 | | 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
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 42, Issue 4 / 2007 | Next article >> |
| S. A. Kuliev, "The stress state of a plate subjected to a piecewise homogeneous load," Mech. Solids. 42 (4), 619-629 (2007) |
| Year |
2007 |
Volume |
42 |
Number |
4 |
Pages |
619-629 |
| Title |
The stress state of a plate subjected to a piecewise homogeneous load |
| Author(s) |
S. A. Kuliev (Azerbaijan Architecture-Construction University, Ayny Sultanovoy 5, Baku, AZ 1000, Azerbaijan, gulin2@bp.com) |
| Abstract |
We consider the stress-strain state of a plate having a doubly connected domain S bounded from the outside by a circle of radius R and from the inside by an ellipse with two rectilinear cuts. The cuts lie symmetrically on the x-axis. The plate is subjected to various forces: the hole contour (the ellipse) is under the action of uniformly distributed forces of intensity q, and the cut shores are free of loads; at the points ±ib of the imaginary axis, the plate is under the action of a lumped force P.
The solution of the problem is reduced to determining two analytic functions φ(z) and ψ(z) satisfying certain boundary conditions (depending on the type of the acting loads).
We use the Kolosov-Muskhelishvili method to reduce the problem to a system of linear algebraic equations for the coefficients in the expansions of the functions φ(z) and ψ(z). The solution thus obtained is illustrated by numerical examples. |
| References |
| 1. | Yu. A. Amenzade,
Theory of Elasticity
(Vysshaya Shkola, Moscow, 1976)
[in Russian]. |
| 2. | L. T. Berezhnitskii, M. V. Delyavskii, and V. V. Panasyuk,
Bending of Thin Plates with Crack-Type Defects
(Naukova Dumka, Kiev, 1979)
[in Russian]. |
| 3. | A. S. Kosmodamianskii,
Plane Problem of Elasticity Theory for
Plates with Holes, Cuts, and Protuberances
(Vishcha Shkola, Kiev, 1975)
[in Russian]. |
| 4. | S. A. Kuliev,
Two-Dimensional Problems of Theory of Elasticity
(Stroiizdat, Moscow, 1991)
[in Russian]. |
| 5. | S. A. Kuliev,
Conformal Mapping
(Izd. Azerb. Politekh. Inst., Baku, 1995)
[in Russian]. |
| 6. | S. A. Kuliev,
"Stressed State of Polygonal Plate with Central Circular Hollow
and Two Linear Cracks,"
Eng-ng Fracture Mech.
27 (6), 601-613 (1987). |
| 7. | N. I. Muskhelishvili,
Some Fundamental Problems of Mathematical Elasticity Theory
(Nauka, Moscow, 1966)
[in Russian]. |
| 8. | G. N. Savin,
Stress Distribution Near Holes
(Naukova Dumka, Kiev, 1968)
[in Russian]. |
| 9. | S. P. Timoshenko and J. N. Goodyear,
Theory of Elasticity
(McGraw-Hill, New York, 1951; Nauka, Moscow, 1975). |
| 10. | D. I. Sherman,
"Elastic Plane with Rectilinear Cuts,"
Dokl. Akad. Nauk SSSR
26 (7), 635-638 (1940)
[Soviet Math. Dokl. (Engl. Transl.)]. |
| 11. | G. C. Sih, P. C. Paris, and F. Erdogan,
"Crack-Tip, Stress-Intensity Factors
for Plane Extension and Plate Bending Problems,"
Proc. Amer. Soc. Mech. Eng., Ser. E, Appl. Mech.
29 (2), 102-108 (1962). |
| 12. | G. P. Cherepanov,
Mechanics of Brittle Failure
(Nauka, Moscow, 1974)
[in Russian]. |
|
| Received |
30 October 2004 |
| Link to Fulltext |
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