Asymmetric problem of a row of revolutional ellipsoidal cavities using singular integral equations

Noda, Nao–Aki; Ogasawara, Nozomu; Matsuo, Tetsuji

doi:10.1016/s0020-7683(03)00023-4

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…Circular and elliptical gaps in an elastic medium, a small spherical cavity in a twisted cylindrical rod, and some other problems are considered in the research (Lurie and Belyaev 2010). Some axisymmetric problems are usually solved either in displacements using the Lame equations or with the help of the Love function (Love 1944;Edwards 1951;Noda et al 2003;Noda and Moriyama 2004). It should be mentioned that when solving specific problems it is difficult to provide solution subjection to boundary conditions because of the complex boundary values.…”

Section: Introductionmentioning

confidence: 99%

Stress-strain state of an elastic half-space with a cavity of arbitrary shape

Kalentev

2018

Int J Mech Mater Eng

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Background: Analytical method for studying stress concentration around arbitrary shape cavity is proposed. Methods: The method is based on the assumption that it is possible to simulate the influence of cavity on the redistribution of internal forces by including fictitious forces in the solution. To determine the stress-strain state, additional forces acting on cavity surface are used. The magnitude of these forces is chosen on the basis of the value of stress tensor flow through the examined surfaces limiting cavity volume. Results: Research of stress-strain state for the most general three-dimensional case is done: an elastic halfspace with a cubic shape cavity under action of a concentrated force applied to a free surface. The obtained results are comprehensively compared with the solution of a similar problem by the finite element method. Distributions of the stress tensor components in the vicinity of these cavities are constructed. The estimation of accuracy and efficiency of the proposed calculation model is made; the boundary of applicability of the proposed solution is determined. Conclusions: It seems promising to use the resource of structural materials advantageously, namely, creating in the bodies of the cavity system the required shape and size, to obtain stress reduction at critical points, thereby increasing the strength of the product.

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Section: Introductionmentioning

confidence: 99%

Stress-strain state of an elastic half-space with a cavity of arbitrary shape

Kalentev

2018

Int J Mech Mater Eng

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“…As a model of defects elliptical and ellipsoidal inclusions are important because they cover a lot of particular cases, such as line, circular, and spherical defects. Previously, several researchers studied an ellipsoidal inclusion (3) - (6) , and discussed interactions among elliptical, and ellipsoidal inclusions (5) - (16) . Tsuchida et al treated several elasticity problems of a spheroidal inclusion in a half-space (17) - (20) .…”

Section: Introductionmentioning

confidence: 99%

Interaction among Ellipsoidal Inclusions and a Bimaterial Interface

Noda

Ono

Moriyama

2005

JSME Int. J., Ser. A

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Ellipsoidal inclusions can be regarded as a general model of defects in structures because they cover a lot of particular cases, such as line, circular and spherical defects. This paper deals with three-dimensional stress analysis for ellipsoidal inclusions in a bimaterial body under tension. The problem is formulated as a system of singular equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r-and z-directions in bimaterial bodies having the same elastic constants of those of the given problem. In order to satisfy the boundary conditions along the ellipsoidal boundary, four types of fundamental density functions proposed in the previous paper are applied. Then the body force densities are approximated as a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distribution along the boundaries of both the matrix and inclusion even when the inclusion is very close to the bimaterial interface. Then, the effect of bimaterial surface on the stress concentration factor is discussed with varying the distance from bimaterial interface, shape ratio, and elastic modulus ratio.

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“…In earlier studies, ellipsoidal inclusions have been studied by several researchers, [3][4][5][6]. Also, interactions among elliptical and ellipsoidal inclusions have been discussed in [7][8][9][10][11][12][13][14][15][16][17]. Several elasticity problems involving a half-space with a spheroidal inclusion have been studied in [18][19][20][21][22].…”

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confidence: 99%

Stress concentration of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension

Noda

Moriyama

2004

Archive of Applied Mechanics

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This paper deals with the stress concentration problem of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r-and z-directions in semi-infinite bodies having the same elastic constants as the ones of the matrix and inclusion. In order to satisfy the boundary conditions along the ellipsoidal boundary, four fundamental density functions proposed in [24,25] are used. The body-force densities are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distribution along the boundaries even when the inclusion is very close to the free boundary. The effect of the free surface on the stress concentration factor is discussed with varying the distance from the surface, the shape ratio and the elastic modulus ratio. The present results are compared with the ones of an ellipsoidal cavity in a semi-infinite body. IntroductionStructural materials usually contain some defects in the form of cracks, cavities, and inclusions. For various metals, the size, shape, and distribution of microdiscontinuities have been investigated e.g. in [1,2]. To evaluate their defects on the strength, it is fundamental to know the stress concentration of elliptical and ellipsoidal inclusions, which cover many particular cases, such as linear, circular, and spherical defects. In earlier studies, ellipsoidal inclusions have been studied by several researchers, [3][4][5][6]. Also, interactions among elliptical and ellipsoidal inclusions have been discussed in [7][8][9][10][11][12][13][14][15][16][17]. Several elasticity problems involving a half-space with a spheroidal inclusion have been studied in [18][19][20][21][22]. However, there has been little discussion about ellipsoidal inclusions in a half-space.In this study, therefore, stress concentration of an ellipsoidal inclusion of revolution in a semi-infinite body under bi-axial tension is considered. An ellipsoidal inclusion can be regarded as a general model of the defect because many kinds of defects can be expressed by changing the elastic modulus ratio and the shape ratio of the inclusion. The body-force method, [23], is used here to formulate the problem as a system of singular integral equations. Then, the unknown body-force densities are approximated by a linear combination of fundamental density functions and polynomials [24][25][26]. The results will be compared with the ones in [18][19][20][21][22] by setting the elastic modulus of the inclusion E I ¼ 0, see Fig. 1. It will be shown that the present method gives smooth variations of interface stresses along the boundary. Analysis and numerical procedureConsider a semi-infinite body under biaxial tension having an ellipsoidal inclusion as shown in Fig. 1. The body force method is used to formulate the problem...

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Asymmetric problem of a row of revolutional ellipsoidal cavities using singular integral equations

Cited by 6 publications

References 18 publications

Stress-strain state of an elastic half-space with a cavity of arbitrary shape

Stress-strain state of an elastic half-space with a cavity of arbitrary shape

Interaction among Ellipsoidal Inclusions and a Bimaterial Interface

Stress concentration of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension

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