 
 
 
 
 
 
 
  
The expansion of a shell node leads to a set of nodes lying on a straight line. Therefore, the stretch tensor 
 is reduced to the stretch along this line. Let
 is reduced to the stretch along this line. Let 
 be a unit vector parallel to the expansion and
 be a unit vector parallel to the expansion and 
 and
 and 
 unit vectors such that
 unit vectors such that 
 and
 and 
 . Then
. Then 
 can be written as:
 can be written as:
leading to one stretch parameter  . Since the stretch along
. Since the stretch along 
 and
 and 
 is immaterial, Equation (54) can also be replaced by
 is immaterial, Equation (54) can also be replaced by 
|  | (55) | 
representing an isotropic expansion. Equation (53) can now be replaced by
|  |  | |
| ![$\displaystyle + \boldsymbol{w_0}+[\alpha_0 \boldsymbol{R} (\boldsymbol{\theta_0}) - \boldsymbol{I}] \cdot (\boldsymbol{p}-\boldsymbol{q})-\boldsymbol{u_0}.$](img509.png) | (56) | 
Consequently, a knot resulting from a shell expansion is characterized by 3 translational degrees of freedom, 3 rotational degrees of freedom and 1 stretch degree of freedom.
 
 
 
 
 
 
