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Mathematical models and methods for determination of axisymmetric residual stresses in a finite cylinder are considered. The model of residual stresses is built using the conception of incompatible eigenstrain tensor. Within the frame of this model, a direct problem for residual stresses determination is formulated. A method based on the variational method of homogeneous solutions is developed for solving the direct problem. Using the obtained solution, features of residual stresses, caused by continuous and piece-wise homogeneous distributions of eigenstrain components are studied. A variational formulation of the inverse problem for residual stresses determination on the base of empirical data obtained by a photoelasticity method is suggested. The inverse problem is solved numerically with the use of iterative calculations of values of the criterion functional. The results presented in the paper can be used for the development of methods and means for nondestructive testing and engineering characterization of materials and structural elements.

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