The stress–strain state of thin spherical, conical, and ellipsoidal shells made of nonlinear elastic orthotropic composites is analyzed numerically. The methods of successive approximations, the finite-difference method, and an original algorithm for the numerical discretization of a plane curve are used. The effect of the orthotropy and nonlinearity of composite materials, the geometry of shells, and the stiffness of the reinforcement (rings, inclusions) on the stress–strain state is studied
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. P. Georgievskii, V. A. Maksimyuk, and I. S. Chernyshenko, “Reinforcement of the edge of a hole in orthotropic physically nonlinear shells of revolution,” Prikl. Mekh., 23, No. 6, 125–127 (1987).
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., Kyiv (1998).
V. A. Lomakin, “On the theory of anisotropic plasticity,” Vestn. MGU, Ser. Mat. Mekh., No. 4, 49–53 (1964).
Yu. S. Solomonov, V. P. Georgievskii, A. Ya. Nedbai, and V. A. Andryushin, Methods for the Design of Cylindrical Shells Made of Composite Materials [in Russian], Fizmatlit, Moscow (2009).
D. H. Bonde and and K. P. Rao, “Thermal stresses in a cylindrical shell containing a circular hole or a rigid inclusion,” Nucl. Eng. Design, 40, No. 2, 337–346 (1977).
V. N. Chekhov and S. V. Zakora, “Stress concentration in a transversely isotropic spherical shell with two circular rigid inclusions,” Int. Appl. Mech., 47, No. 4, 441–448 (2011).
I. S. Chernyshenko, “Elastic-plastic state of shells of revolution with a rigid circular inclusion,” Int. Appl. Mech., 16, No. 2, 130–134 (1980).
I. S. Chernyshenko, “Nonlinear deformation of isotropic and orthotropic shells with holes reinforced by a rigid elastic element,” Int. Appl. Mech., 25, No. 1, 54–59 (1989).
I. S. Chernyshenko and V. A. Maksimyuk, “On the stress–strain state of toroidal shells of elliptical cross section formed from nonlinear elastic orthotropic materials,” Int. Appl. Mech., 36, No. 1, 90–97 (2000).
V. P. Georgievskii, A. N. Guz, V. A. Maksimyuk, and I. S. Chernyshenko, “Numerical analysis of the nonlinearly elastic state around cutouts in orthotropic ellipsoidal shells,” Int. Appl. Mech., 25, No. 12, 1207–1212 (1989).
A. N. Guz, E. A. Storozhuk, and I. S. Chernyshenko, “Nonlinear two-dimensional static problems for thin shells with reinforced curvilinear holes,” Int. Appl. Mech., 45, No. 12, 1269–1300 (2009).
V. A. Maksimyuk, E. A. Storozhuk, and I. S. Chernyshenko, “Using mesh-based methods to solve nonlinear problems of statics for thin shells,” Int. Appl. Mech., 45, No. 1, 32–56 (2009).
E. Reissner and F. Y. M. Wan, “Further considerations of stress concentration problems for twisted or sheared shallow spherical shells,” Int. J. Solids Struct., 31, No. 16, 2153–2165 (1994).
E. Reissner and F. Y. M. Wan, “Static-geometric duality and stress concentration in twisted and sheared shallow spherical shells,” Comp. Mech., 22, 437–442 1999.
V. P. Shevchenko and S. V. Zakora, “On the mutual influence of closely located circular holes with rigid contours in a spherical shell,” J. Math. Sci., 174, No. 3, 322–330 (2011).
S. V. Zakora and Val. N. Chekhov, “Stress state of a transversely isotropic spherical shell with a rigid circular inclusion,” Int. Appl. Mech., 41, No. 12, 1384–1390 (2005).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Mekhanika, Vol. 49, No. 6, pp. 67–74, November–December 2013.
Rights and permissions
About this article
Cite this article
Maksimyuk, V.A., Storozhuk, E.A. & Chernyshenko, I.S. Nonlinear Deformation of Thin Isotropic and Orthotropic Shells of Revolution with Reinforced Holes and Rigid Inclusions. Int Appl Mech 49, 685–692 (2013). https://doi.org/10.1007/s10778-013-0602-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-013-0602-x