Modified direct method in static problems of axi-symmetric non-thin plates

Abstract

The initial equations for solving the axisymmetric problem are given and consideredboundary conditions on the end surfaces and average section of the design element. As a result, we get a system of partial differential equations that can be solved by the numerical-analytical (modified) method of straight lines. The transformation of the reduced equations of equilibrium in parts, as well as the reduced models of the boundary conditions of the end surfaces and the average section, are shown. As a result, a boundary value problem for the system of reduced differential equations in ordinary derivatives written in the Cauchy form with boundary conditions of the general form is obtained.
 The thermal conductivity of the cylindrical wall was calculated, the results were compared with analytical calculations and results of other authors, which confirms the reliability of the developed methodology.
 A computer simulation of the stress-strain state of a cylindrical structural element due to the complex action of temperature, force and kinematic effects was carried out.
 Important conclusions have been made for the use of the modified method of straight lines, which is free from the complications that arise when using the classical method of straight lines.