Some problems of analysis and optimization of plates and shells

The classical optimization problems of plates and shells to satisfy a priori given geometry and dynamical characteristics are considered. Orthotropic plates and shells with variable thickness and low transverse stiffness are analyzed. First, some useful theorems and their proofs are given. Then the finite approximation of the problem related to optimization of free vibrations of shells with transverse deformation and rotary inertia is discussed. The varational iteration (MVI) and Bubnov-Galerkin (MB) methods are applied, and their convergence and suitability for application to plates and shells analysis are discussed and numerically evaluated.