Biomedical Engineering Reference
In-Depth Information
Exercises
17.1 A MATLAB script to calculate the shape functions and the derivatives with
respect to the isoparametric coordinates of 4-noded isoparametric bi-linear
elements in some point of the elements may consist of the following code:
% Shape = program to calculate shape functions
xi= ;
eta= ;
x=[,,,]';
y=[,,,]';
N=[0.25
*
(1-xi)
*
(1-eta);
0.25
*
(1+xi)
*
(1-eta);
0.25
*
(1+xi)
*
(1+eta);
0.25
*
(1-xi)
*
(1+eta)]
dNdxi=[-0.25
*
(1-eta);
0.25
*
(1-eta);
0.25
*
(1+eta);
-0.25
*
(1+eta)]
dNdeta=[-0.25
*
(1-xi);
-0.25
*
(1+xi);
0.25
*
(1+xi);
0.25
*
(1-xi)]
y
(10, 6)
(5, 6)
1
2
3
2
4
(0, 4)
(8, 5)
4
1
2
3
(6, 2)
1
(0, 0)
x
To study some of the properties of the shape functions the script will be
completed by considering the elements in the figure above and extended
in the following. In this figure the local node numbering has also been
indicated.
