The axisymmetric problem of the theory of elasticity for a non-uniform plate of variable thickness

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

doi:10.1016/0021-8928(95)00057-v

Cited by 3 publications

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“…44 are some constants. Substituting (3)-( 10) into (1) and ( 2) and taking into account (11), we obtain the equilibrium equations in displacements We introduce a new dimensionless radial variable ρ associated with r by the relation…”

Section: Statement Of Boundary Problem and Construction Of Solutionmentioning

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%

“…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%

“…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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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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Section: Statement Of Boundary Problem and Construction Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 97%