Stability of structural elements of special lifting mechanisms in the form of circular arches

The system of differential equations of stability of circular arches with symmetric sections and the sixth-order resolving ordinary differential equation are derived. It is noted that these equations have variable coefficients and their analytical solution under existing external loads leads to serious mathematical difficulties. The problem of finding exact solutions can be substantially simplified if we use the numerical-analytical version of the boundary element method (BEM). Here it is necessary to have a solution of the resolving equation of the problem, but with constant coefficients. This problem is much simpler than the initial one and can be realized according to the known procedure for constructing the fundamental functions of an ordinary differential equation. In this regard, the constants for integrating the general solutions of the differential equation are determined for the two most common cases and rationing of the fundamental functions in the matrix resolving form is performed. Recommendations are given on the solution of various boundary-value problems of stability of the simple bending of arch elements of special lifting mechanisms using them.