B.P. Geghamyan (email@example.com)
The article considers the problem of optimal design of inhomogeneous orthotropic cylindrical shells. Coefficients of elasticity and density of the shell material are variable. We consider the case where both the elasticity coefficients and the density depend on the same function, with correspondingly different multipliers of precision. That function is the optimal design control parameter. The objective functional in the problem is the mass of the shell. To solve the problem, uncertain Lagrange multipliers are introduced and an extended objective function is constructed. Using the extremum variational principle of functionals, a system of nonlinear differential equations is obtained, which, together with the boundary conditions, constitutes a necessary condition for optimality.
Problems of this kind, in addition to their theoretical significance, are also of great practical importance. These problems will be of particular importance in the design, development and production of wear parts and assemblies of technical equipment necessary for rescue operations in emergency situations, as well as in order to reduce costs and increase service life, which is directly related to the problem under consideration.
Key words: membrane, optimal, design, inhomogeneous, orthotropic, mass, functional, variational, elasticity, coefficient.