• Title/Summary/Keyword: singularity

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Analysis of Jacobian and Singularity of Planar Parallel Robots Using Screw Theory (스크류 이론을 이용한 평면형 병렬로봇의 자코비안 및 특이점 해석)

  • Choi, Jung-Hyun;Lee, Jeh-Won;Lee, Hyuk-Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.11
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    • pp.1353-1360
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    • 2012
  • The Jacobian and singularity analysis of parallel robots is necessary to analyze robot motion. The derivations of the Jacobian matrix and singularity configuration are complicated and have no geometrical earning in the velocity form of the Jacobian matrix. In this study, the screw theory is used to derive the Jacobian of parallel robots. The statics form of the Jacobian has a geometrical meaning. In addition, singularity analysis can be performed by using the geometrical values. Furthermore, this study shows that the screw theory is applicable to redundantly actuated robots as well as non-redundant robots.

Analysis for Strength Estimation of Adhesive Joints (접착이음의 강도평가에 대한 해석)

  • Park Sung-Oan
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.14 no.5
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    • pp.62-73
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    • 2005
  • The objects of this research are to establish the criteria of peel occurrence considering the shape of bond terminus and to compare the strength properties of adhesive joint of different three type such as butt joint, T-shape, and single lap Joints. The criteria of peel occurrence at the bond terminus was suggested. Peel loads of three type adhesive joint (butt Joint, T-shape specimen, single lap joint) were determined from tensile tests. Principal stress distributions of these joints were determined from finite element method analysis. Then, peel occurrence was estimated with stress singularity factor$(K_{prin})$ when the terminus shape was square, with average principal stress when the terminus shape was rounded. The conclusions are summarized as follows; (1) In the non-filleted model(e.g., butt joint, T-shape specimen), principal stress shows singularity at the bond terminus, intensity of stress(principal stress) singularity $(K_{prin})$ can use as the criteria of peel occurrence at the bond terminus. (2) In the filleted model(e.g., single lap joint), principal stress has not affected singularity at the bond terminus. Average principal stress$(K_{av})$ can use as the criteria of peel occurrence at the bond terminus.

Boundary Element Analysis of Stress Singularity at the Interface Corner of Viscoelastic Adhesive Layer Bonded Between Rigid Adherends (강체모재들을 결합하고 있는 점탄성 접착재층의 계면모서리에서 발생하는 응력특이성의 경제요소해석)

  • 이상순;박준수
    • Computational Structural Engineering
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    • v.10 no.2
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    • pp.131-138
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    • 1997
  • This paper concerns the stress singularity at the interface corner of the viscoelastic adhesive layer bonded between rigid adherends, subjected to a uniform transverse tensile strain. The characteristic equation is derived in the Laplace transformed space, following Williams, and the transformed characteristic equation is inverted analytically into real time space for the viscoelastic model considered here. The order of the singularity is obtained numerically. The time-domain boundary element method is employed to investigate the nature of stresses along the interface. Numerical results show that the order of the singularity increases with time while the free-edge stress intensity factors are relaxed with time.

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A 2-D four-noded finite element containing a singularity of order λ

  • Abdel Wahab, M.M.;de Roeck, G.
    • Structural Engineering and Mechanics
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    • v.3 no.4
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    • pp.383-390
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    • 1995
  • A 2-D four-noded finite element which contains a ${\lambda}$ singularity is developed. The new element is compatible with quadratic standard isoparametric elements. The element is tested on two different examples. In the first example, an edge crack problem is analyzed using two different meshes and different integration orders. The second example is a crack perpendicular to the interface problem which is solved for different material properties and in turn different singularity order ${\lambda}$. The results of those examples illustrate the efficiency of the proposed element.

Polynomial Unknotting and Singularity Index

  • Mishra, Rama
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.271-292
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    • 2014
  • We introduce a new method to transform a knot diagram into a diagram of an unknot using a polynomial representation of the knot. Here the unknotting sequence of a knot diagram with least number of crossing changes can be realized by a family of polynomial maps. The number of singular knots in this family is defined to be the singularity index of the diagram. We show that the singularity index of a diagram is always less than or equal to its unknotting number.

Boundary Element Analysis of Interface Stresses in a Thin Film Due to Moisture Absorption (수분 흡수로 인해 얇은 필름에 발생하는 계면 응력의 경계요소해석)

  • 이상순
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1999.04a
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    • pp.19-26
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    • 1999
  • This paper deals with the stress singularity induced at the interface corner between the viscoelastic thin film and the rigid substrate as the film absorbs moisture from the ambient environment. The rime-domain boundary element method is employed to investigate the behavior of interface stresses. The order of the free-edge singularity is obtained numerically for a given viscoelastic model. It is shown that the free-edge stress intensity factor is relaxed with time,'while the order of the singularity increases with time for the viscoelastic model considered.

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Analysis of Thermal Stresses Developed in Bonding Interface of Semiconductor Chip (반도체 칩의 접착계면에 발생하는 열응력 해석)

  • 이상순
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • 1999.10a
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    • pp.437-443
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    • 1999
  • This paper deals with the stress singularity induced at the interface corner between the viscoelastic thin film and the rigid substrate subjected to uniform temperature change. The viscoelastic film has been assumed to be thermorheologically simple. The time-domain boundary element method(BEM) has been employed to investigate the behavior of interface stresses. The order of the free-edge singularity has been obtained numerically for a given viscoelastic model. It is shown that the free-edge stress intensity factor is relaxed with time, while the order of the singularity increases with time for the viscoelastic model considered.

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SINGULARITY FORMATION FOR A NONLINEAR VARIATIONAL SINE-GORDON EQUATION IN A MULTIDIMENSIONAL SPACE

  • Fengmei Qin;Kyungwoo Song;Qin Wang
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.6
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    • pp.1697-1704
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    • 2023
  • We study a multidimensional nonlinear variational sine-Gordon equation, which can be used to describe long waves on a dipole chain in the continuum limit. By using the method of characteristics, we show that a solution of a nonlinear variational sine-Gordon equation with certain initial data in a multidimensional space has a singularity in finite time.

SINGULARITY ORDER OF THE RIESZ-NÁGY-TAKÁCS FUNCTION

  • Baek, In-Soo
    • Communications of the Korean Mathematical Society
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    • v.30 no.1
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    • pp.7-21
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    • 2015
  • We give the characterization of H$\ddot{o}$lder differentiability points and non-differentiability points of the Riesz-N$\acute{a}$gy-Tak$\acute{a}$cs (RNT) singular function ${\Psi}_{a,p}$ satisfying ${\Psi}_{a,p}(a)=p$. It generalizes recent multifractal and metric number theoretical results associated with the RNT function. Besides, we classify the singular functions using the singularity order deduced from the H$\ddot{o}$lder derivative giving the information that a strictly increasing smooth function having a positive derivative Lebesgue almost everywhere has the singularity order 1 and the RNT function ${\Psi}_{a,p}$ has the singularity order $g(a,p)=\frac{a{\log}p+(1-a){\log}(1-p)}{a{\log}a+(1-a){\log}(1-a)}{\geq}1$.

Strength Evaluation of Friction Welded SUH35/SUB3 Considering Stress Singularity (응력특이성을 고려한 SUH35/SUH3 마찰용접재의 강도평가)

  • Chung, Nam-Yong;Park, Chul-Hee
    • Transactions of the Korean Society of Automotive Engineers
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    • v.14 no.4
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    • pp.59-67
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    • 2006
  • Recently, application of friction welded SUH35/SUH3 is increasing in the manufacturing process of automotive engine valves For securing its reliability and a reasonable strength evaluation method, it is necessary to assess stress singularity under the residual stress condition on the friction welded interface between dissimilar materials. In this paper, strength evaluation method of friction welded materials was investigated by boundary element method and static tensile testing. An advanced method of quantitative strength evaluation for SUH35/SUH3 friction welded material is to be suggested by establishing fracture criterion by using stress singularity factors.