An axisymmetric nonlinear problem of magnetoelasticity for an orthotropic spherical shell of variable stiffness with orthotropic conductivity is solved. The governing system of nonlinear differential equations that describes the stress–strain state of flexible orthotropic shells of variable stiffness in mechanical and magnetic fields is presented. A numerical example is given. The stress state of an orthotropic spherical shell is analyzed by varying the external current and mechanical force
Similar content being viewed by others
References
R. E. Bellman and R. E. Kalaba, Quasilinearization and Nonlinear Boundary-Value Problems, Elsevier, New York (1965).
Ya. M. Grigorenko and L. V. Mol’chenko, Fundamentals of the Theory of Plates and Shells [in Ukrainian], Lybid’, Kyiv (1993).
Ya. M. Grigorenko and L. V. Mol’chenko, Fundamentals of the Theory of Plates and Shells with Elements of Magnetoelasticity (Textbook) [in Russian], IPTs Kievskii Universitet, Kyiv (2010).
Yu. I. Sirotin and M. P. Shaskol’skaya, Fundamentals of Crystal Physics [in Russian], Nauka, Moscow (1979).
A. F. Ulitko, L. V. Mol’chenko, and V. F. Koval’chuk, Magnetoelasticity under Dynamic Loading [in Ukrainian], Lybid’, Kyiv (1994).
W. Flugge, Stresses in Shells, Springer-Verlag, Berlin (1973).
M. A. Hussain and S. L. Pu, “Dinamic stress intensity factors for anunbounded plate having collinear cracks,” Eng. Fact. Mech., 4, No. 4, 865–876 (1972).
H. G. Lippmann, “Principle de la conservation de l’electricite,” Ann. Chim., No. 2, 17–35 (1976).
G. A. Maugin, Nonlinear Electromechanical Effects and Applications, World Scientific, Singapore (1985).
L. V. Mol’chenko and I. I. Loos, “Influence of conicity on the stress–strain state of a flexible orthotropic conical shell in a nonstationary magnetic field,” Int. Appl. Mech., 46, No. 11, 1261–1267 (2010).
L. V. Mol’chenko and I. I. Loos, “Influence of the boundary conditions on the stress state of a flexible cylindrical shell of variable stiffness in a magnetic field,” Int. Appl. Mech., 48, No. 1, 94–100 (2012).
L. V. Mol’chenko and I. I. Loos, “The stress state of a flexible orthotropic spherical shell subject to external current and mechanical force in a magnetic field,” Int. Appl. Mech., 49, No. 5, 528–533 (2013).
L. V. Mol’chenko, I. I. Loos, and L. M. Fedorchenko, “Axisymmetric magnetoelastic deformation of a flexible orthotropic ring with orthotropic conductivity,” Int. Appl. Mech., 49, No. 3, 322–327 (2013).
L. V. Mol’chenko, I. I. Loos, and R. Sh. Indiaminov, “Nonlinear deformation of conical shells in magnetic fields,” Int. Appl. Mech., 33, No. 3, 221–226 (1997).
L. V. Mol’chenko, I. I. Loos, and R. Sh. Indiaminov, “Determining the stress state of flexible orthotropic shells of revolution in magnetic field,” Int. Appl. Mech., 44, No. 8, 882–891 (2008).
L. V. Mol’chenko, I. I. Loos, and R. Sh. Indiaminov, “Stress–strain state of flexible ring plates of variable stiffness in a magnetic field,” Int. Appl. Mech., 45, No. 11, 1236–1242 (2009).
L. V. Mol’chenko, I. I. Loos, and I. V. Plyas, “Stress analysis of a flexible ring plate with circumferentially varying stiffness in a magnetic field,” Int. Appl. Mech., 46, No. 5, 567–573 (2010).
L. V. Mol’chenko, I. I. Loos, and I. V. Plyas, “Effect of the tangential components of magnetic-flux density on the stress state of a flexible circular cylinder with variable stiffness,” Int. Appl. Mech., 47, No. 3, 313–319 (2011).
F. C. Moon, Magneto-Solid Mechanics, John Wiley & Sons, New York (1984).
F. C. Moon and S. Chattopadhyay, “Magnetically induced stress waves in a conducting solid: Theory and experiment,” Trans. ASME, J. Appl. Mech., 41, No. 3, 641–646 (1974).
N. M. Newmark, “A method of computation for structural dynamics,” ASCE, J. Eng. Mech. Div., 85, No. 7, 67–97 (1959).
J. F. Nye, Physical Properties of Crystals, Clarendon Press, Oxford (1964).
Y.-H. Pao and K. Hutter, “Electrodynamis for moving elastic solids and viscous fluids,” Proc. IEEE, 63, No. 7, 1011–1021 (1975).
R. T. Smith, “Stress-induced anisotropy in solids—the acousto-elastic effect,” Ultrasonics, 1, No. 3, 135–147 (1963).
C. Truesdell and W. Noll, “The nonlinear field theories of mechanics,” in: S. Flügges (ed.), Handbuch der Physic, Vol. III/3, Springer-Verlag, Berlin (1960), pp. 1–602.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Translated from Prikladnaya Mekhanika, Vol. 52, No. 1, pp. 127–133, January–February, 2016.
Rights and permissions
About this article
Cite this article
Mol’chenko, L.V., Loos, I.I. & Fedorchenko, L.N. Deformation of a Flexible Orthotropic Spherical Shell of Variable Stiffness in a Magnetic Field. Int Appl Mech 52, 56–61 (2016). https://doi.org/10.1007/s10778-016-0732-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10778-016-0732-z