Abstract
A contact problem is solved for an infinite anisotropic plate weakened by a circular opening, stiffened by inclusions of variable stiffness, and subjected to bending. For the unknown contact force of interaction between the plate and an inclusion, an integro-differential equation is derived and then reduced to an infinite system of linear algebraic equations. The system is analyzed for regularity.
Similar content being viewed by others
REFERENCES
V. M. Aleksandrov and S. M. Mkhitaryan, Contact Problems for Bodies with Thin Coatings and Layers [in Russian], Nauka, Moscow (1983).
I. N. Vekua, “On the Prandtl integro-differential equation,” Prikl. Mat. Mekh., 9, No. 2, 143–150 (1945).
L. V. Kantorovich and V. M. Krylov, Approximate Methods of Higher Analysis [in Russian], Fizmatgiz, Moscow–Leningrad (1962).
S. G. Lekhnitskii, Anisotropic Plates [in Russian], Gostekhizdat, Moscow (1957).
L. G. Magnaradze, “On one integral equation in airfoil theory,” Soobshch. AN GSSR, 3, No. 6, 503–508 (1942).
G. Ya. Morar' and G. Ya. Popov, “On a contact problem for a half-plane with an elastic finite fastener,” Prikl. Mat.Mekh., 34, No. 3 (1970).
N. I. Muskheshvili, Singular Integral Equations [in Russian], Fizmatgiz, Moscow (1962).
B. M. Nuller, “An elastic wedge stiffened on a finite section with a rod of variable cross section,” Izv. AN SSSR, Mekh.Tverd. Tela, No. 5, 150–155 (1972).
O. V. Onishchuk and G. Ya. Popov, “On some bending problems for plates with cracks and thin inclusions,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 4, 141–150 (1980).
O. V. Onishchuk, G. Ya. Popov, and Yu. S. Protserov, “On some contact problems for stiffened plates,” Prikl. Mat.Mekh., 48, No. 2, 307–314 (1948).
O. V. Onishchuk, G. Ya. Popov, and P. G. Farshait, “On singularities of the contact forces in plates with thin inclusions subjected to bending,” Prikl. Mat. Mekh., 50, No. 2, 293–302 (1986).
G. Ya. Popov, Concentration of Elastic Stresses near Dies, Cuts, Thin Inclusions, and Stiffeners [in Russian], Nauka, Moscow (1982).
V. S. Sarkisyan, Contact Problems for Half-Planes and Strips with Elastic Cover Plates [in Russian], Izd. Yerevanskogo Univ., Yerevan (1983).
N. N. Shavlakadze, “An elastic isotropic half-plane stiffened with a rod of variable cross section,” Soobshch. AN GSSR, 130, No. 3, 509–512 (1988).
N. Shavlakadze, “On some contact problems for bodies with elastic inclusions,” Georgian Math. J., 5, No. 3, 285–300 (1998).
N. Shavlakadze, “A contact problem of the interaction of a semi-finite inclusion with a plate,” Georgian Math. J., 6, No. 5, 489–500 (1999).
N. Shavlakadze, “On singularities of contact stress upon tension and bending of plates with elastic inclusions,” Proc. A.Razmadze Math. Inst., 120, 135–147 (1999).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shavlakadze, N.N. Bending of an Elastic Anisotropic Plate with a Circular Opening Stiffened Over Finite Areas. International Applied Mechanics 38, 356–364 (2002). https://doi.org/10.1023/A:1016094514318
Issue Date:
DOI: https://doi.org/10.1023/A:1016094514318