FEMII-problems 2009.pdf

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FEMII-problems 2009
FEMII - problems
1. Consider the rod shown below and its model made of 2 rod elements. Find the condition number of the
matrix of the FE equations for the structure for E 1 /E 2 =1000 and E 1 /E 2 =2
1
l
2
l
3
E 1
E 2 F
2. Left rod (with the cross-section A 1 ) has been heated by T.
Find the displacement of the node 2 and stresses in the both
elements. YoungÓs modulus E, thermal exp. coef. T .
1
l
2
l
3
A = 2A
A = A
2
1
3. Determine the displacement of the joint D of the truss where the member CD is heated by T= 50°C and
the joint D is loaded by P=1kN.
BD l=1m, d=20mm (steel), =30°
A
B
D
C
P
4. Find the natural frequencies and mode shapes for the rod constrained at:
a) both ends
b) node 1
c) node 3
1
l
2
l
3
5. Build the set of free vibrations equations for the presented problem.
Use the model consisted of 2 beam elements.
Find the natural frequencies for the case a. M=ȾAl.
A =2A A = A
2
M
K
K
M
1/2 l
1/2 l
1/2 l
1/2 l
E,J,A,
E,J,A,
a)
b)
6. Describe the most important factors having impact on accuracy of finite element linear static analysis.
7.What factors influence the frequencies of free vibrations? What information about the dynamic behaviour of
the structure can be provided by performing modal analysis of vibrations.
8.Describe the specific features of nonlinear FEM analysis in comparison to linear model.
1
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