• Title/Summary/Keyword: corner singularity

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CORNER SINGULARITY AT THE MULTIPLE JUNCTION OF THE ELECTRIC TRANSMISSION

  • Choe, Hi-Jun;Park, Kyong-Yop;Sohn, Ayoung
    • Journal of the Korean Mathematical Society
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    • v.42 no.6
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    • pp.1311-1322
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    • 2005
  • We consider the several plane sector domains which are bonded together along common edges with vertex at the origin. Such domains appear in electric conducting problem with multi-layered heterogeneous media. Our aim is to give a structure theorem of the singularities of the electric field at the corner. Also, we provide a regularity theorem for the electric field.

Analysis of Moisture Stresses Induced in Polymeric Thin Film (고분자 박막에서 발생하는 수분응력 해석)

  • 이상순
    • Proceedings of the International Microelectronics And Packaging Society Conference
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    • 2002.11a
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    • pp.137-142
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    • 2002
  • This paper deals with the stress singularity induced at the interface corner between the elastic substrate and the viscoelastic thin film as the polymeric film absorbs moisture from the ambient environment. The boundary element method is employed to investigate the behavior of Interface stresses. The order of the singularity is obtained numerically for a given viscoelastic model. It is shown that the stress singularity factor is relaxed with time, while the order of the singularity increases with time for the viscoelastic model considered.

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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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Geometric Optimization Involving Contact Stress Singularities (특이 접촉응력 문제의 형상 최적화)

  • Park, Jung-sun;Lee, Soo-Yong
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.20 no.1
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    • pp.180-188
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    • 1996
  • The stress singularity of a sharp wedge contacting a half plane can be avoided by changing the wedge shape. Shape optimization is accomplished with the geometric strain method (GSM), an optimality criterion method. Several numerical examples are provided for different materials in the wedge and half plane to avoid stress singularity neal the sharp corner of the wedge. Optimum wedge shapes are obtained and critical corner angles are compared with the angles from analytical contact mechanics. Numerical results are well matched to analytical and experimental results. It is shown that shape optimization by the geometric strain method is a useful tool to reshape the wedge and to avoid a stress singulatiry. The method applies to more general geometries where the singular behavior would be difficult to avoid by classical means.

FINITE ELEMENT DUAL SINGULAR FUNCTION METHODS FOR HELMHOLTZ AND HEAT EQUATIONS

  • JANG, DEOK-KYU;PYO, JAE-HONG
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.22 no.2
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    • pp.101-113
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    • 2018
  • The dual singular function method(DSFM) is a numerical algorithm to get optimal solution including corner singularities for Poisson and Helmholtz equations. In this paper, we apply DSFM to solve heat equation which is a time dependent problem. Since the DSFM for heat equation is based on DSFM for Helmholtz equation, it also need to use Sherman-Morrison formula. This formula requires linear solver n + 1 times for elliptic problems on a domain including n reentrant corners. However, the DSFM for heat equation needs to pay only linear solver once per each time iteration to standard numerical method and perform optimal numerical accuracy for corner singularity problems. Because the Sherman-Morrison formula is rather complicated to apply computation, we introduce a simplified formula by reanalyzing the Sherman-Morrison method.

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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Viscoelastic Stress Analysis of Polymeric Thin Layer Under Moisture Absorption (수분 흡수로 인해 고분자 박막에서 발생하는 점탄성 응력 해석)

  • 이상순;장영철
    • Journal of the Microelectronics and Packaging Society
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    • v.10 no.1
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    • pp.25-29
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    • 2003
  • This paper deals with the stress singularity induced at the interface corner between the elastic substrate and the viscoelastic thin film as the polymeric film absorbs moisture from the ambient environment. The boundary element method is employed to investigate the behavior of interface stresses. The order of the singularity is obtained numerically for a given viscoelastic model. It is shown that the stress singularity factor is relaxed with time, while the order of the singularity increases with time for the viscoelastic model considered.

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Boundary Element Analysis of Singular Stresses in a Viscoelastic Thin Film due to Moisture Absorption (수분 흡수로 인해 점탄성 필름에 발생하는 특이 응력의 경계요소해석)

  • Lee, Sang-Sun
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.24 no.3 s.174
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    • pp.685-690
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    • 2000
  • 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. Th e time 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 stress singularity factor is relaxed with time, while the order of the singularity increases with time for the viscoelastic model considered.

FINITE ELEMENT SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATION WITH MULTIPLE CONCAVE CORNERS

  • Kim, Seokchan;Woo, Gyungsoo
    • Honam Mathematical Journal
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    • v.40 no.4
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    • pp.785-794
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    • 2018
  • In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with homogeneous Dirichlet boundary condition with one corner singularity at the origin, and compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then pose a PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor, which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. This approach uses the polar coordinate and the cut-off function to control the singularity and the boundary condition. In this paper we consider Poisson equations with multiple singular points, which involves different cut-off functions which might overlaps together and shows the way of cording in FreeFEM++ to control the singular functions and cut-off functions with numerical experiments.