Models of Deformation of Plates with Double Anisotropy

Abstract

Special cases of transverse bending of structurally orthotropic annular plates made of materials whose deformation and strength characteristics depend on the type of stress state are considered. Such plate materials can be characterized as structures with anisotropy of a twofold nature. The plates were loaded with a uniformly distributed transverse load. In addition, when setting the problem of structural mechanics of plates, it was taken into account that all structures are operated not in an inert space, but in an environment with variable temperature parameters. The connectedness of thermomechanical problems is noticeable only in the short initial time interval of the heat transfer process before the steady-state temperature drop is stabilized. Therefore, in the present study, the problem of thermal force loading of annular plates was considered in an unrelated formulation. In this case, the general problem is divided into two independent ones: structural mechanics and thermodynamics. Given that the generally accepted theories of plates, in the case of anisotropy of a twofold nature, do not allow us to obtain acceptable results, and the known models intended for calculating their stress-strain states have gross non-physical limitations and disadvantages, the presented work is focused on the use of the normalized stress method. The system of differential equations for the problem of transverse bending of annular plates made of materials with complicated thermomechanical properties is obtained below. Particular solutions with characteristic results of calculating the stress-strain state of plates are presented, and their brief analysis is carried out.