2020
DOI: 10.1177/1081286520932363
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Asymptotic behavior of the solution of an axisymmetric problem of elasticity theory for a sphere with variable elasticity modules

Abstract: In the paper the axisymmetric problem of elasticity theory is studied for the radially inhomogeneous sphere of small thickness that does not contain any of the poles 0 and [Formula: see text]. Here the case is considered when the elasticity modules vary linearly with respect to the radius. It is assumed that the lateral surface of the sphere is free of stresses, and at the ends of the sphere (at the conical sections) the stresses are set, leaving it in equilibrium. A characteristic equation is obtained and, ba… Show more

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Cited by 8 publications
(7 citation statements)
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“…Substituting (64) into (93), on the basis of (91) taking into account (92), we obtain that for the second group of roots the leading term of the asymptotic solution of Equation ( 21) at ε ! 0 takes the form 40,41…”
Section: Construction Of Asymptotic Formulae For Displacements and St...mentioning
confidence: 99%
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“…Substituting (64) into (93), on the basis of (91) taking into account (92), we obtain that for the second group of roots the leading term of the asymptotic solution of Equation ( 21) at ε ! 0 takes the form 40,41…”
Section: Construction Of Asymptotic Formulae For Displacements and St...mentioning
confidence: 99%
“…The solvability and convergence of the reduction method for (113) was proved in Ustinov. 13 For defining the unknown constants M k , T 65)-( 70) and ( 72)-( 88), the asymmetric solution to system (113) may be constructed using the smallness of the parameter ε: 40,41 homogeneous transversely isotropic sphere is greater than for a radially inhomogeneous transversely isotropic one, and on the outer spherical surface, it is less (Figure 3).…”
Section: Satisfaction Of the Boundary Conditions At The Sphere Endsmentioning
confidence: 99%
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