Finite Element Techniques for Fluid Flow

50 WEIGHTED RESIDUAL AND VARIATIONAL METHODS

Thus we can write (d) as

„ EI(

2

/π\

4

/

2

/3π\

4

Π _

where a

1

and a

2

are independent of each other. Minimising (f), we

have

OF EI( (π\

4

ΐ) -

n

dF EIL /3π\

4

Π ~

Λ

Solving these equations, we obtain

Til?'

Λι

~~ΤΐΐΑΐ

(g)

a

2=--F7Z4UI (

h

)

We can generalise this result and obtain

α

3

,α

4

,

etc. The n terms

solution for the centre deflection is

»c = ^-4 1+^4 + ^4 + · I (i)

This is a convergent series, thus when n

-►

oo, we obtain the exact

result

^clexact

-

£/

48

1.7 SUBSIDIARY CONDITIONS

In certain cases we want a function to satisfy, in addition to the

boundary conditions, certain other relations, called subsidiary ...