Residual stresses in a finite cylinder. Direct and inverse problems and their solving using the variational method of homogeneous solutions

Чекурін, В. Ф.; Постолакі, Л. І.

doi:10.23939/mmc2018.02.119

Cited by 4 publications

(13 citation statements)

References 9 publications

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“…Hence, its components can be expressed by using the Cauchy relations via the components u r and u z of the vector of displacements. As a result, we arrive at the system of equations [13]:…”

Section: Statement Of the Problemmentioning

confidence: 99%

“…A cylindrical body with axisymmetric residual stresses induced by the inconsistent eigenstrains that depend only on the radial coordinate was studied in [6,13]. On the basis of the variational method of homogeneous solutions, a method for the solution of the direct problem of evaluation of residual stresses in the body with a given distribution of inconsistent eigenstrains was developed in [11,12].…”

mentioning

confidence: 99%

“…These parameters can be empirically determined by the method of polarization-optical sounding of the object in the directions lying in the equatorial plane of the cylinder. A variational method aimed at the solution of the inverse problem of determination of residual stresses was developed in [13]. This method is based on the expansion of the required solution in the systems of eigenfunctions of the biharmonic problem for a cylinder with homogeneous conditions imposed on the lateral face [11].…”

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confidence: 99%

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Polarization-Optical Parameters of the Axisymmetric Residual Stresses in an Isotropic Dielectric Cylinder

2022

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We consider the direct problem of determination of axisymmetric residual stresses in a finite isotropic dielectric cylindrical body caused by the diagonal tensor of inconsistent eigenstrains whose components depend only on the radial coordinate. The parameters of the stress field are investigated by using the obtained solution of the problem. These parameters can be empirically found by the polarization-optical method as a result of sounding of the body with rays of polarized light in different directions and then used as input data for the inverse problems of nondestructive determination of the residual stress-strain state. We consider three sets of directions in the planes of space symmetry of the stress-strain state. For each set, we establish the integral relations connecting the values of the corresponding polarizationoptical parameters with the distributions of the components of stresses in a body in the direction of raysounding. We perform quantitative investigations of the polarization-optical parameters depending on the level of residual stresses and their gradients. The results of these investigations enable us to estimate the informativity of the empirical data that can be obtained as a result of ray-sounding of the cylinder along these three sets of directions.

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“…Hence, its components can be expressed by using the Cauchy relations via the components u r and u z of the vector of displacements. As a result, we arrive at the system of equations [13]:…”

Section: Statement Of the Problemmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Polarization-Optical Parameters of the Axisymmetric Residual Stresses in an Isotropic Dielectric Cylinder

2022

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“…A variational method of homogeneous solutions was used in [ 38 , 39 ] for the analysis of axisymmetric residual stresses in a finite-length cylinder. The residual stresses are modeled with the use of concept of incompatible residual strains ( 1 ) with the latter strains being regarded as the cause of the residual stresses appearance.…”

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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“…In [20][21][22], the variational method of homogeneous solutions was extended to axially symmetric elasticity problems for the solid cylinder of semi-infinite and finite length, with the traction-free lateral boundary and loaded end faces. In [23], this method was used to solve an inverse problem for determining axially symmetric residual stresses in a finite solid cylinder with the use of the data obtained by the photo-elasticity method.…”

Section: Introductionmentioning

confidence: 99%

Axially symmetric elasticity problems for the hollow cylinder with the stress-free ends. Analytical solving via a variational method of homogeneous solutions

Чекурін¹,

Постолакі²

2020

Math. Model. Comput.

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An axially symmetric problem for a hollow cylinder with unloaded bases is considered. On the inner and outer cylindrical surfaces, the normal and tangential loads are prescribed. The problem is reduced to a biharmonic equation with corresponding boundary conditions. Application of the method of variables separation results in a homogeneous boundary value problem for the ordinary differential equation. Its eigenfunctions have been used to construct an infinite system of homogeneous solutions for the initial biharmonic problem. Its solution, represented as a series expansion in terms of homogeneous solutions, depends on four infinite sequences of real constants. To determine them, the variational method has been applied, in which the subordination of the solution to the boundary conditions, given on cylindrical surfaces, is performed in the norm L 2. It brings to an infinite system of algebraic equations which has been solved by the reduction method. The quantitative studies have confirmed the good convergence of the method.

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Residual stresses in a finite cylinder. Direct and inverse problems and their solving using the variational method of homogeneous solutions

Cited by 4 publications

References 9 publications

Polarization-Optical Parameters of the Axisymmetric Residual Stresses in an Isotropic Dielectric Cylinder

Polarization-Optical Parameters of the Axisymmetric Residual Stresses in an Isotropic Dielectric Cylinder

Axisymmetric residual stresses in a solid cylinder of finite length

Axially symmetric elasticity problems for the hollow cylinder with the stress-free ends. Analytical solving via a variational method of homogeneous solutions

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