Чисельне дослідження впливу довжини стрижня на його критичні сили

Abstract

The effect of changing the length of a longitudinally compressed rod on its critical forces is numerically investigated. The research is carried out on the example of a two-span rectilinear rod of bending stiffness constant along length, which is compressed by a constant lengthwise longitudinal force and hinged on one of the ends on an absolutely rigid support, and inside - on a support of finite stiffness. The change in the length of the rod occurs due to the movement of the end hinge support with the corresponding increase or decrease of the adjacent section of the rod without changing the position and characteristics of the remaining constraints. The dependence of the critical forces of the rod on the position of this support and, accordingly, on the length of the adjacent compressed section of the rod is investigated. Calculations are performed on the basis of the use of known exact analytical expressions of the influence functions of a rod of constant cross-section compressed by a longitudinal force constant by length. In the considered examples, qualitative signs of increase, decrease, and extremum of simple critical forces when changing the length of the rod, related to the qualitative features of the corresponding buckling forms, established earlier theoretically, were fully confirmed. In particular, exact calculations have shown that the increase or decrease of the simple critical force when the length of the fragment of the rod adjacent to the movable support is changed is determined by the type of the corresponding buckling form in the neighborhood of this support. Different possible configurations of buckling forms are considered, and the behavior of critical forces when changing the length of the rod are considered for each of the configurations. In order to verify the previously established theoretical results, which relate to the study of the behavior of not only the main critical forces, but also higher simple critical forces, which have an arbitrary number in the spectrum, the calculations are carried out in the article for the second critical forces of the rods considered in the given examples. The results of the calculations are shown in the form of graphs, which represent configurations of buckling forms of various possible types in connection with the corresponding changes in critical forces. Graphs of the dependence of the second critical force of the studied rods on their length are also given. It has been demonstrated that under certain conditions, reducing the length of the rod can lead to a reduction in its critical force.