АНИЗОТРОПТЫ ЖӘНЕ БІРТЕКТІ ЕМЕС СЫРЫҚТАРДЫҢ БҰРАЛУЫ

Abstract

Torsion of anisotropic and inhomogeneous rods is a complex elastic problem in which the mechanical properties of the material depend on its spatial direction. This phenomenon is characterized by twisting of its cross-sections along their axis under the action of a torque acting on the rod. Anisotropic and composite materials are widely used in modern construction, aviation, and mechanical engineering. To predict their strength, reliability, and long-term service life, it is necessary to understand their behavior under torsion. Therefore, it is necessary to generalize the classical formulas obtained for traditional isotropic materials. In this regard, the study of torsion of anisotropic inhomogeneous rods has become a relevant area in modern mechanics and the theory of composite materials. Analytical calculation of anisotropic torsion is quite complex. Therefore, this topic provides impetus for the development of new analytical theory and numerical methods. This article demonstrates that the stress function arising from the torsion of an elastic rod is expressed by Poisson's equation. This paper uses a new generalized theory of complex numbers to find a general solution to the Poisson equation containing a mixed independent second-order derivative.