feasibility of 3D polyhedron element at the case of femur meshing.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.404-409
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• 2004

A compressor loop pipe is the most important part in a refrigerator from the view of structural vibration and noise. Vibration energy generated from a compressor's inner body is transmitted to the shell and outside through the loop pipe. For this reason it is very important to design a compressor loop pipe. But, for geometrical complexity and dynamic nonlinearity of the loop pipe, analysis and design of the loop pipe is very difficult. So the statistical and experimental methods have to be used for design of this system. The response surface method (RSM) becomes a popular meta-modeling technique f3r the complex system as this loop pipe. As starting point of loop pile's optimization, FEA model and simple experimental model are used instead of the real loop pipe model. After RS model was constructed, using sensitivity-based optimizer performed optimization for the loop pipe. And the moving least square method (MLSM) was applied to reduce the approximation error.

• Computers and Concrete
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• v.16 no.5
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• pp.669-682
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• 2015

Degradation of reinforced concrete (RC) structures due to chloride penetration followed by reinforcement corrosion has been a serious problem in civil engineering for many years. The numerical simulation methods at present are mainly finite element method (FEM) and finite difference method (FDM), which are based on mesh. Mesh generation in engineering takes a long time. In the present article, the numerical solution of chloride transport in concrete is analyzed using radial point interpolation method (RPIM) and element-free Galerkin (EFG). They are all meshless methods. RPIM utilizes radial polynomial basis, whereas EFG uses the moving least-square approximation. A Galerkin weak form on global is used to attain the discrete equation, and four different numerical examples are presented. MQ function and appropriate parameters have been proposed in RPIM. Numerical simulation results are compared with those obtained from the finite element method (FEM) and analytical solutions. Two case of chloride transport in full saturated and unsaturated concrete are analyzed to test the practical applicability and performance of the RPIM and EFG. A good agreement is obtained among RPIM, EFG, and the experimental data. It indicates that RPIM and EFG are reliable meshless methods for prediction of chloride concentration in concrete structures.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.5
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• pp.393-399
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• 2013

In this paper, a novel approach to estimate cohesive laws for the mode I fracture of the graphene is presented by combining molecular dynamic simulations and an inverse algorithm based on field projection method and finite element method. The determination of crack-tip cohesive laws of the graphene based on continuum mechanics is a non-trivial inverse problem of finding unknown tractions and separations from atomic simulations. The displacements of molecular dynamic simulations in a region far away from the crack tip are transferred to finite element nodes by using moving least square approximation. Inverse analyses for extracting unknown cohesive tractions and separation behind the crack tip can be carried out by using conservation nature of the interaction J- and M-integrals with numerical auxiliary fields which are generated by systematically imposing uniform surface tractions element-by-element along the crack surfaces in finite element models. The preset method can be a very successful approach to extract crack-tip cohesive laws from molecular dynamic simulations as a scale bridging method.