CONGM

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

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

   Figure 1.

   
   
   
   where, (1)

   $$\text{mass}={\displaystyle \int \rho dV}$$
   and, (2)

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