Analysis of a three-dimensional problem of the theory of elasticity for an inhomogeneous truncated hollow cone

Akhmedov, N.K.; Mekhtiyev, M.F.

doi:10.1016/0021-8928(93)90153-d

Cited by 7 publications

(5 citation statements)

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“…In the present article, the homogenous solutions are obtained that can satisfy the boundary conditions at the butt ends of a cylinder. The case of non-homogenous boundary conditions at the lateral surface of the cylinder can be studied by the methods developed in references [21,22].…”

Section: Asymptotic Derivation Of the Homogeneous Solutionsmentioning

confidence: 99%

Asymptotic Analysis of the Dynamic Problem of the Theory of Elasticity for a Transverse Isotropic Hollow Cylinder

Mekhtiev

Bergman²

2001

Journal of Sound and Vibration

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Section: Asymptotic Derivation Of the Homogeneous Solutionsmentioning

confidence: 99%

Asymptotic Analysis of the Dynamic Problem of the Theory of Elasticity for a Transverse Isotropic Hollow Cylinder

Mekhtiev

Bergman²

2001

Journal of Sound and Vibration

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“…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%

“…Asymptotic methods have made a significant contribution to the solution of three-dimensional problems of the theory of elasticity. [10][11][12][13]17,18,20,21,36 In previous studies, 37,38 on the basis of three-dimensional equations of elastodynamics, using a discrete-analytical method, the natural oscillations of a three-layer sphere with an average radially inhomogeneous layer were studied. It was assumed that the moduli of elasticity and the density of the material of the middle layer are a power law along the radius.…”

Section: Introductionmentioning

confidence: 99%

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Investigation of elasticity problem for the radially inhomogeneous transversely isotropic sphere

Akhmedov

Yusubova

2022

Math Methods in App Sciences

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The axisymmetric problem of the theory of elasticity for the radially heterogeneous transverse‐isotopic nonclosed spheres is studied, which does not contain any of the poles 0 and π. The elasticity modules are taken as the linear functions of the radius of the sphere. It is assumed that the lateral surface of the sphere is free from stresses, and in the conical sections, the arbitrary stresses are set that provide equilibrium for the sphere. After consideration of the homogeneous boundary conditions, set on the lateral surfaces of the sphere, the characteristic equation for the spectral parameter is obtained. On the basis of the asymptotic analysis, a classification of the roots of the characteristic equation is made relatively small parameter that characterizes the thickness of the sphere. Corresponding asymptotic solutions are constructed depending on the roots of the characteristic equation. The behavior of the constructed solutions is studied in the internal parts of the sphere, as well as in the neighborhood of the conical sections.

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“…The problem of determining the nonstationary wave field of an elastic truncated cone, taking into account its own weight, is investigated in [17]. In [18] the stressed state of the inhomogeneous thin truncated hollow cone is investigated. In [19] obtained an exact solution of the problem of torsion of a truncated hollow cone.…”

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confidence: 99%

Torsion problem for an elastic twice-truncated cone

Mysov¹

2018

RMM

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The problem of an elastic twice-truncated cone wave field estimation is investigated in case of steady state torsional oscillations. The G. Ya. Popov integral transform with regard to an angular coordinate is applied. Thus reducing the original problem to one-dimensional boundary value problem in the transform's domain. The Green's function is build for onedimensional boundary value problem. With it's help the solution of one-dimensional problem is constructed in an explicit form. The G. Ya. Popov inverse transformation helped to derive the solution in original domain in form of an infinite sum. With it's help dependence of the eigenfrequencies from the cone's geometric parameters is investigated. Stress field was found with the use of asymptotic procedure. Comparison plots are build for different opening angles. MSC: 74G70, 74H99, 74J10.

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Analysis of a three-dimensional problem of the theory of elasticity for an inhomogeneous truncated hollow cone

Cited by 7 publications

References 1 publication

Asymptotic Analysis of the Dynamic Problem of the Theory of Elasticity for a Transverse Isotropic Hollow Cylinder

Asymptotic Analysis of the Dynamic Problem of the Theory of Elasticity for a Transverse Isotropic Hollow Cylinder

Investigation of elasticity problem for the radially inhomogeneous transversely isotropic sphere

Torsion problem for an elastic twice-truncated cone

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