Relationship between the results of analytical solutions of elasticity theory problems and of stress state optimization in the vicinity of singular points

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Дәйексөз келтіру

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Аннотация

The paper presents the results of two directions of the study of the stress-strain state in the vicinity of singular points of elastic bodies, namely: change of the type of boundary conditions; edges of the contact surface of different materials. The result of the first direction is the solution of elasticity theory problems in the vicinity of singular points, from which the possibility of infinite stresses at these points follows. The second direction is associated with the analysis by numerical and experimental methods of the stress state in the vicinity of singular points, which, as a rule, occur when modeling real objects and are potential stress concentration zones. The main content of the article is to establish, based on a comparison of the results of the two directions, the relationship between variants with a minimum stress level in the vicinity of singular points with the results on the nature of the stress singularity at these points.

Толық мәтін

Рұқсат жабық

Авторлар туралы

A. Fedorov

Institute of Continuous Media Mechanics UB RAS

Хат алмасуға жауапты Автор.
Email: fedorov@icmm.ru
Ресей, Perm

V. Matveenko

Institute of Continuous Media Mechanics UB RAS

Email: mvp@icmm.ru
Ресей, Perm

Әдебиет тізімі

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2. Fig. 1. Calculation diagrams for cylinders under mass forces (a) and tensile forces (b).

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3. Fig. 2. Uniform (a) and composite (b) plane wedges in polar coordinates.

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4. Fig. 3. Solution regions with and without stress singularity (angle  in degrees).

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5. Fig. 4. Test scheme: 1 - steel fungus, 2 - specimen, 3 - bottom grip (a); dependence of the joint strength  (in MPa) on the joint angle  (in degrees) under normal detachment (1) and under cantilever bending (2) (b).

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6. Fig. 5. Calculation diagram of a two-layer hollow cylinder.

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7. Fig. 6. Connection of two trapezoidal plates.

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8. Fig. 7. Computational scheme for a compound cylinder (a); curve separating solutions with and without singularity in the plane of parameters 1 and 2 (for 1 = 2 = 0.3, E2/E1 = 10) (b).

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9. Fig. 8. Geometries of the samples.

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10. Fig. 9. Photographs of surface cracks: cracked earth at Rann of Kutch (India) (a); dried aqueous solution of cornstarch [29] (b); surface of dried salt marsh (Sicily) (c); cracks at the bottom of an impact crater on Mars [30] (d); old ceramic surface (e); surface of a heat-resistant steel specimen after thermal fatigue test [26] (f).

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11. Fig. 10. Calculation scheme of intersection of two (a), three (b) and four (c) wedge cracks.

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