<s>
As	O
one	O
of	O
the	O
methods	O
of	O
structural	B-Algorithm
analysis	I-Algorithm
,	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
,	O
also	O
known	O
as	O
the	O
matrix	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
,	O
is	O
particularly	O
suited	O
for	O
computer-automated	O
analysis	O
of	O
complex	O
structures	O
including	O
the	O
statically	B-Algorithm
indeterminate	I-Algorithm
type	O
.	O
</s>
<s>
The	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
is	O
the	O
most	O
common	O
implementation	O
of	O
the	O
finite	B-Application
element	I-Application
method	I-Application
(	O
FEM	O
)	O
.	O
</s>
<s>
The	O
material	O
stiffness	O
properties	O
of	O
these	O
elements	O
are	O
then	O
,	O
through	O
matrix	B-Architecture
mathematics	I-Architecture
,	O
compiled	O
into	O
a	O
single	O
matrix	B-Architecture
equation	I-Architecture
which	O
governs	O
the	O
behaviour	O
of	O
the	O
entire	O
idealized	O
structure	O
.	O
</s>
<s>
The	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
forms	O
the	O
basis	O
for	O
most	O
commercial	O
and	O
free	O
source	O
finite	B-Application
element	I-Application
software	O
.	O
</s>
<s>
The	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
originated	O
in	O
the	O
field	O
of	O
aerospace	O
.	O
</s>
<s>
These	O
included	O
elasticity	O
theory	O
,	O
energy	B-Algorithm
principles	I-Algorithm
in	I-Algorithm
structural	I-Algorithm
mechanics	I-Algorithm
,	O
flexibility	B-Algorithm
method	I-Algorithm
and	O
matrix	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
It	O
was	O
through	O
analysis	O
of	O
these	O
methods	O
that	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
emerged	O
as	O
an	O
efficient	O
method	O
ideally	O
suited	O
for	O
computer	O
implementation	O
.	O
</s>
<s>
The	O
second	O
major	O
breakthrough	O
in	O
matrix	O
structural	B-Algorithm
analysis	I-Algorithm
occurred	O
through	O
1954	O
and	O
1955	O
when	O
professor	O
John	O
H	O
.	O
Argyris	O
systemized	O
the	O
concept	O
of	O
assembling	O
elemental	O
components	O
of	O
a	O
structure	O
into	O
a	O
system	O
of	O
equations	O
.	O
</s>
<s>
Finally	O
,	O
on	O
Nov	O
.	O
6	O
1959	O
,	O
M	O
.	O
J	O
.	O
Turner	O
,	O
head	O
of	O
Boeing	O
’s	O
Structural	O
Dynamics	O
Unit	O
,	O
published	O
a	O
paper	O
outlining	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
as	O
an	O
efficient	O
model	O
for	O
computer	O
implementation	O
.	O
</s>
<s>
If	O
are	O
member	O
deformations	O
rather	O
than	O
absolute	O
displacements	O
,	O
then	O
are	O
independent	O
member	O
forces	O
,	O
and	O
in	O
such	O
case	O
(	O
1	O
)	O
can	O
be	O
inverted	O
to	O
yield	O
the	O
so-called	O
member	O
flexibility	O
matrix	O
,	O
which	O
is	O
used	O
in	O
the	O
flexibility	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
method	O
is	O
then	O
known	O
as	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
advantages	O
and	O
disadvantages	O
of	O
the	O
matrix	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
are	O
compared	O
and	O
discussed	O
in	O
the	O
flexibility	B-Algorithm
method	I-Algorithm
article	O
.	O
</s>
<s>
The	O
first	O
step	O
when	O
using	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
is	O
to	O
identify	O
the	O
individual	O
elements	O
which	O
make	O
up	O
the	O
structure	O
.	O
</s>
<s>
Other	O
elements	O
such	O
as	O
plates	O
and	O
shells	O
can	O
also	O
be	O
incorporated	O
into	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
and	O
similar	O
equations	O
must	O
be	O
developed	O
.	O
</s>
<s>
In	O
the	O
case	O
of	O
a	O
truss	O
element	O
,	O
the	O
global	O
form	O
of	O
the	O
stiffness	B-Algorithm
method	I-Algorithm
depends	O
on	O
the	O
angle	O
of	O
the	O
element	O
with	O
respect	O
to	O
the	O
global	O
coordinate	O
system	O
(	O
This	O
system	O
is	O
usually	O
the	O
traditional	O
Cartesian	O
coordinate	O
system	O
)	O
.	O
</s>
<s>
Once	O
the	O
global	O
stiffness	O
matrix	O
,	O
displacement	O
vector	O
,	O
and	O
force	O
vector	O
have	O
been	O
constructed	O
,	O
the	O
system	O
can	O
be	O
expressed	O
as	O
a	O
single	O
matrix	B-Architecture
equation	I-Architecture
.	O
</s>
<s>
There	O
are	O
several	O
different	O
methods	O
available	O
for	O
evaluating	O
a	O
matrix	B-Architecture
equation	I-Architecture
including	O
but	O
not	O
limited	O
to	O
Cholesky	O
decomposition	O
and	O
the	O
brute	O
force	O
evaluation	O
of	O
systems	O
of	O
equations	O
.	O
</s>
<s>
The	O
method	O
described	O
in	O
this	O
section	O
is	O
meant	O
as	O
an	O
overview	O
of	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
was	O
developed	O
specifically	O
to	O
effectively	O
and	O
easily	O
implement	O
into	O
computer	O
software	O
to	O
evaluate	O
complicated	O
structures	O
that	O
contain	O
a	O
large	O
number	O
of	O
elements	O
.	O
</s>
<s>
Today	O
,	O
nearly	O
every	O
finite	B-Application
element	I-Application
solver	I-Application
available	O
is	O
based	O
on	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
One	O
of	O
the	O
largest	O
areas	O
to	O
utilize	O
the	O
direct	B-Algorithm
stiffness	I-Algorithm
method	I-Algorithm
is	O
the	O
field	O
of	O
structural	B-Algorithm
analysis	I-Algorithm
where	O
this	O
method	O
has	O
been	O
incorporated	O
into	O
modeling	O
software	O
.	O
</s>
