 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
|
| << Previous article | Volume 53, Issue 2 / 2018 | Next article >> |
| V.G. Popov, "Two Cracks Emerging from a Single Point, under the Influence of a Longitudinal Shear Wave," Mech. Solids. 53 (2), 195-202 (2018) |
| Year |
2018 |
Volume |
53 |
Number |
2 |
Pages |
195-202 |
| DOI |
10.3103/S0025654418020103 |
| Title |
Two Cracks Emerging from a Single Point, under the Influence of a Longitudinal Shear Wave |
| Author(s) |
V.G. Popov (Odessa National Maritime Academy, ul. Didrikhsona 8, Odessa, 65029 Ukraine, dr.vg.popov@gmail.com, vs_popov@math.onma.edu.ua) |
| Abstract |
The problem of determining the dynamic stress intensity coefficients for two cracks emerging from a single point is solved. The cracks are affected by a longitudinal shear wave. The original problem is reduced to solving a system of two singular integro-differential equations with fixed singularities. For an approximate solution of this system, a numerical method is proposed that takes into account the real asymptotics of the unknown functions and uses special quadrature formulas for singular integrals. |
| Keywords |
cracks, harmonic oscillations, stress intensity factor, singular integro-differential equation, fixed singularity |
| References |
| 1. | B. A. Afyan,
"On Integral Equations with Fixed Singularities in the Theory of Branching Cracks,"
Dokl. Akad Nauk Arm. SSR
79 (4), 60-65 (1984). |
| 2. | V. Vitek,
"Plain Strain Stress Intensity Factors for Branched Cracks,"
Int. J. Fract.
13 (4), 481-501 (1977). |
| 3. | R. V. Duduchava,
"Integral Equations of Convolution with Discontinuous Symbols, Singular Integral Equations with Fixed Singularities and Their Applications to Problems of Mechanics,"
Trudy Tbilissk. Mat. Inst. Akad Nauk GSSR
60, 31-35 (1979). |
| 4. | M. Isida and H. Noguchi,
"Stress Intensity Factors at Tips of Branched Cracks under Various Loadings,"
Int. J. Fract.
54 (4), 293-316 (1992). |
| 5. | P. N. Osiv and M. P. Savruk,
"Determination of Stresses in an Infinite Plate with Broken or Branching Crack,"
Zh. Prikl. Mekh. Techn. Fiz.,
No. 2, 142-147 (1983)
[J. Appl. Mech. Tech. Phys. (Engl. Transl.)
24 (2), 266-271 (1983)] |
| 6. | Yan. Xiangqiao,
"Stress Intensity Factors for Asymmetric Branched Cracks in Plane Extension by Using Crack-Tip Displacement Discontinuity Elements,"
Mech. Res. Comm.
32 (4), 375-384 (2006). |
| 7. | M. R. Savruk,
Two-Dimensional Elasticity Problems for Bodies with Cracks
(Naukova Dumka, Kiev, 1981)
[in Russian]. |
| 8. | V. G. Popov,
"Studies of Stress and Displacement Fields in Diffraction of Elastic Shear Waves at a Thin Rigid Separated Inclusion,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 3, 139-146 (1992)
[Mech. Solids (Engl. Transl.)]. |
| 9. | V. G. Popov,
"Diffraction of Elastic Shear Waves on the Inclusion of a Complex Shape Located in an Unbounded Elastic Medium,"
in Hydroaeromechanics and Elasticity Theory of elasticity. Numerical and Analytical Methods for Solving Problems of Hydroaerodynamics and Elasticity Theory.
MezhVUZov. Sb. Nauch. Tr.
(DGU, Dnepropetrovsk, 1986),
pp. 121-127
[in Russian]. |
| 10. | A. V. Andreev,
"Direct Numerical Method for Solving Singular Integral Equations of the First Kind with Generalized Kernels,"
Izv. Akad. Nauk. Mekh. Tverd. Tela,
No. 1, 126-146 (2005)
[Mech. Solids (Engl. Transl.)
40 (1), 104-119 (2005)]. |
| 11. | V. I. Krylov,
Approximate Computations of Integrals
(Nauka, Moscow, 1967)
[in Russian]. |
| 12. | G. Ya. Popov,
Concentration of Elastic Stresses Near Punches, Cuts, Rigid Inclusions, and Stiffeners
(Nauka, Moscow, 1962)
[in Russian]. |
| 13. | G. Szegö,
Orthogonal Polynomials
(Amer. Math. Soc, Providence, 1959; Fizmatiz, Moscow, 1962). |
|
| Received |
05 July 2014 |
| Link to Fulltext |
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