• Proceedings of the Korean Society of Precision Engineering Conference
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• 2003.10a
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• pp.240-240
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• 2003

V-노치 균열에서 열하중이 작용하는 경우는 비제차형 경계조건의 문제가 되고, 이 조건에 대한 방정식의 일반해를 구하기 위해서 재차형 연립방정식에 대한 일반해(Homogeneous solution)와 비제차형 연립방정식에 대한 특수해(Particular solution)의 두 가지 해를 구할 수 있다. 이들 해는 V-노치 균열에 대한 고유치가 되고 이 고유치가 중복근을 가지게 되는 경우에는 로그항(1n[r])이 나타나게 되고 이 항에 의해서 응력을 무한대로 발산시키므로 이를 대수응력특이성이라 한다. 열하중이 작용할 때 대수응력특이성을 나타내는 로그항의 계수가 영(0)이 되어 대수응력특이성이 사라지게 되므로 V-노치 선단에서의 응력특이성은 고유치와 그에 대한 고유벡터에 의해 결정된다. 본 논문에서는 비정상상태 열하중이 가해지는 등방성 이종재료 내의 V-노치 균열문제에서 패기 각도와 이종재료의 기계적 성질에 의해 결정되는 응력특이성지수를 구하고 이에 대한 응력강도계수를 유한요소해석 프로그램인 ANSYS와 상반일 경로 적분법(RWCIM)을 이용하여 구하였다.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.1A
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• pp.39-48
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• 2012

This study deals with numerical determination of stress intensity factors of adhesively patch-repaired plates with cracks at V-shaped or semicircular notches. The p-convergent anisoparametric model are considered and then three-dimensional virtual crack closure technique is presented using formulations of anisoparametric elements. In assumed displacement fields of an element, strain-displacement relations and three-dimensional constitutive equations are derived with three-dimensional hierarchical shape functions expanded from one-dimensional Lobatto functions. Transfinite mapping technique is used to represent a circular boundary. The present model provides accuracy and simplicity in terms of stress concentration factor, stress distribution, the number of degrees of freedom, and non-dimensional stress intensity factor as compared with previous works in literatures. Stress intensity factors obtained by the three-dimensional virtual crack closure technique are estimated with respect to the variation of width of finite plate, radius of notch root, angular inclination of V-shaped notch, and crack length.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.10a
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1890-1899
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• 1992

In bonded structures, there are V-notched cracks in dissimilar materials and the stress concentration of these V-notched cracks causes to occur interface cracks in dissimilar materials Therefore the strength evaluation of V-notched cracks in dissimliar materials seems to be important. The stress fields of a V-notched cracks is known as .sigma.$_{ij}$ .var. K $r_{p-1}$,where K is the stress intensity factor and p-1 is the stress singularity. When the distance, r, approaches to 0 at the stress fields of V-notched cracks, the stresses become infinites by two more stress singularities of p-1 and p-1 is no more -0.5. Stress singularities and stress intensity factors for V-notched cracks in dissimilar materials are treated and discussed. The Newton-Raphson method which is an efficient numerical method for solving a non-linear equation is used for solving stress sigularities. And stress intensity factors are solved by the collocation method using the Newton-Raphson and least squares method. The effects of stress intensity factors and stress singularities on stress fields of V-notched cracks in dissimilar materials are studied by using photoelasic isochromatic frings patterns obtained from computer graphics.s.

• Journal of the Korean Society for Precision Engineering
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• v.20 no.9
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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.

• 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.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.12
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• pp.88-94
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• 2001

The V-notched crack problem in dissimilar materials can be formulated as an eigenvalue problem. The RWCIM(Reciprocal Work Contour Integral Method) is applied to the determination of the eigenvector coefficients associated with eigenvalues for V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials. The RWCIM algorithm is programed by the commercial numerical program, MATHEMATICA. The numerical results obtained are shown that the RWCIM is a useful method for determining the eigenvector coefficients of V-notched cracks in pseudo-isotropic and anisotropic dissimilar materials.

• 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.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.115-120
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• 2000

This paper examines that it is possible to apply RWCIM for determining eigenvector coefficients associated with eigenvalues for V-notched cracks in anisotropic dissimilar materials using the complex stress function. To verify the RWCIM algorithm, two tests will be shown. First it is performed to ascertain whether predicted coefficients associated with eigenvectors is obtained exactly. Second, it makes an examination of the state of stress for FEM and RWCIM according to a number of eigenvectors at a location far away from the V-notched crack tip.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.9
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• pp.1368-1375
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• 2001

This paper examines that it is possible to apply RWCIM for determining eigenvector coefficients associated with eigenvalues for V-notched cracks in anisotropic dissimilar materials using the complex stress function. To verify the RWCIM algorithm, two tests will be shown. First, it is performed to ascertain whether predicted coefficients associated with eigenvectors are obtained exactly. Second, it makes an examination of the state of stresses for FEM and RWCIM according to a number of eigenvectors at a location far away from the v-notched crack tip.