2011
DOI: 10.3103/s0025654411040133
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Asymptotic analysis of a 3D elasticity problem for a radially inhomogeneous transversally isotropic hollow cylinder

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Cited by 5 publications
(7 citation statements)
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“…The nature of the constructed solutions is explained. Paper [16] shows that when homogeneous mixed boundary conditions are set on the lateral surfaces of a heterogeneous cone, the stressed-strained state is composed only of a solution having the character of a boundary layer. In [17], the axisymmetric problems of the theory of elasticity for a transversal-isotropic cone of variable thickness are studied.…”
Section: Literature Review and Problem Statementmentioning
confidence: 99%
“…The nature of the constructed solutions is explained. Paper [16] shows that when homogeneous mixed boundary conditions are set on the lateral surfaces of a heterogeneous cone, the stressed-strained state is composed only of a solution having the character of a boundary layer. In [17], the axisymmetric problems of the theory of elasticity for a transversal-isotropic cone of variable thickness are studied.…”
Section: Literature Review and Problem Statementmentioning
confidence: 99%
“…In [8], the problem of torsion of a radial inhomogeneous cylinder with a fixed lateral surface was studied. In [9], an asymptotic method is used to study the behavior of solutions of an axisymmetric problem of elasticity theories for a radial inhomogeneous transversely isotropic cylinder of small thickness. The analysis of the stress-strain state determined by homogeneous solutions is carried out.…”
Section: Literature Review and Problem Statementmentioning
confidence: 99%
“…The study of the stress–strain state of inhomogeneous bodies on the basis of three‐dimensional equations of the theory of elasticity is associated with significant mathematical difficulties. Along with this, from a physical point of view, new qualitative and quantitative effects arise 9–13 …”
Section: Introductionmentioning
confidence: 97%
“…Along with this, from a physical point of view, new qualitative and quantitative effects arise. [9][10][11][12][13] A number of studies were devoted to the study of three-dimensional problems of the theory of elasticity for a sphere. Such problems were studied by Saint-Venant.…”
Section: Introductionmentioning
confidence: 99%
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