Thermoelastic bending of composite plates-disks of a car transmission

Abstract

Anisotropic plates, disks, and shells are currently one of the most common composite elements of constr uctions in machine-building, transport, and instrument-making directions. They are important supporting elements of most machines and mechanisms. At the same time, their safe use requires more advanced calculation methods and models compared to isotropic ones. There is an extremely large number of methods for calculating plates and shells, the use of which should ensure greater or lesser accuracy of the calculation of the entire structure. In some cases, it is enough to calculate the structural element for tension or compression, and in others, it is necessary to add calculations for bending according to the simplest models. One of these models is the classical Kirchhoff-Leav model of the bending of isotropic plates. But in cases where plates or shells are anisotropic, this model can already give large errors and therefore the practice of calculations requires a more accurate model. Therefore, in more complex cases, for structural elements whose physical characteristics in the thickness direction have different values compared to the values along their plane, bending theories of transversely (transversely) isotropic or transtropical plates and shells are used. At the same time, many of these elements work at elevated temperatures, so their influence on the characteristics of the stress-strain state must also be taken into account.

The article uses a model built based on hypotheses that take into account transverse shear and compression and considers the problem of thermoelastic bending of circular transversely isotropic plates-discs. Two cases are considered: when the disc is hard and pinched at the edge; when this disk is in the form of a ring with a free hole. To construct solutions to the problem, the method of linear conjugation of analytic functions of the Mushelishvili complex variable was used.

Key words: refined model of the transtropical plate, transverse shear, compression deformation, linear conjugation method, thermoelastic bending of the disk.