ENERGY BEGINNING IN THE THEORY OF STRUCTURE SYNTHESIS

Abstract

The theory of construction synthesis is based on the principle of stationary action. The fundamental beginning of the design of structure is the variational principle of structural synthesis with energy content. The increment in the energy of external forces and the potential energy of deformation depends not only on the increments of displacements and internal forces, as provided by the principles of Lagrange and Castigliano, but also on the changes of configuration body and materials modules. The influence of these factors on the potential strain energy is discussed on the example of a tensioned rod and a rod system. A generalization of Vasyutinskii's theorem to the case of a system with stretched and compressed rods is given, which makes it possible to make a transition from minimizing the potential strain energy functional to minimizing the volume of material. Outside of this theorem, volume minimization is possible only when the energy principle is introduced into an additional condition, as evidenced by the dual substitution of the problem for a conditional extremum with integral connections. This situation is illustrated by the example of the formation of an I-section of a console loaded at the end with a moment. When the condition is set in the form of a relative deflection of the end of the console, the dual substitution of the problem takes place. It is unacceptable in the case of setting the admissible stress, excluding the energy content of the additional condition.