Thermal and mechanical stresses in cylinders and spheres obeying polar and transversal anisotropy

Andro Alujevič

Theoretical and applied mechanics, Tome 13 (1987) no. 1, p. 1 .

Résumé

In the article, we present analytical resolutions of stresses that occur in the body of thin and long shafts (discs, rings, canes, pipes) and solid and hollow balls made of polar or transversely anisotropic homogeneous linear elastic material. Shafts and balls are subjected to a temperature field, internal and external pressures, and body forces due to centrifugation are taken into account only in shafts. Gravity is also not taken into account. The samples mentioned represent an extension of the known records that were known for a tube and a ball with surface pressures, and partly for rotational disks. We performed the act of conducting with the help of the Navier-Lame equation, which for the radial problem of a shaft and a ball is only one, but contains elastic parameters that depend on the type of anisotropy under discussion. Mathematically, this Euler differential equation is taken, the homogeneous part of which solves the boundary conditions, and the inhomogeneous part contains the influence of temperatures and rotation of the body. The particular solution contains a singularity on the axis of the body of revolution (full body), which can possibly be eliminated by taking into account that there is no difference between the radial and hoop directions. Because of this, radial and hoop stresses are equal to each other on the axis of the body, as required by the equilibrium equation.