I've chosen to use
Prof. Rieg's Z88 Finite Elements Program because
it's free and unlimited and ideal for student use. The theory behind FEM is beyond the scope of this tutorial but you can learn
a great deal from the Z88 manual.
Using a Beam Element No. 13 we create a
General Structure Data File, Z88i1.txt which basically consists of : 2D Analysis, 5 Nodes, 4 Elements, 3DOF per node 15 in total.
Nodal co-ordinates, elements defined and adjacent elements. All elements 1 to 4 have the same properties
Young's Modulus but this time working in metres = 2e11 N/m^2. Poisson's Ratio = 0.3 from tables, Area = 1e-2 m^2,
I = 3.33e-5 m^4
2 5 4 15 1 0 1 0 Z88I1.TXT,produced by Ty
1 3 +0.00000E-000 +0.00000E+000 +0.00000E+000 node #1
2 3 +2.50000E-001 +0.00000E+000 +0.00000E+000 node #2
3 3 +5.00000E-001 +0.00000E+000 +0.00000E+000 node #3
4 3 +7.50000E-001 +0.00000E+000 +0.00000E+000 node #4
5 3 +1.00000E+000 +0.00000E+000 +0.00000E+000 node #5
1 13 element #1
1 2
2 13 element #2
2 3
3 13 element #3
3 4
4 13 element #4
4 5
1 4 +2.00000E+011 +3.00000E-001 1 +1.00000E-002 +0.00000E+000 +0.00000E+000 +3.33333E-005 +1.00000E-001 +0.00000E+000 +0.00000E+000
and the boundary conditions file
Z88i2.txt: Node 1 has 3 DOF u,y,rotz all zero and the load applied to node 5 in the -y direction. More details on the
exact formatting can be found within the Z88 manual.
4 Z88I2.TXT,produced by Ty
1 1 2 +0.00000E+000
1 2 2 +0.00000E+000
1 3 2 +0.00000E+000
5 2 1 -2.00000E+004
Copy the txt files to z88com directory and then launch z88com.
run the z88F
run the z88D nodal stress processor.
run the z88E nodal force processor.
run the z88P to plot the deflection.
Figure 1 - Screen Shot of the Z88 plot program
The nodal results can be found in z88o4.txt file:
output file Z88O2.TXT : displacements, computed by Z88F V10
*************
Knoten U(1) U(2) U(3) U(4) U(5) U(6)
1 +0.0000000E+000 +0.0000000E+000 +0.0000000E+000
2 +0.0000000E+000 -8.5937586E-005 -6.5625066E-004
3 +0.0000000E+000 -3.1250031E-004 -1.1250011E-003
4 +0.0000000E+000 -6.3281313E-004 -1.4062514E-003
5 +0.0000000E+000 -1.0000010E-003 -1.5000015E-003
It's node 5 we're interested in and the displacement in the y direction is U(2) =1 mm.
