# CONGM

Concentrated Mass ElementCONGM defines a concentrated mass element at an NLFE grid.

## Format

```
<CONGM
id = "integer"
gid = "integer"
mass = "real"
[
x = "real"
y = "real"
z = "real"
]
i11 = "real"
i22 = "real"
i33 = "real"
[
i21 = "real"
i31 = "real"
i32 = "real"
]/>
```

## Attributes

`id`- Unique identification number.
`gid`- Grid identification number.
`mass`- First grid identification number.
`xyz`- X, Y and Z offset distance from the grid point to the center of gravity. Default for
`x`,`y`and`z`is 0. `i11``i22``i33`- Mass product of inertia about X, Y and Z axes respectively.
`i21``i32``i33`- Mass product of inertia about X-Y, X-Z and X-Y respectively. Default value for all three attributes is 0.

## Example

The example demonstrates the definition of a CONGM element.

`<CONGM id="1" gid="17" mass="10" i11="1" i22="1" i33="1"/>`

## Comments

- The x, y and z coordinates of the mass center of gravity are represented in the global coordinate system.
- The form of the inertia matrix about its center of gravity is
calculated as:

where,

$$\text{mass}={\displaystyle \int \rho dV}$$and,

$$\begin{array}{l}i11=\rho {\displaystyle \int \left({y}^{2}+{z}^{2}\right)dV=}\rho {\displaystyle \int {y}^{2}dV+\rho {\displaystyle \int {z}^{2}dV}}\\ i22=\rho {\displaystyle \int \left({x}^{2}+{z}^{2}\right)dV}=\rho {\displaystyle \int {x}^{2}dV+\rho {\displaystyle \int {z}^{2}dV}}\\ i33=\rho {\displaystyle \int \left({y}^{2}+{x}^{2}\right)dV}=\rho {\displaystyle \int {y}^{2}dV+\rho {\displaystyle \int {x}^{2}dV}}\\ i12=-\rho {\displaystyle \int xydV}\\ i13=-\rho {\displaystyle \int xzdV}\\ i23=-\rho {\displaystyle \int yzdV}\end{array}$$ - All four grids defined for this element must be unique.