<s>
The	O
applied	B-Algorithm
element	I-Algorithm
method	I-Algorithm
(	O
AEM	O
)	O
is	O
a	O
numerical	O
analysis	O
used	O
in	O
predicting	O
the	O
continuum	O
and	O
discrete	O
behavior	O
of	O
structures	O
.	O
</s>
<s>
Exploration	O
of	O
the	O
approach	O
employed	O
in	O
the	O
applied	B-Algorithm
element	I-Algorithm
method	I-Algorithm
began	O
in	O
1995	O
at	O
the	O
University	O
of	O
Tokyo	O
as	O
part	O
of	O
Dr.	O
Hatem	O
Tagel-Din	O
'	O
s	O
research	O
studies	O
.	O
</s>
<s>
The	O
term	O
"	O
applied	B-Algorithm
element	I-Algorithm
method	I-Algorithm
"	O
itself	O
,	O
however	O
,	O
was	O
first	O
coined	O
in	O
2000	O
in	O
a	O
paper	O
called	O
"	O
Applied	B-Algorithm
element	I-Algorithm
method	I-Algorithm
for	O
structural	O
analysis	O
:	O
Theory	O
and	O
application	O
for	O
linear	O
materials	O
"	O
.	O
</s>
<s>
The	O
modeling	O
of	O
objects	O
in	O
AEM	O
is	O
very	O
similar	O
to	O
modeling	O
objects	O
in	O
FEM	B-Application
.	O
</s>
<s>
The	O
main	O
difference	O
between	O
AEM	O
and	O
FEM	B-Application
,	O
however	O
,	O
is	O
how	O
the	O
elements	O
are	O
joined	O
together	O
.	O
</s>
<s>
To	O
have	O
a	O
general	O
stiffness	B-Algorithm
matrix	I-Algorithm
,	O
the	O
locations	O
of	O
element	O
and	O
contact	O
springs	O
are	O
assumed	O
in	O
a	O
general	O
position	O
.	O
</s>
<s>
The	O
stiffness	B-Algorithm
matrix	I-Algorithm
components	O
corresponding	O
to	O
each	O
degree	O
of	O
freedom	O
are	O
determined	O
by	O
assuming	O
a	O
unit	O
displacement	O
in	O
the	O
studied	O
direction	O
and	O
by	O
determining	O
forces	O
at	O
the	O
centroid	O
of	O
each	O
element	O
.	O
</s>
<s>
The	O
2D	O
element	O
stiffness	B-Algorithm
matrix	I-Algorithm
size	O
is	O
6	O
×	O
6	O
;	O
the	O
components	O
of	O
the	O
upper	O
left	O
quarter	O
of	O
the	O
stiffness	B-Algorithm
matrix	I-Algorithm
are	O
shown	O
below	O
:	O
</s>
<s>
The	O
stiffness	B-Algorithm
matrix	I-Algorithm
depends	O
on	O
the	O
contact	O
spring	O
stiffness	O
and	O
the	O
spring	O
location	O
.	O
</s>
<s>
The	O
stiffness	B-Algorithm
matrix	I-Algorithm
is	O
for	O
only	O
one	O
pair	O
of	O
contact	O
springs	O
.	O
</s>
<s>
However	O
,	O
the	O
global	O
stiffness	B-Algorithm
matrix	I-Algorithm
is	O
determined	O
by	O
summing	O
up	O
the	O
stiffness	O
matrices	O
of	O
individual	O
pairs	O
of	O
springs	O
around	O
each	O
element	O
.	O
</s>
<s>
Consequently	O
,	O
the	O
developed	O
stiffness	B-Algorithm
matrix	I-Algorithm
has	O
total	O
effects	O
from	O
all	O
pairs	O
of	O
springs	O
,	O
according	O
to	O
the	O
stress	O
situation	O
around	O
the	O
element	O
.	O
</s>
<s>
The	O
3D	O
stiffness	B-Algorithm
matrix	I-Algorithm
may	O
be	O
deduced	O
similarly	O
.	O
</s>
<s>
The	O
applied	B-Algorithm
element	I-Algorithm
method	I-Algorithm
is	O
currently	O
being	O
used	O
in	O
the	O
following	O
applications	O
:	O
</s>
