Computer Aided Engineering Design

FINITE ELEMENT METHOD 329

Example 11.4. Consider a rectangular plate cantilevered at one edge as shown in Figure 11.13. The
loads of 1 kN and 2 kN act along the vertical and horizontal directions at node 2. Take the elastic
modulus as 2.24 GPa, Poisson’s ratio as^14 and the out-of-plane thickness as 10 mm.

y

4

2

1

2

3

1 m

2 m

x

2 kN

1 kN

Figure 11.13 Displacement analysis of a

rectangular plate

1

Noting that there are two degrees of freedom per node, the global displacement vector U can be
composed such that for node j,U(2j–1) represents x displacement while U(2j) the y displacement. For
element (1), the stiffness matrix can be calculated as follows:
The strain displacement matrix B 1 from Eq. (11.10i) is

B 1 =^1

2

–1 0 1 0 0 0

00 0–202

0–1–2120

⎛

⎝

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

and the elasticity matrix Dfrom Eq. (11.10l) is

D =^16

15

224 10

1 1

4

0

1

4

10

003

8

××^7

⎛

⎝

⎜

⎜

⎜

⎜

⎞

⎠

⎟

⎟

⎟

⎟

so that ke1 from Eq. (11.10m) is
12 3 4 5 6

kBDBe AtT

sym

111 1

= =^167

15

10

0.56 0 – 0.56 0.28 0 – 0.28

0.21 0.42 – 0.21 – 0.42 0

1.4 – 0.7 – 0.84 0.28

2.45 0.42 – 2.24

0.84 0

2.24

1 2 3 4 5 6

×

⎛

⎝

⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟