Inverse problem of optical monitoring of residual stresses in piecewise-homogeneous cylindrical shells

Abstract

We consider the inverse problem of determination of the stress-strain state of a circular cylindrical shell formed by two pans of different nature joined with a circular weld. As initial data, we use the results of polarization-optical measurements. For the general case without axial symmetry, we establish the relationships between the measured parameters and the stressed state of the shell. The inverse problem is posed within the framework of a mathematical model according to which residual stresses are caused by the geometric incompatibility of elastic strains. In this model, the tensor of total strain includes the elastic and inelastic (free) components. The latter takes into account the structural inhomogeneity acquired by a material in the processes of manufacturing and technological treatment. We propose a method for the solution of the inverse problem based on the minimization of a functional combining the mathematical model of the stressed state with the results of optical measurements. The results of qualitative analysis are presented for the axially symmetric case.