Abstract
The elastoplastic state of thin spherical shells with an elliptic hole is analyzed considering that deflections are finite. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. Problems are formulated and a numerical method for their solution with regard for physical and geometrical nonlinearities is proposed. The distribution of stresses (strains or displacements) along the hole boundary and in the zone of their concentration is studied. The results obtained are compared with the solutions of problems where only physical nonlinearity (plastic deformations) or geometrical nonlinearity (finite deflections) is taken into account and with the numerical solution of the linearly elastic problem. The stress—strain state in the neighborhood of an elliptic hole in a shell is analyzed with allowance for nonlinear factors
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REFERENCES
V. G. Bazhenov, A. G. Ugodchikov, and L. P. Shinkarenko, “Numerical analysis of the elastic-plastic deformation of shells with curved openings under impulsive loading,” Int. Appl. Mech., 15, No.5, 398–402 (1979).
I. N. Garashchuk, V. S. Medvedev, and I. S. Chernyshenko, “Numerical analysis of the elastoplastic state of ring plates and shallow shells with notches,” Sopr. Mater. Teor. Sooruzh., 48, 94–97 (1986).
Ya. M. Grigorenko, Ya. G. Savula, and I. S. Mukha, “Linear and nonlinear problems on the elastic deformation of complex shells and methods of their numerical solution,” Int. Appl. Mech., 36, No.8, 979–1000 (2000).
V. G. Dmitriev and I. N. Preobrazhenskii, “Deformation of flexible shells with notches,” Izv. AN SSSR, Mekh. Tverd. Tela, No. 1, 177–184 (1988).
M. S. Kornishin, V. N. Paimushin, and V. F. Snigirev, Computational Geometry in Problems of the Mechanics of Shells [in Russian], Nauka, Moscow (1989).
M. S. Kornishin and M. M. Suleimanova, “Geometrically and physically nonlinear bending of deep shells of various shapes under the joint action of temperature and external forces,” Probl. Prochn., No. 12, 80–83 (1983).
A. N. Guz, I. S. Chernyshenko, V. N. Chekhov, et al., Theory of Thin Shells Weakened by Openings, Vol. 1 of the five-volume series Methods of Shell Design [in Russian], Naukova Dumka, Kiev (1980).
A. N. Guz, A. S. Kosmodamianskii, V. P. Shevchenko, et al., Stress Concentration, Vol. 7 of the 12-volume series Mechanics of Composite Materials [in Russian], A.S.K., Kiev (1998).
E. A. Gotsulyak, V. I. Gulyaev, I. Kubor, and I. S. Chernyshenko, “Nonlinear deformation of doubly connected shells of complex outline,” in: Theory and Methods for Design of Nonlinear Plates and Shells [in Russian], Izd. Saratov. Univ., Saratov (1981), pp. 51–53.
G. N. Savin, Stress Distribution near Openings [in Russian], Naukova Dumka, Kiev (1969).
V. A. Salo, Boundary-Value Problems of Statics for Shells with Openings [in Russian], Nats. Tekhn. Univ “KhPI,” Kharkov (2003).
E. A. Storozhuk, I. S. Chernyshenko, and V. L. Yaskovets, “Elastoplastic state of spherical shells in the region of an elliptical hole,” Int. Appl. Mech., 25, No.7, 667–672 (1989).
V. A. Firsov, “Applying flow theory to study the elastoplastic state of shells with an opening,” Prikl. Mekh., 18, No.11, 114–118 (1982).
I. S. Chernyshenko, “Elastic-plastic deformation of a flexible shallow shell with a circular hole, ” Int. Appl. Mech., 20, No.3, 231–236 (1984).
E. A. Gotsulyak, V. I. Gulyaev, K. Pemsing, and I. S. Chernyshenko, “Numerical analysis of stressed state of thin shells with curvilinear holes,” Int. Appl. Mech., 18, No.8, 734–740 (1982).
A. N. Guz, I. S. Chernyshenko, and K. I. Shnerenko, “Stress concentration near openings in composite shells,” Int. Appl. Mech., 37, No.2, 139–181 (2001).
A. N. Guz, E. A. Storozhuk, and I. S. Chernyshenko, “Physically and geometrically nonlinear static problems for thin-walled multiply connected shells,” Int. Appl. Mech., 39, No.6, 679–687 (2003).
A. N. Guz, E. A. Storozhuk, and I. S. Chernyshenko, “Inelastic deformation of flexible spherical shells with two circular openings,” Int. Appl. Mech., 40, No.6, 672–678 (2004).
A. N. Guz, E. A. Storozhuk, and I. S. Chernyshenko, “Elastoplastic state of flexible cylindrical shells with two circular holes,” Int. Appl. Mech., 40, No.10, 1152–1156 (2004).
V. A. Maksimyuk and I. S. Chernyshenko, “Mixed functional in the theory of nonlinearly elastic shells, ” Int. Appl. Mech., 40, No.11, 1226–1262 (2004).
V. A. Maksimyuk, V. P. Mulyar, and I. S. Chernyshenko, “Stress state of thin spherical shells with an off-center elliptic hole,” Int. Appl. Mech., 39, No.5, 595–598 (2003).
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 95–104, June 2005.
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Storozhuk, E.A., Chernyshenko, I.S. Physically and Geometrically Nonlinear Deformation of Spherical Shells with an Elliptic Hole. Int Appl Mech 41, 666–674 (2005). https://doi.org/10.1007/s10778-005-0134-0
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DOI: https://doi.org/10.1007/s10778-005-0134-0