Optimization Problems Arising from the Design of Pipes Made of Composite Materials

Abstract

The work is devoted to the construction of analytical solutions for the stress-strain state of a cylindrical hollow elastic rod with a layered structure along the radius. Earlier, the problem of finding the stress-strain state of a rod of composite material fixed at one end with the applied forces and moments of forces at the other end was considered. An approximate representation of the solutions was given, which included auxiliary problems on one fragment of the cylinder, consisting of periodically repeating similar fragments. Such auxiliary problems in the general case do not have an analytical solution. In this paper it is shown that in the presence of radial symmetry of the rod section, it is possible to construct a stress-strain state in an analytical form. In addition, tensile and bending stiffness can be presented in an analytical form. The latter circumstance allows us to set a problem of optimizing the stiffness characteristics of a rod with its fixed weight. Optimization is carried out by varying the thickness of the layers of the same materials.