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MAE 4700/5700 (Fall 2008) Example problem – Non-uniform beam
Finite Element Analysis for Mechanical & Aerospace Design Page 1 of 4
In the provided MATLAB software, we consider the following example shown in the
figure. The beam ABC is clamped at the left side and simply supported at the right side.
Dimensions are in m, forces in N and loading p in N/m. Also
4 2
10EI Nm=
. At x=12m,
20V Nt= -
and
20M N m= ×
. Find the deflections, shear forces and moments.
In the given example, we use three elements. We place a node at the application of load
1
P
. We define a variable which controls the discretization in the distributed load region.
Run the program and check that you obtain the following results. Use your ENGRD202
knowledge to verify these results.
Three Elements:
0 2 4 6 8 10 12
-1.5
-1
-0.5
0
x
displacement
Displacements: FE versus analytical beam solutions
FE
Exact Solution