# zbMATH — the first resource for mathematics

Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads. (English) Zbl 1016.74020
Summary: We study the thermomechanical states in a class of functionally graded cylinders under extension, torsion, shearing, pressuring, and temperature changes. Referred to the cylindrical coordinates, the material is cylindrically anisotropic. The only material symmetry is reflectional symmetry with respect to cylindrical surfaces $$r=const$$. The material properties are considered to be radially dependent, such that the conductivity coefficients, thermal coefficients as well as elastic constants depend in a specific manner on $$r$$. Exact solutions for the temperature distribution, thermoelastic deformations and stress fields are determined for inhomogeneous hollow and solid cylinders, with power law dependence of the moduli, subjected to an axial force and a torque at the ends and to surface loads that may vary circumferentially but not axially. In addition, we obtain exact solutions for thermoelastic responses of rotating cylinders.

##### MSC:
 74F05 Thermal effects in solid mechanics 74E10 Anisotropy in solid mechanics 74G05 Explicit solutions of equilibrium problems in solid mechanics
Full Text: