Mechanics of Shells
The course includes the linear dynamic theory of thermoelastic shells. Theory of shells includes the most general shell theory of 12th order, which is useful when describing the nanosized scale level objects, the shell theory of 10th order, designed for engineering applications in the case of sufficiently thick shells, as well as the Kirchhoff-Love shell theory. The main peculiarity of the theory is that it can be used to model the dynamics of thin objects with complex internal structure. In particular, it can model multi-layer shells, as well as shells with complex microstructure. In the course the use of the following methods is demonstrated: the general methods of the continuum mechanics with rotational degrees of freedom, the differential geometry, the direct tensor calculus, the generalized theory of symmetry, the dimension theory, methods for constructing exact solutions of differential equations, asymptotic methods for solving differential equations, and in particular, differential equations with a small parameter at the highest derivative.