Steady thermal stresses in functionally graded eccentric polygonal cylinder with circular hole

Steady thermal stresses in functionally graded, eccentric, regular polygonal cylinders with a circular hole are analyzed by the stress function method. The Young’s modulus E, thermal conductivity k, and the thermal expansion coefficient \(\alpha \) are assumed to be power functions of inner radius r. Cylindrical coordinates (r, \(\theta \)) are used to formulate the basic equations in terms of a stress function. The unknown coefficients of the stress function are determined using both the boundary conditions and the conditions of the single-valuedness of rotation and displacements for non-homogeneous materials. Numerical calculations were performed for eccentric, regular triangular, quadrangular, pentagonal, hexagonal, heptagonal, and octagonal cylinders with a circular hole. The locations of maximum thermal stresses for each polygon, and the effects of eccentricity, the number of vertices, and radial thickness on thermal stresses are clarified.