Przybliżone Wyznaczanie Siły Krytycznej z Oszacowaniem Bledu przy Wyboczeniu Pręta o Zmiennym Przekroju Poprzecznym

In the present paper, the trace of the kernel of an integral equation is used to obtain the solution of the buckling problem of a simply supported bar with variable rigidity. A numerical example is given in which, for a certain practical case of variable rigidity, the critical force is approximated from above and from below, thus obtaining an appraisal of the error. The lower value of the critical force is obtained by means of the general solution by the trace method,
and the upper value by means of the Galerkin method. The practical advantage of using both methods simultaneously is shown. The trace method, which enables the obtainment of an approximation from above, requires usually more labour than energy and orthogonalization methods, which, however, give only an approximation from below.
For various ratios of the moments of inertia at the support and the middle point, coefficients enabling practical determination of the critical force are computed and tabulated, using the equations derived.