Stability analysis of thin-walled rods by the numerical analytical method of boundary elements

The application of the numerical analytical method of boundary elements for solving problems of flat bending stability of thin-walled rod systems under any arbitrary combination of transverse loads is presented. The basic cases when the bending moment is zero and when it is constant are considered. A solution is also constructed for the case when clean bending takes place only in some part of the rod. In the considered cases the rod is hinged at the ends, which does not influence in any way the generality of the solution because of peculiarities of NA BEM; the difference will be only in expressions of constants of integration and fundamental functions of this or that problem. Numerical realization of the developed algorithm is shown on the example of an I-beam cross-section rod. The value of the minimum critical moment calculated in the paper is exactly equal to its value determined by S. P. Timoshenko’s formula It is pointed out that this approach allows us to obtain the solutions of the complex problems of the theory of stability of thin-walled rods when restrictions on boundary conditions are removed, different transverse loadings and any structure of rod systems including frames and uncut beams can be taken into account. With an arbitrary law of bending moment change, it is proposed to replace this arbitrary law by a stepwise dependence, i.e., a system with distributed parameters is replaced by a set of systems with constant parameters.