Mass Distribution

The calculation of the mass and inertia of the structure are as follows

$$\begin{aligned}m &= \sum_{}^{}m_{i} \\ \mathbf{x}_{c} &= \frac{\sum_{}^{}\left( m_{i}\mathbf{x}_{i} \right)}{m} \\ \mathbf{I} &= \begin{bmatrix} \sum_{}^{}{I_{xx} + \sum_{}^{}m_{i}\left( {y_{i}}^{2} + {z_{i}}^{2} \right)} & \sum_{}^{}{I_{xy} + \sum_{}^{}m_{i}\left( x_{i}y_{i} \right)} & \sum_{}^{}{I_{xz} + \sum_{}^{}m_{i}\left( x_{i}z_{i} \right)} \\ & \sum_{}^{}{I_{xx} + \sum_{}^{}m_{i}\left( {z_{i}}^{2} + {x_{i}}^{2} \right)} & \sum_{}^{}{I_{yz} + \sum_{}^{}m_{i}\left( y_{i}z_{i} \right)} \\ & & \sum_{}^{}{I_{xx} + \sum_{}^{}m_{i}\left( {x_{i}}^{2} + {y_{i}}^{2} \right)} \\ \end{bmatrix}\end{aligned}$$

where the summations are over all the nodes and $x,y,z$ are the coordinates of the node relative to the centre of mass.

If the mass option is set to ignore the element mass, this calculation is only carried out over the nodal masses. If an additional mass due to load is set the load vector resulting from the load description is calculated and the required component is extracted scaled and converted to mass

$$m_{i} = s\frac{f_{i,j}}{g}$$

where $s$ is the scale factor, $j$ is the specified component and $g$ is the gravity value.