• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.365-372
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• 2006

A new meshfree formulation is developed for material discontinuity problems. A local interfacial jump function which is defined as hyperplane function is embedded in the meshless approximation and the approximation accurately models functions with jumps in the displacement and the derivative fields. Diffuse derivative technique copes with difficulty due to complexity of derivative computation of meshfree approximation. Collocation method with diffuse derivative accelerates computing speed for numerical solution. By solving inclusion and composite material problems, the robustness and effectiveness of the method are verified.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.2
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• pp.67-85
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• 2013

Reproducing Polynomial Particle Method (RPPM) is one of meshless methods that use meshes minimally or do not use meshes at all. In this paper, the RPPM is employed for free vibration analysis of shear-deformable plates of the first order shear deformation model (FSDT), called Reissner-Mindlin plate. For numerical implementation, we use flat-top partition of unity functions, introduced by Oh et al, and patchwise RPPM in which approximation functions have high order polynomial reproducing property and the Kronecker delta property. Also, we demonstrate that our method is highly effective than other existing results for various aspect ratios and boundary conditions.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.3-14
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• 1998

Computational structural engineering is the base on which most of the achievements of engineering and physics are built. Since most of the theory underlying physical phenomena is involved differential equations for which closed forms of solution are seldom possible, the numerical approximation is necessary for a quantitative solution. Some areas where progress and research on computational mechanics are currently active are discussed. In the first part of this paper the development of the improved non-conforming elements for the analysis of plates and shells is described. Recent developments in the adaptive analysis for the structural and the wind problem and meshless method are also discussed in the second part.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2007.04a
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• pp.495-500
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• 2007

A Meshfree is a method used to establish algebraic equations of system for the whole problem domain without the use of a predefined mesh for the domain discretization. A point interpolation method is based on combining radial and polynomial basis functions. Involvement of radial basis functions overcomes possible singularity. Furthermore, the interpolation function passes through all scattered points in an influence domain and thus shape functions are of delta function property. This makes the implementation of essential boundary conditions much easier than the meshfree methods based on the moving least-squares approximation. This study aims to investigate a stress analysis of structural element between a meshfree method and the finite element method. Examples on cantilever type plate and stress concentration problems show that the accuracy and convergence rate of the meshfree methods are high.

• Nuclear Engineering and Technology
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• v.39 no.3
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• pp.207-214
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• 2007

A new Monte Carlo method for solving heat conduction problems is developed in this study. Differing from other Monte Carlo methods, it is a transport approximation to the heat diffusion process. The method is meshless and thus can treat problems with complicated geometry easily. To minimize the boundary effect, a scaling factor is introduced and its effect is analyzed. A set of problems, particularly the heat transfer in the fuel sphere of PBMR, is calculated by this method and the solutions are compared with those of an analytical approach.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.679-698
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• 2020

In this paper, the meshless local Petrov-Galerkin (MLPG) method is developed for dynamic analysis of non-symmetric nanocomposite cylindrical shell equations of elastic wave motion with nonlinear grading patterns under shock loading. The mechanical properties of the nanocomposite cylinder are obtained based on a micro-mechanical model. In this study, four kinds of grading patterns are assumed for carbon nanotube mechanical properties. The displacements can be approximated using shape function so, the multiquadrics (MQ) Radial Basis Functions (RBF) are used as the shape function. In order to discretize the derived equations in time domains, the Newmark time approximation scheme with suitable time step is used. To demonstrate the accuracy of the present method for dynamic analysis, at the first a problem verifies with analytical solution and then the present method compares with the finite element method (FEM), finally, the present method verifies by using the element free Galerkin (EFG) method. The comparison shows the high capacity and accuracy of the present method in the dynamic analysis of cylindrical shells. The capability of the present method to dynamic analysis of non-symmetric nanocomposite cylindrical shell is demonstrated by dynamic analysis of the cylinder with different kinds of grading patterns and angle of nanocomposite reinforcements. The present method shows high accuracy, efficiency and capability to dynamic analysis of non-symmetric nanocomposite cylindrical shell, which it furnishes a ground for a more flexible design.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.713-732
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• 2002

A local radial point interpolation method (LRPIM) based on local residual formulation is presented and applied to solid mechanics in this paper. In LRPIM, the trial function is constructed by the radial point interpolation method (PIM) and establishes discrete equations through a local residual formulation, which can be carried out nodes by nodes. Therefore, element connectivity for trial function and background mesh for integration is not necessary. Radial PIM is used for interpolation so that singularity in polynomial PIM may be avoided. Essential boundary conditions can be imposed by a straightforward and effective manner due to its Delta properties. Moreover, the approximation quality of the radial PIM is evaluated by the surface fitting of given functions. Numerical performance for this LRPIM method is further studied through several numerical examples of solid mechanics.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.4
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• pp.35-43
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• 2003

In this paper, an efficient computational algorithm for the implementation of the newly proposed node activation technique is presented, and its computational aspects are thoroughly investigated. To verify the validity, convergence, and efficiency of the node activation technique, various numerical examples are worked out including the problems of Poisson equation, 2D elasticity problems, and 3D elasticity problems. From the numerical tests, it is verified that one can arbitrarily activate and handle the nodal points of interest in finite element model with very little loss of the numerical accuracy.