Forecasting the Preservation of the Stability of the Forms of Engineering Systems

EasyChair Preprint no. 6969

Abstract

The phenomenon of loss of stability can occur in many cases and in any structures. And in plates, and in shells, and in rod systems. Thus, it is obvious that stability as a phenomenon for both simple systems and complex structures consisting of many elements depends on the stability of individual elements and on their joint work in structures. The loss of stability in many cases can be characterized as a bifurcation[1] of the equilibrium form. For example, a rectilinear rod, when the longitudinal force reaches a critical value, can also take a curved shape, i.e. lose stability.

Two approaches are usually used to establish the equilibrium of the system: 1) the principle of possible displacements, in which: if the system is in equilibrium, the sum of all external and internal forces in any infinitely small displacements equal to zero. 2) the property of the potential energy of the system, which: if the system is in equilibrium, its potential energy (i.e. the energy external and internal forces) has an extreme value.

However, these methods, as signs, do not answer the question whether the equilibrium is stable or unstable. It is known that the Lagrange-Dirichlet principle can answer this question: the equilibrium of a system is stable if its total potential energy is minimal compared to all sufficiently close positions of the system.

In the future, approach №1 will be used in the work to eliminate the problems that have arisen

[1] Bifurcation – splitting, doubling.

Keyphrases: calculation scheme, critical force, critical parameter of L. Euler., loss of stability, main system, Stability equation

@Booklet{EasyChair:6969,
  author = {Vladimir Kulikov},
  title = {Forecasting the Preservation of the Stability of the Forms of Engineering Systems},
  howpublished = {EasyChair Preprint no. 6969},

  year = {EasyChair, 2021}}