• Korea-Australia Rheology Journal
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• 제17권3호
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• pp.99-110
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• 2005

This work presents results of finite element analysis of isothermal incompressible creeping viscoelastic flows with the tensor-logarithmic formulation of the Leonov model especially for the planar geometry with singular comers in the domain. In the case of 4:1 contraction flow, for all 5 meshes we have obtained solutions over the Deborah number of 100, even though there exists slight decrease of convergence limit as the mesh becomes finer. From this analysis, singular behavior of the comer vortex has been clearly seen and proper interpolation of variables in terms of the logarithmic transformation is demonstrated. Solutions of 4:1:4 contraction/expansion flow are also presented, where there exists 2 singular comers. 5 different types spatial resolutions are also employed, in which convergent solutions are obtained over the Deborah number of 10. Although the convergence limit is rather low in comparison with the result of the contraction flow, the results presented herein seem to be the only numerical outcome available for this flow type. As the flow rate increases, the upstream vortex increases, but the downstream vortex decreases in their size. In addition, peculiar deflection of the streamlines near the exit comer has been found. When the spatial resolution is fine enough and the Deborah number is high, small lip vortex just before the exit comer has been observed. It seems to occur due to abrupt expansion of the elastic liquid through the constriction exit that accompanies sudden relaxation of elastic deformation.

• Journal of applied mathematics & informatics
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• 제7권2호
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• pp.493-506
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• 2000

Recently the first author and his coworker report a new finite element method for the Poisson equations with homogeneous Dirichlet boundary conditions on a polygonal domain with one re-entrant angle [7], They use the well-known fact that the solution of such problem has a singular representation, deduced a well-posed new variational problem for a regular part of solution and an extraction formula for the so-called stress intensity factor using tow cut-off functions. They use Fredholm alternative an Garding's inequality to establish the well-posedness of the variational problem and finite element approximation, so there is a maximum bound for mesh h theoretically. although the numerical experiments shows the convergence for every reasonable h with reasonable size y imposing a restriction to the support of the extra cut-off function without using Garding's inequality. We also give error analysis with similar results.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1994년도 추계학술대회 논문집
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• pp.235-239
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• 1994

In this paper, the fatigue behaviour of typical axisymmetric forward extrusion die is investigated and extrusion process is analyzed by the rigid-plastic finite element method and elasto-plastic finite element method. To approach the crack problem involving crack initiation and propagation in extrusion die, LEFM(Linear Elastic Fracture Mechanics) is introduced and singular element which models stress.strain singularity in the crack tip vincity has been used to obtain an accurate stress intensityu factor values and other results. Form the displacement around the crack tip the stress intensity factor and the effective stress intensity factor at the beginning of the die inlet radius has been calculated. Applying proper fatigue crack propagation criterion such as Paris/Erdogan fatigue law to this data the angle and direction of fatigue crack growth has been simulated and these are compared with some experimental results. Using the computed crack growth rate, fatigue life of the extrusion die has been evaluated.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.317-329
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• 2006

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.234-239
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• 2001

The stress intensity factors have been widely used in numerical studies of crack growth direction. However in many cases, omissive terms of the series expansion are quantitatively significant, so we consider the computation of such terms. For this purpose, we used the finite element method with isometric quadratic quarter-point elements. For examples, infinite square plate with a slant crack subjected to a uniaxial load is analyzed. The numerical analysis were performed for the wide range of crack tip element lengths and inclined angles. The numerical results obtained are compared with the theoretical solutions. Also they were accurate and efficient.

• Structural Engineering and Mechanics
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• 제43권3호
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• pp.321-336
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• 2012

As an improvement on the isoparametric element method, the derivation presented in this paper is close to that done by Wang (1990) for the 2-D finite element. We extend this idea to solve 3-D crack problems in this paper. A new displacement modelling is constructed with local solutions of three-dimensional cracks and a quasi-compatible isoparametric element for three-dimensional fracture mechanics analysis is presented. The stress intensity factors can be solved directly by means of the present method without any post-processing. A new method for calculating the stress intensity factors of three-dimensional cracks with complex geometries and loads is obtained. Numerical examples are given to demonstrate the validity of the present method. The accuracy of the results obtained by the proposed element is demonstrated by solving several crack problems. The results illustrate that this method not only saves much calculating time but also increases the accuracy of solutions. Because this quasi-compatible finite element of 3-D cracks contains any singularities and easily meets the requirement of compatibility, it can be easily implemented and incorporated into existing finite element codes.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권2호
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• pp.119-123
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• 2005

This paper describes a fuzzy-based system for analyzing the stress intensity factors (SIFs) of three-dimensional (3D) cracks. 3D finite element method(FEM) was used to obtain the SIF for subsurface cracks and surface cracks existing in inhomogeneous materials. A geometry model, i.e. a solid containing one or several 3D cracks is defined. Several distributions of local node density are chosen, and then automatically superposed on one another over the geometry model by using the fuzzy theory. Nodes are generated by the bucketing method, and ten-noded quadratic tetrahedral solid elements are generated by the Delaunay triangulation techniques. The singular elements such that the mid-point nodes near crack front are shifted at the quarter-points, and these are automatically placed along the 3D crack front. The complete FE model is generated, and a stress analysis is performed. The SIFs are calculated using the displacement extrapolation method. The results were compared with those surface cracks in homogeneous materials. Also, this system is applied to analyze cladding effect of surface cracks in inhomogeneous materials.

• 대한토목학회논문집
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• 제26권4A호
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• pp.693-700
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• 2006

정적 손상 탐지방법은 동적 방법과 비교해서 실제 적용하기에 단순하고 효과적이다. 본 논문에서는 정적데이타를 이용하는 방법으로 변위, 처짐각, 곡률을 이용한 강박스 교량의 손상 탐지 방법에 대해서 연구하였다. 변위는 유한요소 해석에서 얻고, 처짐각과 곡률은 변위로부터 중앙차분법을 이용하여 구하였다. 손상되지 않은 경우와 손상된 경우의 응답차의 절대값으로 손상의 위치를 탐지하였다. 손상은 박스의 모서리 균열을 singular 요소를 사용하여 직접 모델링하여, 실질적인 거동을 분석하였다. 해석 결과 응답차의 절대값으로 손상의 위치를 탐지하기에 매우 효과적이었다.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1997년도 봄 학술발표회 논문집
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• pp.35-42
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• 1997

The two-state or mutual M-integral which is derived from tile M-integral and is applicable for two elastic states, is applied for computing all intensity of a singular near-tip field around the vertex of a class of wedge, encountered in adhesive lap joints under mechanical loading. Numerically we verify that a simple auxiliary field associated with every eigenfunction for the composite wedge under consideration exists in the form of the conjugate solution in the sense of tile M-integral. The auxiliary field is then employed for superposition with the elastic field under consideration, and the associated two-state M-integral is computed via the domain integral technique. This enables us to extract the intensity for a singular field information for a singular elastic boundary layer is extracted form the domain integral representation without resort to singular finite element for the wedge vertex.