2. Benchmark solution

Analytical solution.

2.1. Benchmark results

Displacement of the middle sheet

Middle sheet constraints, upper and lower sheets.

In modeling \(I\) we calculate the mass, the coordinates of the center of gravity and the terms of the inertia matrix. Analytic expressions are given in the documentation [R3.07.02].

2.1.1. Calculation method used for the reference solution in displacements and constraints

In incompressible:

Passage through the Cartesian system:

2.1.2. Determination of masses, center of gravity and inertia tensor

For shell-type modeling of revolution around an axis \(\mathrm{OZ}\)

1. the mass is equal to:

   

;

1. the coordinates of the center of gravity are:

   

;

2. the inertia tensor with respect to \(O\) is equal to:

1. the inertia tensor with respect to \(G\) is equal to:

Note:

In practice, we overlook the terms en

in these expressions.