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 glass shells by a computational-experimental method

A method is proposed for determining the technological residual stresses in glass shells of revolution based on the solution of inverse problems of shell theory with proper stresses and the use of experimental data obtained by the photoelastic method. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 100–105.     

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.     

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.     

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.     

The axisymmetric problem of determining the residual stresses in thick plates

We propose a method of determining the residual (technological) stresses in structural elements that can be regarded as plates in a computational model. The initial data are the equations of mechanics for bodies with initial stresses and experimental information obtained using nondestructive physical testing.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 113–119.     

Effect of cooling regime on the shrinkage stresses in glass-reinforced plastic cylindrical shells

Approximate stepwise cooling of the product is proposed as a means of taking into account the effect of the inelastic properties of the resin at high temperatures on the macroscopic shrinkage stresses in glass-reinforced plastic cylindrical shells.     

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.     

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.     

Critical compressive stresses in cylindrical shells composed of orthotropic layers with different orientations

The laws of variation of the strains and critical stresses for smooth thin circular cylindrical glass-reinforced plastic shells based on ÉDT-10P resin have been experimentally investigated at different orientations of the fabric reinforcement. The results of the tests are compared with the theoretical data obtained from the relations of the theory of elasticity of an orthotropic body and orthotropic shells.N. E. Zhukovskii Central Aerohydrodynamic Institute of Production Technology and Organization, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 684–690, July–August, 1973.     

A practical method for determining Green's functions using Hadamard's variational formula

This article studies the behavior of the Green's function as a function of the length of the interval. The solution of the boundary-value problem

$$\begin{gathered} \ddot u - q(t)u = - g(t), 0< t< a \hfill \\ u(0) = 0, \dot u(a) = 0 \hfill \\ \end{gathered} $$     

A generalized Green's function

Summary We present a method in which the given boundary conditions are replaced by integral boundary conditions, so chosen that the Green's function can be constructed without changing the principal spectral properties of the operator.Translated from Litovskii Matematicheskii Sbornik, Vol. 13, No. 1, pp. 109–114, January–March, 1973.