The paper presents an algorithm for calculating the stability of the form of equilibrium of the first kind of compressed discrete systems by the method of displacements in combination with themethods of iterations and bisection. The use of the displacement method in combination with the iteration and bisection methods makes it possible to effectively determine the minimum critical stress or strain at the first bifurcation and their corresponding form of loss of stability, both for statically determined and statically undetectable systems. This approach, using matrixforms, makes it possible to significantly simplify the calculations of the analytical condition for the loss of stability of compressed discrete systems (the stability loss equation), which has high orders, as well as to construct the form of loss of stability corresponding to a critical load, that is, to solve the problem of loss of stability of equilibrium. The calculation of the compressed discrete system on the stability of the form of equilibrium actually reduces to the solution of the difficultly described nonlinear transcendental equation, which is the equation of loss of stability. The difficulty lies in the absence of an analytical solution of such an equation due to the presence of complex functions of Zhukovsky, which have transcendental functions in their structure. Such solution can be performed only with the use of numerical methods. This algorithm for calculating the loss of equilibrium of the first kind of compressed discrete systems by displacement in combination with the methods of iteration and bisection is implemented in the software complex "Persist" for a PC in Windows OS. The program was approbated and implemented in theeducational process at the Department of Structural and Theoretical Mechanics of the Poltava National Technical Yuri Kondratyuk University during the training of specialists in engineering specialties.
Stability of Nonlinear Autonomous Quadratic Discrete Systems in the Critical Case
