The effect of a homogeneous cylindrical inlay on cracks in the doubly-periodic complete plane strain problem
Source abstract
Abstract
The effect of a homogeneous cylindrical inlay on cracks in the doubly-periodic complete plane strain (CPS) problem is investigated in this paper. By employing the solutions of doubly quasi-periodic and doubly-periodic Riemann boundary value problems for analytic functions we obtain the general solution in closed form. And approximate analytical expression of the stress intensity factors, which are identical with the known results, are obtained when there are no holes or gaskets in the periodic parallelogram and e 3=0, F k=0, T k=0, k=1,2, with constant load applied at the edges of the crack.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Numerical methods in engineering · Advanced Mathematical Modeling in Engineering · Elasticity and Wave Propagation
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (21)
Show source-provided references
1. Chibrikova, L.I. (1956). On the Riemann boundary value problem for automorphic functions. Uchenye Zapiski Kazan. Univ. 116, 59–109.
2. Filshtinsky, L.A. (1973). Elastic theory of nonhomogeneous media from regular check, Prik. Mat. Mekh. 37, 263–273 (in Russian).
3. Filshtinsky, L.A. (1972). A doubly periodic problem of the theory of elasticity for an isotropic medium weakened by congruent groups of arbitrary holes, Prik. Mat. Mekh. 36, 682–690.
4. Fomin, V.M. (1998). Antiplane waves in an elastic medium with doubly periodic system of holes, Prik. Mat. Mekh. 63, 479–488 (in Russian).
5. Glingauss, M.G. and Filshtinsky, L.A. (1975). Elastic theory on linear reinforced composite materials, Prik. Mat. Mekh. 39, 537–546 (in Russian).
6. Ioakimidis, N.I. and Theocaris, P.S. (1977). Array of periodic curvilinear cracks in an infinite isotropic medium. Acta Mechanica 28, 239–254.10.1007/BF01208801 ↗
7. Koiter, W.T. (1960). Stress distribution in an infinite elastic sheet with a doubly-periodic set of holes, Boundary problems in differential equations, The Univ. of Wiconsin Press, Madison, 191–213.
8. Krenk, S. (1976). Periodic contact and crack problems in plane elasticity, Let. Appl. Engng. Sci. 4, 343–353.
9. Li, X. and Li, Z.X. (1993). Effect of a periodic elastic gasket on periodic cracks, Engng. Fract.Mech. 46, 127–131.10.1016/0013-7944(93)90309-G ↗
10. Li, X. (1991). On the second fundamental problem of the plane welding of different materials with a doublyperiodic set of holes, Appl. Math., J. Chin. Univ. 6, 538–544 (in Chinese).
11. Li, X. (1993a). Elastic plane welding problem of different materials with a doubly-periodic set of cracks, Acta Mathematica Scientia 13, 124–132 (in Chinese).
12. Li, X. (1993b). On the mathematical problem of composite materials with a doubly-periodic set of cracks. Appl. Math. Mech. (PRC) 14, 1143–1150.10.1007/BF02456652 ↗
13. Li, X. (1992). On the mixed boundary value problems of certain three-dimensional welding body with a doublyperiodic set of holes, Acta Mathematica Scientia 12, 137–146 (in Chinese).
14. Lu, C.K. (1993). Boundary Value Problems for Analytic Functions, World Scientific, Singapore.
15. Lu, C.K. (1995). Complex Variables Methods in Plane Elasticity, World Scientific, Singapore.
16. Lu, C.K. (1986). On the complex Airy functions in doubly-periodic plane elasticity, J. Math. (PRC) 6, 319–330 (in Chinese).
17. Mikhlin, S.G., Morozov, N.F. and Pankshto, M.V. (1995). Integral Equations of the Theory of Elasticity, Teubner, Stuttgart, Leipzig.10.1007/978-3-663-11626-4 ↗
18. Muskhelishvili, N.I. (1953). Some basic problems of the mathematical theory of elasticity, Noordhoff, Groningen.
19. Nakhmein, E.L. and Nuller, B.M. (1992). Periodic combined boundary value problems and their applications in elasticity theory, Prikl. Mat. Mekh. 56, 95–104.
20. Parton, V.Z. and Perlin, P.I. (1982). Integral equations in elasticity, Mir Publishers, Moscow.
21. Zheng, K. (1988). On the doubly-periodic fundamental problems in plane elasticity, Acta Mathematica Scientia 8, 95–104 (in Chinese).10.1016/S0252-9602(18)30480-6 ↗