Finite Element Techniques for Fluid Flow

WEIGHTED RESIDUAL AND VARIATIONAL METHODS 23

These equations can be written, after integration,

(1)

(m)

We can now compare the results for the first and second approxima-

tions:

X =

0-50

100

M

(1)

25/64

25/48

dn

(1)

dx

00

M

(2)

107/278

77/139

du<

2)

~dx~

17/139

Note that, in the second case,

du

dx

7^0

but if we increased the number of trial functions the solution would

tend to satisfy the boundary condition du/dx = 0.

Example 1.9

Consider the case of a prismatic beam on an elastic foundation,

for which the equilibrium equation (Figure 1.4) is

dx

4

EI

^Zi + kv = p

(a)

where E is the modulus of elasticity, / the moment of inertia, k the

foundation constan ...