Mechanics of Thin Shells

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The lecture course includes the nonlinear dynamic theory of spatially curved and naturally twisted thermoviscoelastic rods and the linear dynamic theory of thermoelastic shells. These theories take into account the rotational inertia and all the basic types of deformation: bending, twisting, stretching, transverse shear. The theory of rods includes all the known versions of rod theory, but it has a wider range of applicability. In particular, it describes the experimentally discovered Pointing’s effect, which consists in shortening of a rod under twisting deformations.

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 theories is that they can be used to model the dynamics of thin objects with complex internal structure. In particular, it can model multi-layer rods and rods with internal cavities, multi-layer shells, as well as rods and shells with complex microstructure.

In the course of the dynamics of thin-walled structures, 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.

The purpose of discipline - to teach students to deduce the basic equations of the dynamic theory of elastic rods and shells, to solve problems of the dynamics of rods and shells, using exact and approximate analytical methods. In addition, to give an idea about the different versions of the theory of rods and shells on the generalized theory of symmetry of the tensor quantities and its use in determining the structure of the stiffness tensors, as well as the dimensions of the theory and its application. Also, give an idea of ​​the engineering applications of dynamic theory of rods and shells, and the possibility of using different theories of thin-walled structures for modeling of micro- and nano-objects.

Lectures by prof.E.Ivanova File:Lectures_eng.pdf

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