- BUILDING STRUCTURES, BUILDINGS AND FACILITIES
- Intensity Coefficients In The Angular Zone Of Structures
- UDC 624.042.12:624.044.2 DOI: 10.33622/0869-7019.2020.09.41-47
Lyudmila Yu. FRISHTER, e-mail:FrishterLY@mgsu.ru
Moscow State University of Civil Engineering (National Research University), Yaroslavskoe shosse, 26, Moscow 129337, Russian Federation
Abstract. A relevant task in terms of ensuring reliable functioning of buildings and structures is studying the structural areas with complex boundary shapes. Areas with geometrically non-linear shape of boundaries - angular cut-outs, cuts, and element connections with rupturing forced deformations - are characterized by singularities of the stress-strain state. In experimental research of areas with complex boundary shapes it's necessary to take into account the difference between stress intensity factors and deformation intensity factors. This paper describes a procedure for obtaining the stress-strain state in neighborhood of the angular cut-out apex on the domain boundary using stress intensity factors and deformation intensity factors for a variety of homogeneous boundary conditions. In the angular cut-out area on the domain boundary, the stress-strain state is characterized by limit values of stresses and deformations, similar to stress intensity factors used with force criteria in fracture mechanics. Taking into account the ratios of stress and deformation intensity factors in experimental analysis of the stress-strain state in angular areas of structures is practically relevant for determining critical values of stress and deformation intensity factors.
Key words: angular area of structures, stress-strain state, stress intensity factors, deformation intensity factors, homogeneous boundary conditions.
1. Mahutov N. A., Moskvichev V. V., Morozov E. V., Gol'dshtejn R. V. Unification of methods for testing structural materials for crack resistance. History of the problem and formation of the regulatory framework. Zavodskaya laboratoriya. Diagnostika materialov, 2017, no. 10, pp. 41-54. (In Russian).
2. Mahutov N. A. Prochnost' i bezopasnost': fundamental'nye i prikladnye issledovaniya [Strength and safety: fundamental and applied researches]. Novosibirsk, Nauka Publ., 2008. 528 p. (In Russian).
3. Mahutov N. A., Gadenin M. M., Reznikov D. O., Neganov D. A. Ànalysis of stress-strain and limit states in extremely loaded zones of machines and constructions. Chebyshevskij sbornik, 2017, vol. 18, no. 3 (63), pp. 394-416. DOI: 10.22405/2226-8383-2017-18-3-394-416. (In Russian).
4. Mahutov N. A., Morozov E. M. Test Methods in fracture mechanics. Zavodskaya laboratoriya, 1982, no. 2, pp. 105-109. (In Russian).
5. Razumovskij I. A. Interferencionno-opticheskie metody mekhaniki deformiruemogo tverdogo tela [Interference-optical methods of deformable solid mechanics]. Moscow, MGTU im. N. E Baumana Publ., 2007. 240 p. (In Russian).
6. Metod fotouprugosti [The photoelasticity method] Moscow, Strojizdat Publ., 1975. Vol. 1. 461 p. Vol. 2. 368 p. Vol. 3. 312 p. (In Russian).
7. Froht M. M. Fotouprugost' [Photoelasticity]. Moscow- Leningrad, GITTL Publ., 1948. Vol. 1. 432 p.; 1950. Vol. 2. 488 p. (In Russian).
8. Matvienko Yu. G. Modeli i kriterii mekhaniki razrusheniya [Models and criteria of fracture mechanics]. Moscow, Fizmatlit Publ., 2006. 328 p. (In Russian).
9. Tihomirov V. M. Determination of stress intensity coefficients in three-dimensional problems of fracture mechanics. Prikladnaya mekhanika i tekhnicheskaya fizika, 2014, vol. 55, no. 5 (327), pp. 172-180. (In Russian).
10. Ahmetzyanov M. H., Tihomirov V. M., Surovin P. G. Determination of stress intensity coefficients for a mixed type of crack loading. Izvestiya vuzov. Stroitel'stvo, 2003, no. 1 (529), pp. 19-25. (In Russian).
11. Netrebko V. P. Photoelasticity study of stress intensity coefficients near inclined cracks in orthotropic plates taking into account higher order terms. Problemy mashinostroeniya i nadezhnosti mashin, 2003, no. 6, p. 45. (In Russian).
12. Albaut G. N., Tabanyuhova M. V., Harinova N. V. Determination of the first stress intensity factor in elements with angled cut-out. Eksperimental'naya mekhanika i raschet sooruzhenij (Kostinskie chteniya) [Experimental Mechanics and Calculation of Structures, Kostinsky Readings]. Moscow, MISI Publ., 2004, pp. 166-171. (In Russian).
13. Frishter L. Yu. Photoelasticity-based study of stress-strain state in the area of the plain domain boundary cut-out area vertex. EMMFT 2017: International Scientific Conference Energy Management of Municipal Transportation Facilities and Transport EMMFT 201, 2017, vol. 692, pp. 836-844. Available at: https://doi.org/10.1007/978-3-319-70987-1_89 (accessed 17.08.2020).
14. Kondrat'ev V. A. Boundary value problems for elliptic equations in domains with conical or corner points. Trudy Moskovskogo matematicheskogo obshchestva [Transactions of the Moscow Mathematical Society]. Moscow, MGU Publ., 1967, vol. 16, pp. 209-292. (In Russian).
15. Parton V. Z., Perlin P. I. Metody matematicheskoj teorii uprugosti [Methods of the mathematical theory of elasticity]. Moscow, Nauka Publ., 1981. 688 p. (In Russian).
16. Cherepanov G. P. Mekhanika hrupkogo razrusheniya [Mechanics of brittle failure]. Moscow, Nauka Publ., 1974. 640 p. (In Russian).
17. Timoshenko S. P., Gud'er Dzh. Teoriya uprugosti [Theory of elasticity]. Moscow, Nauka Publ., 1975. 576 p. (In Russian).
18. Kuliev V. D. Singulyarnye kraevye zadachi [Singular boundary value problems]. Moscow, Nauka Publ., 2005. 719 p. (In Russian).
19. Denisyuk I. T. Stress state close to a singular line of the interface boundary. Izvestiya RAN. Mekhanika tverdogo tela, 1995, no. 5, pp. 64-70. (In Russian).
20. Aksentyan O. K. Features of the stress-strain state of the plate in the neighbor-hood of the edge. Prikladnaya matematika i mekhanika, 1967, vol. 31, iss. 1, pp.178-186. (In Russian).
21. Chobanyan K. S., Gevorkyan S. H. The behavior of the stress field near the angular point of the separation line in the problem of plane deformation of a composite elastic body. Izvestiya AN Armyanskoj SSR. Mekhanika, 1971, iss. XXIV, no. 5, pp. 16-24. (In Russian).
22. Vardanyan G. S., Mozgaleva M. L., Savost'yanov V. N., Frishter L. Yu. Of eigenvalues in the solution of problems for areas containing irregular points. Izvestiya vuzov. Stroitel'stvo, 2003, no. 10, pp. 28-31. (In Russian).
23. Pestrenin V. M., Pestrenina I. V., Landik L. V. Stress state near a special point of a flat composite structure. Vestnik TGU. Matematika i mekhanika, 2013, no. 4(24), pp 80-87. (In Russian).
- For citation: Frishter L. Yu. Intensity Coefficients in the Angular Zone of Structures. Promyshlennoe i grazhdanskoe stroitel'stvo [Industrial and Civil Engineering], 2020, no. 9, pp. 41-47. (In Russian). DOI: 10.33622/0869-7019.2020.09.41-47.