1. Reference problem

1.1. Geometry

The configuration studied consists of two coaxial cylindrical shells 4 meters high:

The inner shell has an average radius of \(1m\) and a thickness of \(1\mathrm{cm}\).

The outer shell has an average radius of \(\mathrm{1,10}m\) and a thickness of \(1\mathrm{cm}\).

1.2. Material properties

The material that makes up the two shells is steel. Its physical characteristics are:

\(\rho \mathrm{=}7800\mathit{kg}\mathrm{/}{m}^{3}\)

\(E\mathrm{=}2.{10}^{11}\mathit{Pa}\)

\(\nu \mathrm{=}\mathrm{0,3}\)

1.3. Boundary conditions and loads

The support conditions are the same for both shells: ends embedded in the lower part (\(z\mathrm{=}0\)) and free ends in the upper part (\(z\mathrm{=}4m\)).