2. Reference solution

2.1. Calculation method

Mass and center of gravity:

\(\begin{array}{}m=\rho \underset{v}{\int }\mathrm{dv}=\rho \underset{v}{\int }\mathrm{dx.dy.dz}\\ {x}_{G}=\frac{\underset{v}{\int }\mathrm{x.dv}}{m}{y}_{G}=\frac{\underset{v}{\int }\mathrm{y.dv}}{m}{z}_{G}=\frac{\underset{v}{\int }\mathrm{z.dv}}{m}\end{array}\)

Inertia tensor:

\(\begin{array}{cc}{I}_{\mathrm{xx}}=\rho \underset{v}{\int }(\mathrm{y²}+\mathrm{z²})\mathrm{.}\mathrm{dv}& {I}_{\mathrm{xy}}=\rho \underset{v}{\int }\mathrm{x.y.dv}\\ {I}_{\mathrm{yy}}=\rho \underset{v}{\int }(\mathrm{x²}+\mathrm{z²})\mathrm{.}\mathrm{dv}& {I}_{\mathrm{xz}}=\rho \underset{v}{\int }\mathrm{x.z.dv}\\ {I}_{\mathrm{zz}}=\rho \underset{v}{\int }(\mathrm{x²}+\mathrm{y²})\mathrm{.}\mathrm{dv}& {I}_{\mathrm{yz}}=\rho \underset{v}{\int }\mathrm{y.z.dv}\end{array}\)

2.2. Reference quantities and results

Masses and inertias for the various models.

2.3. Uncertainty about the solution

Note:

For one of the meshes modelled in shells, the solution is numerical (not regression).