• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2001년도 봄 학술발표회 논문집
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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.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2006년도 정기 학술대회 논문집
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• pp.357-364
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• 2006

The meshfree method is extended by the local partition of unity method to model the cohesive cracks in two dimensional continuum The shape function of a particle whose domain of influence is completely cut by a crack is enriched by the step enrichment function. If the domain of influence contains a crack tip inside, it is enriched by the branch enrichment function without the stress singularity. It is found that this method is more accurate and converges faster than the meshless methods for LEFM cracks based on the visibility concept Several staic and dynamic examples are solved to verify the method.

• Geomechanics and Engineering
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• 제2권2호
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• pp.141-156
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• 2010

In the framework of meshfree methods, a new methodology is developed based on radial point interpolation method (RPIM). This methodology is applied to a one-dimensional contaminant transport modelling in the saturated porous media. The one-dimensional form of advection-dispersion equation involving reactive contaminant is considered in the analysis. The Galerkin weak form of the governing equation is formulated using 1D meshfree shape functions constructed using thin plate spline radial basis functions. MATLAB code is developed to obtain the numerical solution. Numerical examples representing various phenomena, which occur during migration of contaminants, are presented to illustrate the applicability of the proposed method and the results are compared with those obtained from the analytical and finite element solutions. The proposed RPIM has generated results with no oscillations and they are insensitive to Peclet constraints. In order to test the practical applicability and performance of the RPIM, three case studies of contaminant transport through the landfill liners are presented. A good agreement is obtained between the results of the RPIM and the field investigation data.

• Coupled systems mechanics
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• 제5권3호
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• pp.203-221
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• 2016

The present study deals with the numerical modelling for the one dimensional contaminant transport through saturated homogeneous and stratified porous media using meshfree method. A numerical algorithm based on element free Galerkin method is developed. A one dimensional form of the advectivediffusive transport equation for homogeneous and stratified soil is considered for the analysis using irregular nodes. A Fortran program is developed to obtain numerical solution and the results are validated with the available results in the literature. A detailed parametric study is conducted to examine the effect of certain key parameters. Effect of change of dispersion, velocity, porosity, distribution coefficient and thickness of layer is studied on the concentration of the contaminant.

• Structural Engineering and Mechanics
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• 제32권2호
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• pp.235-249
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• 2009

The response of concrete structures subjected to shock and blast load involves a rapid transient phase, during which material breach may take place. Such an effect could play a crucial role in determining the residual state of the structure and the possible dispersion of the fragments. Modelling of the transient phase response poses various challenges due to the complexities arising from the dynamic behaviour of the materials and the numerical difficulties associated with the evolving material discontinuity and large deformations. Typical modelling approaches include the traditional finite element method in conjunction with an element removal scheme, various meshfree methods such as the SPH, and the mesoscale model. This paper is intended to provide an overview of several alternative approaches and discuss their respective applicability. Representative concrete material models for high pressure and high rate applications are also commented. Several recent application studies are introduced to illustrate the pros and cons of different modelling options.

• Structural Engineering and Mechanics
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• 제88권3호
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• pp.239-249
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• 2023

The Radial Point Interpolation Method (RPIM) has been proposed to overcome the difficulties associated with the use of the Radial Basis Functions (RBFs). The RPIM has the following properties: Simple implementation in terms of boundary conditions as in the Finite Element Method (FEM). A less expensive CPU time compared to other collocation meshless methods such as the Moving Least Square (MLS) collocation method. In this work, we propose an adaptive high-order numerical algorithm based on RPIM to simulate the thermoviscoplastic behavior of a material mixing observed in the Friction Stir Welding (FSW) process. The proposed adaptive meshfree RPIM algorithm adapts well to the geometric and physical data by choosing a good shape parameter with a good precision. Our numerical approach combines the RPIM and the Asymptotic Numerical Method (ANM). A numerical procedure is also proposed in this work to automatically determine an improved shape parameter for the RBFs. The efficiency of the proposed algorithm is analyzed in comparison with an iterative algorithm.

• 한국전산유체공학회지
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• 제14권4호
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• pp.93-100
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• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved successively in the moving least square sense. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as a FVM.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권2호
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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.

• 한국전산구조공학회논문집
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• 제18권2호
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• pp.113-121
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• 2005

무요소기법이 공통적으로 내재하고 있는 수치적분의 부정확성을 해결하기 위해, 페트로프-갤러킨 자연요소법이라 불리는 향상된 자연요소법을 제안한다. 제안된 방법은 라플라스 기저함수를 시도 형상함수로 사용하는 반면, 시험 형상함수로서 델라우니 삼각형이 지지영역이 되는 함수를 새롭게 정의한다. 이러한 접근은 통상적인 적분영역과 적분함수 지지영역간의 불일치를 제거하게 하며, 이는 적용이 편리할 뿐만 아니라 수치적분의 정확성을 보장한다 본 논문에서는 2차윈 선형 탄성의 대표적인 검증문제를 통하여 제안된 방법의 타당성을 검증한다. 비교를 위해 기존의 부브노프-갤러킨 자연요소법과 일정 변형률 유한요소법을 이용한 해석을 동시에 수행한다. 조각 시험과 수렴율 평가를 통해 제안된 기법의 우수성을 확인할 수 있다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2009년 춘계학술대회논문집
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• pp.239-244
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• 2009

The gridless (or meshfree) methods, such as MPS, SPH, FPM an so forth, are feasible and robust for the problems with moving boundary and/or complicated boundary shapes, because these methods do not need to generate a grid system. In this study, a gridless solver, which is based on the combination of moving least square interpolations on a cloud of points with point collocation for evaluating the derivatives of governing equations, is presented for two-dimensional unsteady incompressible Navier-Stokes problem in the low Reynolds number. A MAC-type algorithm was adopted and the Poission equation for the pressure was solved by successively in the moving least square sense. Some weighing functions were tested in order to investigate the up-winding effect for the convection term. Some typical problems were solved by the presented solver for the validation and the results obtained were compared with analytic solutions and the numerical results by conventional CFD methods, such as FVM.