Analysis of residual stresses in a long hollow cylinder

Tokovyy, Yu. V.; Ma, Chien‐Ching

doi:10.1016/j.ijpvp.2011.04.002

Cited by 14 publications

(5 citation statements)

References 41 publications

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“…Despite significant advances in the development of the methods aimed at the numerical analysis of the problems of mechanics and a wide choice of certified highly efficient software environments intended for the solution of these problems with the help of the finite-element method [12], the interest in analytic methods still remains fairly high. This can be confirmed, in particular, by the appearance of new scientific publications (see, e.g., [10,11,[13][14][15]) and explained by several factors. One of these factors is connected with the fact that the analytic solution of the direct problem enables one to significantly simplify the process of solution of the corresponding inverse problems.…”

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confidence: 81%

Variational Method of Homogeneous Solutions in Axisymmetric Elasticity Problems for a Semiinfinite Cylinder

Чекурін

Постолакі

2014

J Math Sci

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We develop a variational method of homogeneous solutions for the solution of axisymmetric elasticity problems for a semiinfinite cylinder with free lateral surface. We consider four types of boundary conditions imposed on the end of cylinder, namely, the conditions in stresses, in displacements, and two types of mixed conditions. The solution of the problems with the help of this method is reduced to the solution of infinite systems of linear algebraic equations. We perform the numerical analysis of convergence of the obtained solutions. We also consider an example of application of the proposed approach to the determination of stress concentration near the joint of the end of the cylinder with a perfectly rigid lateral surface.The problems of determination of the stress-strain state of cylindrical bodies appear in various scientific disciplines and, in particular, in the applied theories of the strength of solids [9]. Despite significant advances in the development of the methods aimed at the numerical analysis of the problems of mechanics and a wide choice of certified highly efficient software environments intended for the solution of these problems with the help of the finite-element method [12], the interest in analytic methods still remains fairly high. This can be confirmed, in particular, by the appearance of new scientific publications (see, e.g., [10,11,[13][14][15]) and explained by several factors. One of these factors is connected with the fact that the analytic solution of the direct problem enables one to significantly simplify the process of solution of the corresponding inverse problems.We especially mention the following two well-known approaches to the analytic solution of axisymmetric elasticity problems for a circular cylinder: the method of superposition [2, 10] and the method of homogeneous solutions [3,5].The first method is based on the representation of solutions in the form of a sum of two components: one of which guarantees the validity of boundary conditions on the end face and the other component satisfies the conditions imposed on the lateral surface. Each of these components is represented as an expansion in a complete systems of function. Thus, the systems of hyperbolic-cylindrical and trigonometric-cylindrical functions are used for this purpose in the monograph [2]. The coefficients of these expansions are determined by subordinating the solution to the boundary conditions imposed on the end face of the cylinder and on its lateral surface. As a result, an infinite system of algebraic equations is obtained, which enables one to express the coefficients of expansions via the Fourier and Fourier-Bessel coefficients of the functions appearing in the boundary conditions.The second method is based on the representation of required solutions in the form of expansions in complete systems of functions (i.e., in the so-called homogeneous solutions). The role of systems of homogeneous solutions is played by the eigenfunctions of homogeneous axisymmetric problems of the theory of elasticity...

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mentioning

confidence: 81%

Variational Method of Homogeneous Solutions in Axisymmetric Elasticity Problems for a Semiinfinite Cylinder

Чекурін

Постолакі

2014

J Math Sci

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“…Laminated cylinders were investigated numerically by S. Aksoy et al [8]. A residual stress analysis was carried out for a long cylinder by Y. V. Tokovyy and C. C. Ma [9]. Simulation of a multilayer pressure vessel was carried out by Ameya Palekar et al [10].…”

Section: Introductionmentioning

confidence: 99%

Characteristics of stress distribution of a multi layered cylindrical pressure vessel

Somadder¹,

Das²,

Islam³

2023

Journal of Mechanical and Energy Engineering

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The operation of a multilayer pressure vessel subjected to thermomechanical loads is very significant. The cylindrical pressure vessel is widely used in industrial engineering, for example, to hold a variety of different types of liquid. On thick-walled cylinders, various loading circumstances such as internal overpressure, external overpressure, heat, bending, twisting, and combinations of these load characteristics are applied. Researchers have developed a number of strategies for enhancing the strength of cylinders, including the use of multilayer cylinders and increasing the thickness of the walls. This paper presents the results of an analytical and numerical analysis of a three-layer cylinder. Abaqus FEA software is used to determine temperature, displacement, and stress distribution of multilayer cylinder considering the effect of centripetal and centrifugal heat flow. From the numerical analysis it is observed that centrifugal heat flux is more hazardous than centripetal heat flux for multilayered cylinder under thermo-mechanical loading.

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“…The formulation and solution of the inverse problems is based on the so-called conventional-plastic strain hypothesis [ 21 , 22 ] implying the base material of a solid to be elastic, while the expected zone of residual stress distribution exhibits specific elastic–plastic behavior so that the total strain can be represented in the following form: where is the total strain tensor, is the tensor of elastic strains occurring within the entire solid, and denotes the tensor of incompatible strain [ 23 ] distributed within the area affected by the impacts causing the residual stress–strain state. This approach has been efficiently employed for the analysis of residual stresses due to welding residual strains in infinite layers with rectilinear and circular welds [ 24 , 25 ], butt-welded cylindrical vessels [ 26 , 27 ], and rectangular plates [ 28 ]. Special attention in the latter paper was given to the end effects in the butt-welded rectangular plate by performing the exact analysis based on the direct integration method [ 29 ].…”

Section: Introductionmentioning

confidence: 99%

Axisymmetric residual stresses in a solid cylinder of finite length

Postolaki

Tokovyy

2022

J Eng Math

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A solution technique is presented for the determination of residual stresses in a finite-length solid cylinder subject to non-uniform axisymmetric distributions of incompatible residual strains. The problem is reduced to the sequential solving of three individual problems: a problem on the determination of residual stresses in an infinitely long cylinder (the basic state) and two auxiliary problems for evaluating the stresses induced by the end-face effects (the disturbed states). The variational method of homogeneous solutions is implemented in order to determine the disturbed states within the framework of two latter problems. The solution technique is verified numerically for typical distribution profiles of incompatible strains depending on both the radial and axial coordinates. The approach can be used to evaluate residual stresses in a solid cylinder of finite length due to the intense thermal treatment.

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Analysis of residual stresses in a long hollow cylinder

Cited by 14 publications

References 41 publications

Variational Method of Homogeneous Solutions in Axisymmetric Elasticity Problems for a Semiinfinite Cylinder

Variational Method of Homogeneous Solutions in Axisymmetric Elasticity Problems for a Semiinfinite Cylinder

Characteristics of stress distribution of a multi layered cylindrical pressure vessel

Axisymmetric residual stresses in a solid cylinder of finite length

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