• 한국정밀공학회지
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• 제20권9호
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• pp.159-165
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• 2003

Most engineers interested in stress singularities have focused mainly on the research of power stress singularities for v-notched cracks in dissimilar materials. The logarithmic stress singularity was discussed a little in Bogy's paper. The power-logarithmic stress singularity was reported by Dempsey and Sinclair. It was indicated that the logarithmic singularity is only a special case of power-logarithmic stress singularities. Then, Dempsey reported specific cases which have power-logarithmic singularities even fur homogeneous boundary conditions. It was known that logarithmic stress singularities for v-notched cracks in dissimilar materials occurs when the surfaces of a v-notched crack have constant tractions. In this paper, using the complex potential method, the stresses and displacements having logarithmic stress singularities were obtained and the coefficients vectors were calculated by a numerical program code: Mathematica. It was shown that our analysis models don't have logarithmic stress singularities under the constant tractions, although the coefficient vectors are existing.

• 한국자동차공학회논문집
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• 제13권5호
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• pp.104-111
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• 2005

With increasing use of SUH35/SUH3 dissimilar materials for automotive engine valves, it is required that stress singularities under residual stress on an interface for friction welded dissimilar materials analyzed to establish strength evaluation. The stress singularity $index{\lambda}$ and stress singularities $factor{\Gamma}$ were calculated from using the results of stress analysis to consider residual stress and loads. The stress singularities on variations for shapes and thickness of welded flashes were analyzed and discussed. This paper suggested that the strength evaluation by using the stress singularity factors as fracture parameters, considering the stress singularity on an interface edge of friction welded dissimilar materials will be useful.

• International Journal of Precision Engineering and Manufacturing
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• 제3권2호
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• pp.22-32
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• 2002

V-notched crack problems can be formulated as eigenvalue problems. The problem ova v-notched crack in anisotropic and/or pseudo-isotropic dissimilar materials was formulated as an eigenvalue problem to discuss stress singularities. The eigenvalue problem was served by the commercial numerical program; MATHEMATICA. The specific data of eigenvalues possessing the stress singularity were obtained. Stress singularities fur v-notched cracks in anisotropic and/or pseudo-isotropic dissimilar materials were discussed according to the relation between wedge angle and material property. It was shown that there are three cases of eigenvalues possessing the stress singularity; one real, two real and one complex.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 추계학술대회 논문집
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• pp.747-750
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• 1997

Using complex potentials and the concept of repeated roots for general solutions, logarithmic stress singularities and coefficient vectors for v-notched cracks in isotropic dissimilar materials are evaluated and demonstrated to have no influence on the logarithmic stress singularities.

• 한국자동차공학회논문집
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• 제13권2호
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• pp.142-148
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• 2005

In this paper, the stress singularity on interface of friction welded dissimilar materials was investigated by using 2-dimensional elastic boundary element method. It is required that stress distributions and stress singularities on an interface for friction welded dissimilar materials analize to establish strength evaluation. The stress singularity index ($\lambda$) and stress singularity factor ($\Gamma$) were calculated from the results of stress analysis. The stress singularities on variations for shapes and thickness of friction welded flashes were analized and discussed. This paper suggested that the strength evalution by using the stress singularity factors as fracture parameters, considering the stress singularity on an interface edge of friction welded dissimilar materials were very useful.

• East Asian mathematical journal
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• 제36권5호
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• pp.583-591
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• 2020

In [8, 9] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].

• Geomechanics and Engineering
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• 제32권4호
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• pp.397-409
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• 2023

This study examines two traditional approaches (non-linear elastic and elasto-plastic) in association with 2D and 3D FEM analyses of a box-section pile embedded in sand. A particular emphasis is placed on stress singularities concerning both reentrant corners of the pile section and the resulting tension zones. From the experience gained in this study, non-linear elastic soil models are less restrictive when one considers stress singularities and their possible effects on convergence of the solution. At least for monotonic loading, when compared with field tests, non-linear elastic models yield better results than the plasticity ones. On the other hand, although elasto-plastic models are not limited to monotonic loading, they are much more sensitive to stress singularities. For this reason, a spherical elastic region is necessary at the pile tip to ensure convergence. Without this region, one must artificially impose an apparent cohesion to limit the tension stresses within a sand medium.

• 대한기계학회논문집A
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• 제20권1호
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• pp.135-145
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• 1996

Order of stress singularities at bonded Edge Corners with two or three dissimilar isotropic Materials is analyzed. The problem is formulated by Mellin transform and characteristic equation is obtained as a determinant of matrix considering boundary conditions. Roots of characterictic equation are determinde by numerical calculations with ward method, from which the order of stress sigularities is obtained. Applying the results to the electronic packaging, the order of stress singularities is obtained. Applying the results to the electronic packaging, the order of stress singularities at bounded edge corners is calculated as a various bouned edge angle with given material combinations. Comparing the results, the optimal material combinaitons of bounded edge corners and bouned edge angle to reduce stress singularity could be determined. It suggests that the results are used to the basic design of electronic packaging reducing the stress singularity.

• 대한기계학회논문집
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• 제16권10호
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• pp.1890-1899
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• 1992

본 연구에서는 이종재료간의 Ⅴ-노치균열의 노치각도 및 재료의 종류에 따른 응력특이성지수와 응력강도 계수 해석에 각각 뉴톤-랍슨법(newtonraphson method), 뉴톤-랍슨법과 최소자승법을 이용한 선점법(collocation method)인 수치해석적 방법을 응용하고, 광탄성 등색선 무늬를 컴퓨터 그래픽하여 응력특이성지수와 응력강도계수가 모우드(mode)에 미치는 특성과 경계요소법(boundary element method)으로 응력해석한 결과로써 선점법을 이용하여 응력강도계수를 해석하고 기존의 결과등과 비교, 검토하 고자 한다.

• 한국정밀공학회지
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• 제16권10호
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• pp.152-163
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• 1999

The problem of eigenvalue and eigenvector for v-notched cracks in pseudo-isotropic and anisotropic dissimilar materials was obtained to discuss stress singularities from traction free boundary and perfect bonded interface conditions assuming like the form of complex stress function for v-notched cracks in an isotropic material. Eigenvalues were solved by a commercial numerical program, MATHEMATICA. The relation between wedged angle and material property for eigenvalue, ${\lambda}$ indicating stress singularities of v-notched cracks in pseudo-isotropic and anisotropic dissimilar materials was examined.