Biomedical Engineering Reference
In-Depth Information
2
4
3
5
1
0
0
0
0
0
cos
2
b
sin
2
b
0
0
sin 2b
0
sin
2
b
cos
2
b
0
0
sin 2b
0
T
ox
¼
0
0
0
cos b
0
sin b
cos
2
b
sin
2
b
0
sin b
cos b
sin b
cos b
0
0
0
0
0
sin b
0
cos b
ð
2
:
42
Þ
Along the oy axis,
2
4
3
5
sin
2
b
cos
2
b
0
0
0
sin 2b
0
1
0
0
0
0
sin
2
b
cos
2
b
0
0
0
sin 2b
T
oy
¼
0
0
0
cos b
sin b
0
0
0
0
sin b
cos b
0
cos
2
b
sin
2
b
sin b
cos b
sin b
cos b
0
0
0
ð
2
:
43
Þ
Along the oz axis,
2
4
3
5
sin
2
b
cos
2
b
0
sin 2b
0
0
sin
2
b
cos
2
b
0
sin 2b
0
0
0
0
1
0
0
0
T
oz
¼
cos
2
b
sin
2
b
sin b
cos b
sin b
cos b
0
0
0
0
0
0
0
cos b
sin b
0
0
0
0
sin b
cos b
ð
2
:
44
Þ
The material matrix after rotation can be defined as,
h
i
T
oz
T
oy
T
T
oy
x
c
current
¼
T
oz
h
x
c
initial
½
½
h
:
ð
2
:
45
Þ
2.2 Weak Form
The strong form system equations are the partial differential system equations
governing the studied physic phenomenon. In contrast, the weak form requires a
weaker consistency on the adopted approximation (or interpolation) functions. The
ideal would be obtaining the exact solution from strong form system equations,
however this is usually an extremely difficult task in complex practical engineering
problems. Formulations based on weak forms are able to produce stable algebraic
system equations and to give a discretized system of equations which leads to more
