Abstract
The plane stability problem for a rectangular, linearly elastic, isotropic plate with a central crack is solved. The dependence of the critical load on the crack length is studied using exact (the three-dimensional linearized theory of stability of elastic bodies) and approximate (beam approximation) approaches. The results produced by the beam approach are evaluated.
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REFERENCES
V. A. Bazhenov, E. A. Gotsulyak, A. N. Ogloblya, et al., Design of Composite Structures with Delaminations [in Russian], Budivel’nyk, Kiev (1992).
V. V. Bolotin, “Mechanics of delaminations in structures made of laminated composites,” Mekh. Komp. Mater., 37, No.5, 585–602 (2001).
V. V. Bolotin, Z. Kh. Zabelyan, and A. A. Kurzin, “Stability of compressed elements with delaminations,” Probl. Prochn., No. 7, 3–8 (1980).
A. N. Guz, Stability of Three-Dimensional Deformable Bodies [in Russian], Naukova Dumka, Kiev (1971).
A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies [in Russian], Vyshcha Shkola, Kiev (1986).
A. N. Guz and E. Yu. Gladun, “Plane problem of three-dimensional stability of a cracked plate,” Int. Appl. Mech., 37, No.10, 1281–1289 (2001).
A. N. Guz, M. Sh. Dyshel’, and V. M. Nazarenko, Fracture and Stability of Cracked Materials, Vol. 4 of the four-volume five-book series Nonclassical Problems of Fracture Mechanics [in Russian], Naukova Dumka, Kiev (1992).
Yu. V. Kokhanenko, “Numerical study of three-dimensional stability problems for laminated and ribbon-reinforced composites,” Int. Appl. Mech., 37, No.3, 317–345 (2001).
A. N. Mikhailov, “Generalizations of the beam approach to crack problems,” Prikl. Matem. Tekhn. Fiz., No. 3, 171–174 (1969).
B. N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, N. J. (1980).
L. I. Slepyan, Mechanics of Cracks [in Russian], Sudostroenie, Leningrad (1990).
S. P. Timoshenko, Resistance of Materials [in Russian], Fizmatgiz, Moscow (1960).
A. N. Guz, Fundamentals of the Three-Dimensional Theory of Stability of Deformable Bodies, Springer-Verlag, Berlin-Heilberg-New York (1999).
A. N. Guz, “Establishing the fundamentals of the theory of stability of mine workings,” Int. Appl. Mech., 38, No.1, 20–48 (2003).
A. N. Guz, “On one two-level model in the mesomechanics of compression fracture of cracked composites,” Int. Appl. Mech., 39, No.3, 274–285 (2003).
Yu. V. Kokhanenko and V. S. Zelenskii, “Influence of geometrical parameters on the critical load in three-dimensional stability problems for rectangular plates and beams,” Int. Appl. Mech., 39, No.9, 1073–1080 (2003).
I. W. Obreimoff, “The splitting strength of mica,” Proc. Roy. Soc. London, Ser. A, 127, 290–297 (1930).
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Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 117–126, November 2004.
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Gladun, E.Y., Guz, A.N. & Kokhanenko, Y.V. Estimating the error of the beam approximation in the plane stability problem for a rectangular plate with a central crack. Int Appl Mech 40, 1290–1296 (2004). https://doi.org/10.1007/s10778-005-0036-1
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DOI: https://doi.org/10.1007/s10778-005-0036-1