Axisymmetric thermal stresses in an elastic hollow cylinder of finite length

Yuzvyak, M. Yo.; Tokovyy, Yu. V.; Yasinskyy, Anatoliy

doi:10.1080/01495739.2020.1826376

Cited by 13 publications

(4 citation statements)

References 21 publications

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“…Table 3 shows the values of U for higher number of terms in three points on the rectangle displaying the same tendency. This trend agrees with reported results for rectangles [2] and more recently for finite cylinders [5,23].…”

Section: Resultssupporting

confidence: 93%

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

Barulich

Deutsch

Eisenberger

et al. 2021

Mathematics and Mechanics of Solids

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This paper presents a new displacement solution based on a Modified Fourier Series (MFS) for isotropic linear elastic solids under plane strain or plane stress states subject to continuous displacement and traction boundary conditions in a two-dimensional rectangular domain. In contrast with existing approaches that are restricted to Fourier series with a rate of convergence of second order O(m-2), the MFS allows increasing the rate of convergence of the solution. The governing Partial Differential Equations (PDEs) are satisfied exactly by two displacement solutions while the boundary conditions are approximated after solving a finite system of algebraic equations. Numerical results for a solution with an MFS with rate of convergence O(m-3) are compared with results from existing numerical and analytical methods, showing the enhanced behavior of the present solution.

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Section: Resultssupporting

confidence: 93%

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

Barulich

Deutsch

Eisenberger

et al. 2021

Mathematics and Mechanics of Solids

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show abstract

“…The efficiency of solution to the inverse problem of such kind strongly relies on the analytical appearance of a solution to a direct problem for arbitrary boundary conditions on the entire surface of a cylinder. The family of dominant analytical methods for constructing solutions meeting the above requirements is presented by the method of cross-wise superposition [36], the direct integration method [37], and the method of homogeneous solutions [38,39]. The latter method is a natural extension of the classical method of variable separation and allows for constructing the ultimate solution by superposing the so-called homogeneous solutions which meet actual boundary conditions on one segment of the boundary and the homogeneous boundary conditions on the rest of the boundary.…”

Section: F I G U R Ementioning

confidence: 99%

Identification of force loadings on the inner circumference of a finite‐length elastic cylinder

Postolaki

Tokovyy

2023

Z Angew Math Mech

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An inverse problem is solved for identifying unknown force loadings on the inner surface of a finite‐length hollow cylinder using the variational method of homogeneous solutions. The problem is considered within the axisymmetric formulation, and the radial and axial displacements of the outer surface of the cylinder are used as the auxiliary data for solving the inverse problem. The accessible surfaces of the cylinder (the end‐faces and the outer surface) are assumed to be free of force loading. By making use of the variational method of homogeneous solutions, the problem is reduced to an infinite system of linear algebraic equations. The solution is verified numerically and its stability with respect to small errors in the input data is analyzed.

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“…Chekurin and Postolaki [51] derived the solution for the cylinder with stress-free flat ends using the variational principle. Yuzvyak et al [52] based on the direct integration method derived the solution to study the thermal stresses due to a steady field temperature field applied on the axisymmetric hollow cylinder. All the surfaces of the cylinder are considered to be load free.…”

Section: Introductionmentioning

confidence: 99%

Analysis of axisymmetric hollow cylinder under surface loading using variational principle

Sirsat,

Padhee

2024

Mathematics and Mechanics of Solids

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In this work, a variational principle–based approach has been adopted to analyze one of the classical linear elasticity problem of the axisymmetric cylinder under surface loading. The use of variational principle results in a set of governing partial differential equations with associated boundary conditions. The equations have been solved using the separation of variable approach and the Frobenius method. A general solution has been derived and used to solve two test cases. The proposed solution is capable of meeting all the boundary conditions. The solution has been validated by comparing it with a finite element–based numerical solution and considering a special limiting condition of a solid cylinder, for which results are available in the literature. Further various studies have been carried out to understand the robustness and limitation of the presented solution.

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Axisymmetric thermal stresses in an elastic hollow cylinder of finite length

Cited by 13 publications

References 21 publications

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

A modified Fourier series-based solution with improved rate of convergence for two-dimensional rectangular isotropic linear elastic solids

Identification of force loadings on the inner circumference of a finite‐length elastic cylinder

Analysis of axisymmetric hollow cylinder under surface loading using variational principle

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