• Journal of Mechanical Science and Technology
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• v.17 no.1
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• pp.64-76
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• 2003

In this work, a new penalty formulation is proposed for the analysis of Mindlin-Reissner plates by using the element-free Galerkin method. A penalized weak form for the Mindlin-Reissner Plates is constructed through the exterior penalty method to enforce the essential boundary conditions of rotations as well as transverse displacements. In the numerical examples, some typical problems of Mindlin-Reissner plates are analyzed, and parametric studies on the order of integration and the size of influence domain are also carried out. The effect of the types of background cells on the accuracy of numerical solutions is observed and a proper type of background cell for obtaining optimal accuracy is suggested. Further, optimal order of integration and basis order of Moving Least Squares approximation are suggested to efficiently handle the irregularly distributed nodes through the triangular type of background cells. From the numerical tests, it is identified that unlike the finite element method, the proposed element-free Galerkin method with penalty technique gives highly accurate solution without shear locking in dealing with Mindlin-Reissner plates.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.11
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• pp.2705-2712
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• 2000

In meshless methods some techniques to impose essential boundary conditions have been developed since the approximations do not satisfy Kronecker delta properties at nodal points. In this study, new scheme for imposing essential boundary conditions is developed. Weight functions are modified by multiplying with auxiliary weight functions and the resulting shape functions satisfy Kronecker delta property on the bound ary nodes. In addition, the resulting shape functions possess and interpolation features on the boundary segments where essential boundary conditions are prescribed. Therefore the essential boundary conditions can be exactly satisfied with the new method. More importantly, the impositions of essential boundary conditions using the present method is relatively easy as in finite element method. Numerical examples show that the method also retains high convergence rate comparable to Lagrange multiplier method.

• Advances in environmental research
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• v.8 no.1
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• pp.1-21
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• 2019

In the present study, analysis of contaminant transport through one dimensional unsaturated stratified media using element free Galerkin method has been presented. Element free Galerkin method is a meshfree method. A FORTRAN code has been developed for the same. The developed model is compared with the results available in the literature and are found in good agreement. Further a parametric study has been conducted to examine the effects of various parameters like velocity, dispersivity, retardation factor and effect of saturation on the contaminant flow. The results presented conclude that transport of contaminant is retarded in unsaturated zone in comparison with the saturated zone.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.19-26
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• 2001

Previously, an improved crack analysis technique based on Element-Free Galerkin Method (EFGM) which includes a discontinuity function and a singular basis function was presented. The technique needs neither addition of nodes nor modification of the model, but it shows some dependency on the formulation and modeling parameters such as the class of weight function, the size of compact support, dilation parameter and the range controlled by the singular basis function. For those parameters, a parametric study was performed on the calculation of a discrete error and then, a guideline for the choice of adequate parameters in the technique was proposed.

• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.12 no.1
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• pp.47-56
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• 1999

최근 요소망의 구성없이 공학적인 문제의 해석이 가능한 무요소법이 많은 학자들에 의하여 제안되고 이에 관한 집중적인 연구가 이루어지고 있다. 본 연구에서는 갤러킨 정식화에 의한 무요소법을 고체역학적인 문제에 적용하여 이의 특성을 규명하고자 하였다. 특히 일반적으로 사용되고 있는 몇가지 가중 함수를 선정하여 이들이 해석결과에 미치는 특성과 절점 배치방법 및 가중 함수의 영향 영역 변화에 따른 해의 정확도 등을 서로 비교하고 검토하였다. 연구결과로 가중 함수의 형태와 영향 영역의 크기, 기정 함수의 차수와 절점 배치방법 등은 서로 상관관계를 갖고 해의 정확도에 크게 영향을 미침을 확인할 수 있었고 이의 적절한 선정은 무요소해석의 중요한 요건임을 알 수 있었다.