Abstract
This paper deals with spatial axisymmetric boundary-value problems of the physically nonlinear theory of elasticity for piecewise-homogeneous spherical bodies. The passage to dimensionless characteristics of the stress-strain state allows us to extract a physical dimensionless small parameter in the nonlinear state equations. The solution of nonlinear equilibrium equations and boundary-value problems is searched for in the form of series in positive degrees of the small parameter. This approach allows reducing the stated physically nonlinear boundary-value problem to a sequence of corresponding linear nonhomogeneous problems. A specific analytical solution and numerical results are obtained for a two-layer nonlinearly elastic spherical shell under bilateral pressure.
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References
A. N. Guz',Stability of Elastic Bodies Under Triaxial Compression [in Russian], Naukova Dumka, Kiev (1979).
A. N. Guz' and I. A. Tsurpal, “Equilibrium of a physically nonlinear thick-walled spherical shell,” in:Theory of Plates and Shells [in Russian], Nauka, Moscow (1971), pp. 82–84.
G. Kauderer,Nonlinear Mechanics [Russian translation], Izd. Inostr. Lit., Moscow (1961).
O. I. Levchuk, “The effect of the physical nonlinearity of a material on the stress state of a medium with an elastic spherical enclosure under uniform loading,”Prikl. Mekh.,34, No. 11, 46–51 (1998).
A. I. Lurie,Three-Dimensional Problems of the Theory of Elasticity [in Russian], Gostekhizdat, Moscow (1955).
Yu. N. Nemish, “Approximate solution of some spatial physically nonlinear problems of the theory of elasticity,”Prikl. Mekh.,6, No. 7, 53–57 (1970).
Yu. N. Nemish,Elements of the Mechanics of Piecewise-Homogeneous Bodies with Noncharacteristic Interfaces [in Russian], Naukova Dumka, Kiev (1989).
Yu. N. Nemish, “The stress state of a nonlinear elastic medium with a spherical enclosure,”Prikl. Mekh.,33, No. 2, 18–25 (1997).
Yu. N. Nemish and O. I. Levchuk, “Solution of three-dimensional physically nonlinear problems for symmetrically loaded elastic cylinders,”Prikl. Mekh.,35, No. 5, 69–76 (1999).
I. A. Tsurpal,Analysis of Nonlinear Elastic Structural Elements [in Russian], Tekhnika, Moscow (1976).
I. A. Tsurpal and G. G. Kuliev, “Problems of stress concentration with allowance for the physical nonlinearity of aa material (review),”Prikl. Mekh.,10, No. 7, 3–22 (1974).
I. A. Tsurpal and N. G. Tamurov,Design of Multiply Connected Laminated and Nonlinearly Elastic Plates and Shells [in Russian], Vyshcha Shkola, Kiev (1977).
F. Jindra, “Eindimensionale probleme bei einem nichtlinearen Elastizitatsgesetz,”Z. Math. Phys. 6, No. 5 (1955).
Additional information
S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 26–32, December, 1999.
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Nemish, Y.N., Levchuk, O.I. The stress state of a laminated nonlinearly elastic thick-walled spherical shell. Int Appl Mech 35, 1214–1221 (1999). https://doi.org/10.1007/BF02682394
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DOI: https://doi.org/10.1007/BF02682394