A Green's function method of determining the residual stresses in cylindrical glass shells

We propose a way of modifying the mathematical model of the nondestructive theoretical-experimental method of determining the residual stresses for a specific collection of technological conditions for welding two cylindrical glass shells. The method is based on the general theory of boundary-value problems for ordinary differential equations.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 33, 1991, pp. 69–73.     

Determination of the residual stresses in the welded joints of glass structures

We propose a computational model for determining the residual stresses in a welded glass structure taking account of the properties of the formation of residual stresses in glass. The problem is solved in displacements using Galerkin's method in conjunction with a finite-element model. A numerical solution is obtained for the axisymmetric case. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 131–134.     

A nondestructive numerical-experimental method of determining the residual stresses in welded shells of revolution

We propose a numerical-experimental method of determining the residual stresses in welded shells of revolution. We solve the inverse conditionally correct problem of recovering the complete picture of the residual stress state from part of the experimental values obtained by the method of photoelasticity. We apply the numerical spline-collocation method. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 149–151.     

Determination of residual stresses in plastics

A method is proposed for calculating the residual stresses in hot-molded plastics parts. Data are presented for a polyester glass-reinforced plastic.Mekhanika Polimerov, Vol. 3, No. 5, pp. 827–832, 1967     

Inverse problem of nondestructive optical testing of residual stresses in cyclindrical shells

We considered the inverse problem of determination of the stress-strain state of a circular cylindrical shell that consists of two heterogeneous parts joined by a circular seam. As the input data for this problem, the results of polarization-optical measurements are used. The problem is formulated within the framework of a model that considers residual stress as caused by the geometric incompatibility of elastic deformations. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 151–156, April–June, 1998.     

A computational-experimental method for identifying the viscoelastic properties of composites in dynamically loaded shells of revolution

A method for determining the stiffness and rheological characteristics of composite materials, based on minimizing the mismatch of experimental data and the results of numerically modeling nonstationary deformation processes in shells ofrevolution made of composites materials, is presented. This approach is used for analyzing the damping characteristics of chaotically reinforced and cloth-reinforced composites. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 4, pp. 449–464, July–August, 2007.     

Determination of the thermal stresses in anisotropic shells of revolution

Using the relations of the improved model of layered anisotropic shells based on the straight line assumption taking account of the thermal compression over the thickness we obtain a resolvent system of equations for shells whose properties depend on temperature. We carry out a study of the stresses in a two-layer cylindrical shell formed by winding as a function of the winding angle. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 82–85.     

Determination of residual stresses in a layered system during two-sided high-temperature spray-coating

In order to describe the process of high-temperature spray-coating of covering layers, we prescribe boundary conditions determining the effect of the covering layers on the heat-exchange of the sublayer with the medium, and generalize to the case in which the quantity of heat introduced by the jet of plasma-forming gas is taken into account. Analytic expressions for the thermal stress state in a sheet with covering layers on each side are obtained. Computations of residual stresses in a steel sheet and the forces in the spray-coating on its surface are conducted for the cases of nichrome and aluminum alloys.Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie, Polya, No. 29, pp. 8–12, 1989.     

Determination of the residual stresses in wound glass-reinforced plastic rings

The stresses that develop during winding in wound glass-reinforced plastic rings change during polymerization, when the modulus of elasticity in the radial direction is reduced by heating. Further changes occur in connection with cooling and removal from the mandrel. The theoretical relations obtained for determining these stresses are found to be confirmed by experiment.Bauman Moscow Higher Technical College. Translated from Mekhanika Polimerov, No. 5, pp. 892–898, September–October, 1969.     

The inverse conditionally correct problem of determining the residual stresses in compound welded shells of revoltuion

We solve the inverse conditionally correct problem of recovering the complete picture of the residual stressed state for a compound shell welded from two parts, one cylindrical and the othe conical. We apply the partial values of the stresses obtained experimentally by the method of photoelasticity. We also apply the numerical method of spline-collocations. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 130–134.     

Nonlinear analysis of residual stresses in a rail manufacturing process by FEM

The aim of this paper is to study the residual stresses in an UIC-60 rail and their reduction by means of roller straightening. Both experimental and numerical investigations have been carried out in the past to reveal the formation of dominant longitudinal residual stresses. However, the agreement between both investigations was not particularly good. The finite element method (FEM) has also been used to simulate one, two and three-dimensional analyses of a rail during roller straightening processes. The present model considers the longitudinal movement of a rail through the straightening machine, contact conditions between rail and rollers and kinematic hardening so as to take into account the plastic behaviour of the rail material (steel). These results were compared with the experimental investigations and good agreement was observed. In this respect, this paper presents a novel, more realistic numerical simulation by FEM for the roller straightening process. Finally, an improvement of the straightening process in order to obtain smaller residual stress in the rail section is proposed.     

Determination of the vibration displacements and stresses in the vibrations of structurally inhomogeneous shells using the method of holographic interferometry

We develop a method of determining the vibration displacements and stress-strain state of the surface of a shell of revolution with structural singularities during resonance vibrations. We give the results of experimental studies. Four figures. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, 112–118.     

Thermal stresses in anisotropic cylindrical elastic shells

We investigate the deformation of general anisotropic and inhomogeneous shells, under the action of a given temperature distribution. We assume that the temperature field is a polynomial in the axial coordinate, and we establish the displacements produced by the prescribed thermal field. The results are obtained in the framework of the linear theory for Cosserat thermoelastic shells. The solution is used to study the special case of orthotropic cylindrical shells. Copyright © 2009 John Wiley & Sons, Ltd.     

A phenomenological method of calculating the residual stresses and plastic deformations in a hollow surface-hardened cylindrical sample

A phenomenological method is proposed for calculating the residual stress and plastic deformation fields in a hollow surface-hardened cylindrical sample. Versions of the hardening are considered that lead to isotropy and anisotropy in the plastic deformations in the surface layer. A hardening anisotropy parameter is introduced that relates the axial and circumferential components of the residual plastic deformation tensor. The experimentally determined axial and/or circumferential components of the residual plastic stress tensor are used as the initial information. The tensor fields of the residual stresses and deformations are constructed assuming the hypothesis of surface hardening anisotropy and the absence of secondary plastic compression deformations and that the tangential components of the residual stress tensor and the plastic incompressibility of the material are small. A technique is developed for identifying the parameters of the proposed method. The adequacy is checked using experimental data for test pieces of type 45 and 12X18H10T steels hardened by hydro-shot blasting treatment and of type 45 steel hardened by treatment with a roller. Good agreement is observed between the calculated and experimental results. It is noted that the anisotropic hardening procedure leads to a substantial difference between the circumferential and axial components of the residual stresses in the hardened layer, unlike the case of isotropic hardening where they are practically identical.