We present an analytical approach for constructing a solution to the plane axisymmetric elasticity and thermoelasticity problems for a multilayer solid cylinder with arbitrarily variable material properties within each layer. The problems were attempted by means of the direct integration method along with the generalized functions technique. By this means, an explicit-form solution is obtained which allows for the adequate analysis of stresses and displacements in multilayer nonhomogeneous cylinders. Special attention is given to the interlayer stress distributions for the cases of discontinuous, continuous, and smooth variation of the material properties.

Herein, the effect of material inhomogeneity on the temperature and stress distributions in functionally graded solids is analyzed. Assuming the inaccessibility of the inner surface of a multilayer functionally graded hollow sphere for the direct monitoring of the temperature in real time, the problem on identifying the temperature on this surface is formulated by implementing the temperature and circumferential strain given on the outer surface. The material properties within each sphere layer are assumed to be arbitrary functions of the radial coordinate. By representing the material properties of the sphere in the form of stepwise‐variable functions and implementing the generalized derivative technique, a method for the reduction of the formulated problem to an inverse thermoelasticity problem is developed. Using the finite difference method, a numerical algorithm for solving the inverse problem is suggested. The stability of the proposed numerical algorithm concerning the input perturbation is verified.

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