Integration of the Equations of Plane Axisymmetric Problems of the Theory of Elasticity and Thermoelasticity for Layered Solid Cylinders

We propose a modification of the algorithm aimed at the construction of analytic solutions of plane axisymmetric problems of elasticity and thermoelasticity in stresses for solid cylinders formed by radially inhomogeneous coaxial layers. Unlike the original approach based on the application of the method of direct integration and the procedure of generalized differentiation, the proposed modification makes it possible to formulate and solve the governing equations of problems of this kind in terms of the classical derivatives with respect to the radial coordinate. In this way, we simplify the procedure of construction of iterated integral kernels of the resolvent solution of the governing integral equation of continuity to which the solution of the analyzed problems is reduced by the method of direct integration. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.