Computer Aided Engineering Design

FINITE ELEMENT METHOD 321

The assembled matrix K is

123 45678

K = 10

12 6 – 12 6 0 0 0 0

64 –6 2 0 0 0 0

–12 –6 12+6 –6+3 –6 3 0 0

62–6+34+2 –3 1 0 0

0 0 –6 –3 6+12 –3+3 –12 3

0 0 3 1 – 3 + 3 2 +1 – 3 0.5

00 0 0 –12 –312–3

0 0 0 0 3 0.5 – 3 1

6

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎢⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

1 2 3 4 5 6 7 8

12 34 5 67 8

or K = 10

126–1260000

64–620000

–12 –6 18 – 3 – 6 3 0 0

62–36–31 0 0

0 0 – 6 – 3 18 0 – 12 3

003103–30.5

000 0–12–312–3

0 0 0 0 3 0.5 – 3 1

1

2

3

6

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥

44

5

6

7

8

ΕΙ =^54

× 105 Nm^2

EI = 10 × 105 Nm^2

50 kN

100 kN

EI = 5 × 105 Nm^2

1 m 1 m 0.5 m

(a)

1 Element 1^23 Element 2 Element 3

4

(b)

Figure 11.8 (a) A composite beam model and (b) the finite element model