• Title/Summary/Keyword: stress singularities

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Influence of Boundary Stress Singularities on the Vibration of Clamped and Simply Supported Sectorial Plates With Various Radial Edge Conditions (다양한 방사연단 조건을 갖는 고정 및 단순지지 부채꼴형 평판 진동에 대한 경계응력특이도의 영향)

  • Kim, Joo-Woo
    • Journal of Korean Society of Steel Construction
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    • v.10 no.4 s.37
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    • pp.601-613
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    • 1998
  • This paper reports the first-of-its-kind free vibration solutions for sectorial plates having re-entrant corners causing stress singularities when the circular edge is either clamped or simply supported. The Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. Accurate frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of sector angles.

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Analyses of Stress Singularities on Bonded Interfaces in the IC Package by Using Boundary Element method (경계요소법을 이용한 반도체 패키지의 응력특이성 해석)

  • Park, Cheol-Hee;Chung, Nam-Yong
    • Transactions of the Korean Society of Machine Tool Engineers
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    • v.16 no.6
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    • pp.94-102
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    • 2007
  • Applications of bonded dissimilar materials such as large scale integration (LSI) packages, ceramics/metal and resin/metal bonded joints, are very increasing in various industry fields. It is very important to analyze the thermal stress and stress singularity at interface edge in LSI. In order to investigate stress singularities on the bonded interface edges and delamination of die pad and resin in the IC package. In this paper, stress singularity factors(${\Gamma}_i$) and stress intensity factors($K_i$) considering thermal stress in the IC package were analyzed by using the 2-dimensional elastic boundary element method(BEM).

Study on the Stress Singularity of Interface Crack by using Boundary Element Method (경계요소법을 이용한 계면균열의 응력특이성에 관한 고찰)

  • Cho, Chong-Du;Kwahk, Si-Young
    • Journal of the Korean Society for Precision Engineering
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    • v.16 no.4 s.97
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    • pp.197-204
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    • 1999
  • The boundary element method was used for studying singularities of an interface crack with contact zones. The iterative procedure is applied to estimate the contact zone size. Because the contact zone size was extremely small in a tension field, a large number of Gaussian points were used for numerical integration of the Kernels. Stress extrapolation method and J-integral were used ofr determining stress intensity factors. When the interface crack was assumed to have opened tips, oscillatory singularities appear near the tips of the interface crack. But the interface crack with contact zone which Comninou suggested had no oscillatory behavior. The contact zone size under shear loading was much larger than that under tensile. The stress intensity factors computed by stress extrapolation method were close to those of Comninou's solution. And the stress intensity factor evaluated by J-integral was similar to that by stress extrapolation method.

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Analysis of Flexural Vibration of Rhombic Plates with Combinations Clamped and Free Boundary Conditions Including the Effect of Corner Stress Singularities (모서리 응력특이도의 영향을 포함한 고정 또는 자유 경계조건의 조합을 고려한 마름모꼴 평판의 휨 진동 해석)

  • 한봉구
    • Journal of the Earthquake Engineering Society of Korea
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    • v.3 no.1
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    • pp.9-20
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    • 1999
  • An accurate method is presented for flexural vibrations of rhombic plates having all combinations of clamped and free edge conditions. The prime focus here is that the analysis explicitly considers the bending stress singularities that occur in the two opposite, clamped-free corners having obtuse angles of the rhombic plates. Accurate non-dimensional frequencies and normalized contours of the vibratory transverse displacement are presented for rhombic plates having a large enough obtuse angle of 165$^{\circ}$, so that a significant influence of clamped-free corner stress singularities may be understood.

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The Influence of Corner Stress Singularities on the Vibration of Rhombic Plates Having Various Edge Conditions (다양한 연단조건을 갖는 마름모꼴형 평판의 진동에 대한 모서리 응력특이도의 영향)

  • Kim, Joo-Woo;Cheong, Myung-Chae
    • Journal of Korean Society of Steel Construction
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    • v.12 no.4 s.47
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    • pp.363-374
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    • 2000
  • An accurate method is presented for vibrations of rhombic plates having three different combinations of clamped, simply supported, and free edge conditions. A specific feature here is that the analysis explicitly considers the moment singularities that occur in the two opposite corners having obtuse angles of the rhombic plates. Stationary conditions of single-field Lagrangian functional are derived using the Ritz method. Convergence studies of frequencies show that the corner functions accelerate the convergence rate of solutions. In this paper, accurate frequencies and normalized contours of the vibratory transverse displacement are presented for highly skewed rhombic plates, so that a significant effect of corner stress singularities nay be understood.

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REMARKS ON FINITE ELEMENT METHODS FOR CORNER SINGULARITIES USING SIF

  • Kim, Seokchan;Kong, Soo Ryun
    • Honam Mathematical Journal
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    • v.38 no.3
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    • pp.661-674
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    • 2016
  • In [15] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they 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 we could get accurate solution just by adding the singular part. This approach works for the case when we have the accurate stress intensity factor. In this paper we consider Poisson equations with mixed boundary conditions and show the method depends the accrucy of the stress intensity factor by considering two algorithms.

A FINITE ELEMENT METHOD USING SIF FOR CORNER SINGULARITIES WITH AN NEUMANN BOUNDARY CONDITION

  • Kim, Seokchan;Woo, Gyungsoo
    • East Asian mathematical journal
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    • v.33 no.1
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    • pp.1-9
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    • 2017
  • In [8] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities, which is useful for the problem with known stress intensity factor. They consider the Poisson equations with homogeneous Dirichlet boundary condition, compute the finite element solution using standard FEM and use the extraction formula to compute the stress intensity factor, then they 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 accurate solution just by adding the singular part. This approach works for the case when we have the reasonably accurate stress intensity factor. In this paper we consider Poisson equations defined on a domain with a concave corner with Neumann boundary conditions. First we compute the stress intensity factor using the extraction formular, then find the regular part of the solution and the solution.

SIF AND FINITE ELEMENT SOLUTIONS FOR CORNER SINGULARITIES

  • Woo, Gyungsoo;Kim, Seokchan
    • East Asian mathematical journal
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    • v.34 no.5
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    • pp.623-632
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    • 2018
  • In [7, 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 boundary conditions, compute the finite element solutions using standard FEM 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. Their algorithm involves an iteration and the iteration number depends on the acuracy of stress intensity factors, which is usually obtained by extraction formula which use the finite element solutions computed by standard Finite Element Method. In this paper we investigate the dependence of the iteration number on the convergence of stress intensity factors and give a way to reduce the iteration number, together with some numerical experiments.

Some Studies on Stress field in Dissimilar Materials

  • Katsuhiko Watanabe
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1996.11a
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    • pp.631-635
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    • 1996
  • Stress singularities appear at the interface edge in dissimilar materials also under thermal loading. First, these singularities then an interface meets a free side surface with an arbitrary angle are studied for a two-dimensional problem. The singular properties under thermal loading are made clear and the concrete singular field are obtained. Secondly, the dependence of stress field on elastic constants in axisymmetric dissimilar materials are. discussed. That is, it is shown that three elastic constants mutually independent are necessary, in general, to characterize the stress field of axisymmetric dissimilar materials, although Dunders' parameters defined for two-dimensional dissimilar materials have been often applied correspondingly also to axisymmetric problems.

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Three-Dimensional Vibration Analysis of Solid Cylinders of N-Sided Polygonal Cross-Section Having V-notches or Sharp Cracks (V노치 및 예리한 균열을 갖는 N 다변형 단면 입체 실린더의 3차원 진동해석)

  • Kim, Joo Woo
    • Journal of Korean Society of Steel Construction
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    • v.21 no.4
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    • pp.433-442
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    • 2009
  • In this paper, new three-dimensional vibration data for the solid cylinders of the N-sided polygonal cross-section with V-notches or sharp cracks are presented, and a Ritz procedure is employed, which incorporates a mathematically complete set of algebraic-trigonometric polynomials in conjunction with an admissible set of edge functions that explicitly model the tri-axial stress singularities that exist along a terminus edge of the V-notch. Convergence studies demonstrate the necessity of adding the edge functions to achieve the accurate frequencies and mode shapes of N-sided polygonal cylindrical solids with stress singularities.