• Proceedings of the KSME Conference
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• 2001.11a
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• pp.384-388
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• 2001

The higher order singularities[1] are systematically examined, and discussed are their complementarity relation with the nonsingular eigenfunctions and their relations to the configurational forces like J-integral and M-integral. By use of the so-called two state conservation laws(Im and Kim[2]) or interaction energy, originally proposed by Eshelby[3] and later treated by Chen and Shield[4], the intensities of the higher order singularities are calculated, and their roles in elasticplastic fracture are investigated. Numerical examples are presented for illustration.

• Journal of applied mathematics & informatics
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• v.38 no.3_4
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• pp.311-334
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• 2020

The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that arises in the elliptic interface problems are very complex. In this article we propose an exponentially accurate nonconforming spectral element method for these problems based on [7, 18]. A geometric mesh is used in the neighbourhood of the singularities and the auxiliary map of the form z = ln ξ is introduced to remove the singularities. The method is essentially a least-squares method and the solution can be obtained by solving the normal equations using the preconditioned conjugate gradient method (PCGM) without computing the mass and stiffness matrices. Numerical examples are presented to show the exponential accuracy of the method.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1485-1502
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• 2014

The explicit formula for the hyperbolic metric ${\lambda}_{{\alpha},{\beta},{\gamma}}(z){\mid}dz{\mid}$ on the thrice-punctured sphere $\mathbb{P}{\backslash}\{0,1,{\infty}\}$ with singularities of order 0 < ${\alpha}$, ${\beta}$ < 1, ${\gamma}{\leq}1$, ${\alpha}+{\beta}+{\gamma}$ > 2 at 0, 1, ${\infty}$ was given by Kraus, Roth and Sugawa in [9]. In this article we investigate the asymptotic properties of the higher order derivatives of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$ near the origin and give more precise descriptions for the asymptotic behavior of ${\lambda}_{{\alpha},{\beta},{\gamma}}(z)$.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.10
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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.

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.2
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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.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1297-1301
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• 1997

Generally, singularity analysis of 6-DOF parallerl manipulators is very difficult and, as result, velocity relation has many uncertainties. In this paper, an alternative method using the local structurizatioin method(LSM) for the analysis of singular configuraions is presented. With LSM, the velocity relation can be represented in a simple form, and the result is totally equivalent to the conventional velocity relation. The velocity relation suggested in this paper gives a closed-form solution of singularities.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.147-163
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• 2017

We define de Sitter focal surfaces and hyperbolic focal surfaces of hyperbolic space curves. As an application of the theory of unfoldings of function germs, we investigate the singularities of these surfaces. For characterizing the singularities of these surfaces, we discover a new hyperbolic invariants and investigate the geometric meanings.

• International Journal of Precision Engineering and Manufacturing
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• v.8 no.4
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• pp.16-21
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• 2007

Robotic applications, such as automatic fish cutting, require online trajectory planning because the material properties of the object, such as the bone or flesh conditions, are not known in advance. Different trajectories are required when the material properties vary. An effective online trajectory-planning algorithm is proposed using quaternions to determine the position and orientation of a robot manipulator with a spherical wrist. Quaternions are free of representation singularities and permit computationally efficient orientation interpolations. To prevent singular configurations, the exact locations of the kinematic singularities of the PUMA 560 manipulator are derived and geometrically illustrated when a forearm offset exists and the third link length is not zero.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.951-973
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• 1997

We classify up to conjugation all finite abelian subgroups of $GL(2,C)$ of order $\leq 18$ and compute the generators and relations of their rings of invariants. In other words, we classify all 2-dimensional quotient singularities by an abelian group of order $\leq 18$ and compute the generators and relations of their affine coordinate rings.

• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.367-379
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• 1996

Let $V = {(z, y) : f(z, y) = z^n + Ay^\alpha z^p + y^\beta z^q + y^k = 0}$ and $W = {(z, y) : g(z, y) = z^n + By^\gamma z^s + y^\delta z^t + y^k = 0}$ be germs of analytic irreducible subvarieties of a polydisc near the origin in $C^2$ with n < k and (n, k) = 1 where A and B are complex numbers. Assume that V and W are topologically equivalent near the origin.