МЕТОД ЭНЕРГИИ В РАСЧЕТЕ НА УСТОЙЧИВОСТЬ ПЛОСКОЙ ФОРМЫ ИЗГИБА КОНСОЛЬНОЙ ПОЛОСЫ С УЧЕТОМ СОБСТВЕННОГО ВЕСА

Abstract

the problem of bending a strip by a force applied at the end is not of practical interest. Such method of loading and securing the ends is interesting only because it is most convenient to implement it on experience, which makes it possible to verify the Prandtl theory. When conducting experiments, there is a need for two corrections: it is necessary to evaluate the influence of the self-weight of the strip and the effect of increasing or decreasing the point of force application. As we are talking about small corrections, it is quite enough to use only the first approximation for calculations. An effective version of the energy method is recommended. It is used to calculate rectangular cantilever strips for stability of a flat bending shape, taking into account its own weight. The essence of this variant of the method is to use the Lagrange variational principle instead of the condition for equality of the potential strain energy and the work of external forces. The proposed approach allows us to perform machine implementation of calculations and take into account an arbitrary number of members of the series. The presented solution of the problem for the cantilever beam takes into account its own weight and the action of concentrated force.