• 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.

• 대한토목학회논문집
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• 제26권5A호
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• pp.861-872
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• 2006

본 연구에서는 이차원 연속체에 존재하는 점성균열을 무요소법에서 국부 단위분할 원리에 근거하여 정식화하였다. 균열이 한 절점의 영향영역(domain of influence)을 완전히 통과하는 경우 그 절점의 형상함수는 계단함수로 확장되고, 균열 끝이 영향영역 내에 위치하는 경우 특이성이 제거된 가지함수(branch function)로 확장된다. 이러한 해의 영역의 확장은 국부 단위분할 원리를 만족하는 변위계에서만 이루어지므로, 약형 정식화는 표준 Galerkin방법에 의해서 얻어진다. 균열과 상호작용하는 영향영역만 확장되기 때문에, 성긴 형태의 시스템의 행렬을 유지하게 된다. 그러므로 확장에 의해 발생하는 계산비용의 증가는 최소화된다. 동적인 문제에서 균열성장에 관한 조건은 재료안정론으로부터 얻어졌다. 즉, 재료 한 점에서 어느 방향으로든 변형열화가 집중하게 되면, 그 방향에 점성균열을 삽입하여 연속체가 비연속체로 되도록 하였다. 균열의 성장속도도 같은 조건으로부터 자연스럽게 얻어졌다. 전통적인 무요소법보다 더 나은 정확도와 빠른 수렴성을 보이는 것이 확인되었으며, 이 기법의 적용성을 보이기 위해 잘 알려진, 정적 및 동적문제에 적용하였다.

• 한국정밀공학회지
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• 제23권8호
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• pp.89-99
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• 2006

In this paper a new shape reconstruction method that allows us to construct surface models from very large sets of points is presented. In this method the global domain of interest is divided into smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together according to weighting coefficients to obtain a global solution using partition of unity function. The suggested approach gives us considerable flexibility in the choice of local shape functions which depend on the local shape complexity and desired accuracy. At each domain, a quadratic polynomial function is created that fits the points in the domain. If the approximation is not accurate enough, other higher order functions including cubic polynomial function and RBF(Radial Basis Function) are used. This adaptive selection of local shape functions offers robust and efficient solution to a great variety of shape reconstruction problems.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2008년도 정기 학술대회
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• pp.172-176
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• 2008

In this paper, three dimensional linear conforming variable-finite elements are presented with the aid of a smoothed integration (a class of stabilized conforming nodal integration), for mnltiscale mechanics problems. These elements meet the desirable properties of an interpolation such as the Kronecker delta condition, the partition of unity condition and the positiveness of interpolation function. The necessary condition of linear exactness is fully relaxed by employing the smoothed integration, which renders us to meet the linear exactness in a straightforward manner. This novel element description extend the category of the conventional finite elements space to ration type function space and give the flexibility on the number of nodes of element which are fixed in the conventional finite elements. Several examples are provided to show the convergence and the accuracy of the proposed elements, and to demonstrate their potential with emphasis on the multiscale mechanics problems such as global/local analysis, nonmatching contact problems, and modeling of composite material with defects.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2007년도 정기 학술대회 논문집
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• pp.507-512
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• 2007

A new type of extended element-free Galerkin method (XFEM) is proposed on this paper. The blending region which was inevitable in the extended finite element method and the extended meshfree method is removed in this method. For this end, two different techniques are developed. The first one is the modification of the domain of influence so that the crack tip is always placed on the edge of a domain of influence. The second method is the use of the Lagrange multiplier. The crack is virtually extended beyond the actual crack tip. The virtual extension was forced close by the Lagrange multiplier. The first method can be applied to two dimensional problems only Lagrange multiplier method can be used in both two and three dimensions.

• Interaction and multiscale mechanics
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• 제1권1호
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• pp.83-101
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• 2008

A derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2002년도 봄 학술발표회 논문집
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• pp.69-76
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• 2002

In this paper, several improved Element-Free Galerkin (EFG) methods containing singular expression in their approximation functions are compared one another through a patch test with near-tip field. Intrinsic enrichments that expand the basis function partially and fully with known near-tip displacement field and a local enrichment using auxiliary supports based on the partition of unity concept are examined by evaluating a relative stress norm error and the stress intensity factor. Some numerical examinations graphically show that how the size of compact support, dilation parameter and the diffraction parameter can affect the accuracy of the improved EFG methods in the error and the stress intensity factor.

• 한국정밀공학회지
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• 제23권11호
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• pp.93-102
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• 2006

In this study an advanced domain decomposition method is suggested in order to construct surface models from very large amount of points. In this method the spatial domain of interest that is occupied by the input set of points is divided in repetitive manner. First, the space is divided into smaller domains where the problem can be solved independently. Then each subdomain is again divided into much smaller domains where the problem can be solved locally. These local solutions of subdivided domains are blended together to obtain a solution of each subdomain using partition of unity function. Then the solutions of subdomains are merged together in order to construct whole surface model. The suggested methods are conceptually very simple and easy to implement. Since RDDM(Repetitive Domain Decomposition Method) is effective in the computation time and memory consumption, the present study is capable of providing a fast and accurate reconstructions of complex shapes from large amount of point data containing millions of points. The effectiveness and validity of the suggested methods are demonstrated by performing numerical experiments for the various types of point data.