Computer Aided Engineering Design

FINITE ELEMENT METHOD 337

2. Determine the horizontal and vertical displacements at node 2 for the truss assemblage shown. Consider the
   elastic modulus as 65GPa for both trusses.


3. Determine the deflection at node 2 using beam elements for the problem shown below. Verify the result
   with the Euler-Bernoulli analysis for small beam deflections. (Hint: One would have to approximate the
   uniform load distribution with point loads at each node). Will the accuracy improve if the number of beam
   elements is increased? Explain by solving the same problem using three beam elements. Take the elastic
   modulus as 10^6 Nm–2. In both cases, take beam elements of equal lengths.

Figure P11.3

2

(^13)
6 m
60 kN/m

4. Assume the structure in Figure P11.2 as an assemblage of frame elements with the joint at node 2 as rigid.
   Determine the deflections and slope at node 2.


5. Using Eq. (11.10j), derive the elasticity matrix D for the plain strain case. Consider non-zero strains in the
   x-y plane.


6. A triangular lamina is shown in Figure P11.4. Node 4 is the midpoint of nodes 2 and 3. Take the modulus
   as 2.24 GPa, Poisson’s ratio as 0.33 and out-of-plane thickness as 10 mm. Determine the deflections at
   nodes 3 and 4.

Figure P11.4

4

3

1

3kN

1 kN

2

(^12)
4 m
3 m
Figure P11.2
2 10 kN
1
y^3
x
300 m 600 m
400 m
1 2