Management of the Design Parameters in Optimal Design Problems

Abstract

The solution to the problem of designing rational load-bearing structures should be associated with the direct use of the principles that govern the deformation of a solid. If the functional of the direct problem has as Euler – Lagrange equations and natural boundary conditions the equations and boundary conditions of the accepted deformation theory, then they must correspond to the functional of the design problem, in addition, to additional equations indicating the dependence of the system energy change on the configuration change and the elastic modules of the body material. Possible variations of the configuration functions and modules of elasticity of the material will be infinitely small changes of the functions satisfying the prescriptive requirements to the structure and material; they are continuous and satisfy the requirements of differentiability. Due to the small variations in the functions that determine the configuration, we neglect changes in the arrangement of external forces relative to individual parts of the body and changes in the temperature field.