Stability of multispan rods

Abstract

Objective. In the design of complex engineering structures, the problem of stability is now becoming especially relevant. With the need to meet the conditions of strength, rigidity in calculations and design, it is imperative to ensure the stability of equilibrium as the most important requirement. Regardless of the type of strength calculations (verification, design, load), the calculation of a structure for stability, even in the simplest formulation, is reduced to the determination of critical forces. This allows us to estimate the stability margin of the structure under a given load. The complexity of determining the critical parameters of the impact increases with the complexity of the system under consideration.Method. The use of the finite difference method is a feature in solving systems of equations in problems with boundary conditions.Result. The exact values of critical forces in non-classical problems of the stability of compressed rods are determined, which is proved by the obtained curve from the monitor screen.Conclusion. The main points of the theory of calculation in the study of the stability of multi-span rods are outlined. To find the critical forces of a multi-span rod on elastic supports, a simple algorithm for solving problems is given.

Keywords

• многопролётные стержни
• прочность
• устойчивость
• критические силы
• переменные сечения
• упругие опоры
• численные методы
• собственные значения и формы
• метод конечных разностей
• графический способ
• дифференциальные уравнения
• квадратная матрица
• прогибы граничные условия