 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| S. A. Kuliev, "The stress-strain state of a polygonal plate with two unequal rectilinear cuts," Mech. Solids. 39 (2), 120-135 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
2 |
Pages |
120-135 |
| Title |
The stress-strain state of a polygonal plate with two unequal rectilinear cuts |
| Author(s) |
S. A. Kuliev (Baku) |
| Abstract |
The stress-strain state of a polygonal plate with two rectilinear cuts of different length is considered. The cuts lie on the real x-axis. The end points of the cuts are denoted by a1, b1 and a2, b2 (Fig. 1). It can be seen from the figure that a1<b1<a2<b2.
The plate is subjected to uniform tension of intensity p. The origin is placed between the end points b1 and a2.
The problem is solved by using two methods - linear conjugation and mapping functions.
When using the former method, the elastic field of stresses and strains can be represented as the sum of two fields. The first field corresponds to the continuous body subjected to the applied loads. The second field of stresses or strains corresponds to the body with cuts subjected to symmetric loads applied to the surfaces of the cuts (crack surfaces). The solution of the primary problem is obtained by superimposing the solutions of the following two problems:
(A) determination of the stress-strain state of the continuous polygonal plate subjected to tensile forces of intensity P uniformly distributed along the plate contour;
(B) determination of the stress-strain state of the plate with two rectilinear cuts of different length under the action of load (stress) applied to the surfaces of the cut, the value of this load being determined from problem A and being equal to the stress at the lines corresponding to the cuts of the original plate. |
| References |
| 1. | Yu. A. Amenzade, Theory of Elasticity [in Russian], Vyssh. Shkola, Moscow, 1976. |
| 2. | S. A. Kuliev, Two-dimensional Problems of Elasticity [in Russian], Stroiizdat, Moscow, 1991. |
| 3. | N. I. Muskhelishvili, Some Basic Problems of Mathematical Theory of Elasticity [in Russian], Nauka, Moscow, 1966. |
| 4. | S. P. Timoshenko and S. Woinowsky-Krieger, Plates and Shells [in Russian], Nauka, Moscow, 1966. |
| 5. | D. I. Sherman, "On a problem of elasticity," Doklady AN SSSR, Vol. 27, No. 9, pp. 907-910, 1940. |
| 6. | D. I. Sherman, "On a method for solving some problems of elasticity for biconnected domains," Doklady AN SSSR, Vol. 55, No. 8, pp. 701-704, 1947. |
| 7. | L. T. Berezhnitskii, M. V. Delyavskii, and V. V. Panasyuk, Bending of Thin Plates With Crack Type Defects [in Russian], Naukova Dumka, Kiev, 1979. |
| 8. | S. A. Kuliev, "Stress state in a polygonal plate with arc-like cracks," Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 152-162, 1998. |
| 9. | V. A. Merkulov, "Bending of plates with cuts along a line or arcs of a circle," Izv. AN SSSR. MTT [Mechanics of Solids], No. 3, pp. 165-171, 1975. |
| 10. | V. V. Panasyuk and D. T. Berezhnitskii, "On the limit equilibrium of a plate with cracks along the arcs of a circle," Prikl. Mekhanika, Vol. 1, No. 10, pp. 52-60, 1965. |
| 11. | H. F. Bueekner, "The propagation of cracks and the energy of elastic deformation," Trans. ASME, Vol. 8, No. 6, pp. 1225-1230, 1958. |
| 12. | L. T. Berezhnitskii, "Limit forces for a plate with two equal arc cracks," Fiz.-Khim. Mekhanika Materialov, Vol. 1, No. 1, pp. 99-106, 1965. |
| 13. | D. I. Sherman, "An elastic plane with rectilinear cuts," Doklady AN SSSR, Vol. 26, No. 7, pp. 635-638, 1940. |
| 14. | G.C. Sih, P.C. Paris, and F. Erdogan, "Stress intensity factors near the crack tip in plates subjected to plane tension and bending," Trans. ASME. Ser. E. Applied Mechanics [Russian translation], Vol. 29, No. 2,
pp. 101-108, 1963. |
| 15. | G. M. Fikhtengolts, Course in Differential and Integral Calculus. Volume 2 [in Russian], Nauka, Moscow, 1970. |
| 16. | I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products [in Russian], Fizmatgiz, Moscow, 1963. |
|
| Received |
24 December 2001 |
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