<s>
The	O
Unit	B-Algorithm
dummy	I-Algorithm
force	I-Algorithm
method	I-Algorithm
provides	O
a	O
convenient	O
means	O
for	O
computing	O
displacements	O
in	O
structural	O
systems	O
.	O
</s>
<s>
It	O
is	O
applicable	O
for	O
both	O
linear	O
and	O
non-linear	O
material	O
behaviours	O
as	O
well	O
as	O
for	O
systems	O
subject	O
to	O
environmental	O
effects	O
,	O
and	O
hence	O
more	O
general	O
than	O
Castigliano	B-Algorithm
's	I-Algorithm
second	I-Algorithm
theorem	I-Algorithm
.	O
</s>
<s>
Let	O
the	O
consistent	O
set	O
of	O
members	O
 '	O
deformations	O
be	O
given	O
by	O
,	O
which	O
can	O
be	O
computed	O
using	O
the	O
member	B-Algorithm
flexibility	I-Algorithm
relation	I-Algorithm
.	O
</s>
<s>
It	O
can	O
be	O
computed	O
as	O
the	O
inverse	O
of	O
the	O
nodal	O
equilibrium	O
matrix	O
of	O
any	O
primary	B-Algorithm
system	I-Algorithm
derived	O
from	O
the	O
original	O
system	O
.	O
</s>
<s>
It	O
is	O
remarkable	O
that	O
the	O
computation	O
in	O
(	O
2	O
)	O
does	O
not	O
involve	O
any	O
integration	O
regardless	O
of	O
the	O
complexity	O
of	O
the	O
systems	O
,	O
and	O
that	O
the	O
result	O
is	O
unique	O
irrespective	O
of	O
the	O
choice	O
of	O
primary	B-Algorithm
system	I-Algorithm
for	O
B	O
.	O
</s>
<s>
For	O
a	O
general	O
system	O
,	O
the	O
unit	B-Algorithm
dummy	I-Algorithm
force	I-Algorithm
method	I-Algorithm
also	O
comes	O
directly	O
from	O
the	O
virtual	O
work	O
principle	O
.	O
</s>
