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-coUocation method.Residual stresses are those that exist in structural elements in the absence of external forces. Such stresses arise, in particular, as the result of various technological processes and have significant influence on the durability, strength, and reliability of the structures. In the complex of methods of determining and controlling the residual stresses an important place belongs to nondestructive (physical) methods [3]. For shell structures made of optically active materials, especially glass, the method of integral photoelasticity, in which tangential and normal illumination of the shells has been used [4], has proved to be effective. However, by this method one can exhibit only some of the components of the residual stress tensor. For example, for a shell of zero Gaussian curvature (cylinders, cones, and the like) this method does not make it possible to determine the circumferential components of the residual stresses, and for spherical shells with nonzero Gaussian curvature in the presence of metal inclusions it is impossible to find the circumferential components near the inclusion in this way because of the opaqueness of the metal.In this connection an experimental-theoretical method has been proposed and developed for determining the residual stresses in compound glass shells [3]. The method is based on solving inverse conditionally correct problems of recovering the residual strain field and the stress-strain state of a shell from part of the values obtained experimentally.Let us briefly describe the essence of the method. For a specific set of technological conditions of manufacturing a glass structure we describe the field of free residual strains whose incompatibility produces the residual stresses, taking account of the a priori picture of its qualitative behavior, by a certain function e ~ that contains a certain set of unknown parameters. Substituting the function e ~ in the equation of the theory of shells with intrinsic stresses, we find the solution of this system and write expressions for determining the residual stresses in which the unknown parameters occur. Equating the experimental values of some of the components of the residual stress tensor to the expressions corresponding to them computed theoretically, we find the unknown parameters. We find the width of the zone of localization of the residual strain field near the weld seam from the condition that a certain functional for the difference between the theoretical and experimental values of the stresses must have a minimum. Thus we recover the field of free residual strains, as the cause of the residual stresses, from part of the values of the stress tensor obtained experimentally.We now c...

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