In 'data' (type: pandas.Series), the following parameters shall be specified.
keyword |
type |
description |
Submodel name |
str |
name of the submodel |
Start ID |
int |
starting node ID for this element |
Breakdown U |
int |
number of divisions in X direction |
Breakdown V |
int |
number of divisions in Y direction |
Breakdown W |
int |
number of divisions in Z direction |
Node positions |
str |
'EDGE' or 'CENTERED' |
XMax [mm] |
float |
X side length of the rectangle |
YMax [mm] |
float |
Y side length of the rectangle |
ZMax [mm] |
float |
Z side length of the rectangle |
X [mm] |
float |
X coordinate of the element origin |
Y [mm] |
float |
Y coordinate of the element origin |
Z [mm] |
float |
Z coordinate of the element origin |
rot X [deg] |
float |
X roation angle of the ZYX Euler angles |
rot Y [deg] |
float |
Y roation angle of the ZYX Euler angles |
rot Z [deg] |
float |
Z roation angle of the ZYX Euler angles |
XMIN optical |
str |
optical property name of the XMIN surface |
XMAX optical |
str |
optical property name of the XMAX surface |
YMIN optical |
str |
optical property name of the YMIN surface |
YMAX optical |
str |
optical property name of the YMAX surface |
ZMIN optical |
str |
optical property name of the ZMIN surface |
ZMAX optical |
str |
optical property name of the ZMAX surface |
Material |
str |
name of the bulk material |
XMIN group |
str |
analysis group name of the XMIN surface |
XMAX group |
str |
analysis group name of the XMAX surface |
YMIN group |
str |
analysis group name of the YMIN surface |
YMAX group |
str |
analysis group name of the YMAX surface |
ZMIN group |
str |
analysis group name of the ZMIN surface |
ZMAX group |
str |
analysis group name of the ZMAX surface |
Color |
int |
color code |
Comment |
str |
unique comment within the submodel for specifying the element |
In 'data' (type: pandas.Series), the following parameters shall be specified.
keyword |
type |
description |
Submodel name |
str |
name of the submodel |
Start ID |
int |
starting node ID for this element |
Breakdown U |
int |
number of divisions in angular direction |
Breakdown V |
int |
number of divisions in radial direction |
Breakdown W |
int |
number of divisions in height direction |
Node positions |
str |
'EDGE' or 'CENTERED' |
Rmax [mm] |
float |
max radius of the solid cylinder |
Rmin [mm] |
float |
min radius of the solid cylinder |
Height [mm] |
float |
height of the cylinder |
Start angle [deg] |
float |
start angle of the cylinder |
End angle [deg] |
float |
end angle of the cylinder |
X [mm] |
float |
X coordinate of the element origin |
Y [mm] |
float |
Y coordinate of the element origin |
Z [mm] |
float |
Z coordinate of the element origin |
rot X [deg] |
float |
X roation angle of the ZYX Euler angles |
rot Y [deg] |
float |
Y roation angle of the ZYX Euler angles |
rot Z [deg] |
float |
Z roation angle of the ZYX Euler angles |
GMIN optical |
str |
optical property name of the GMIN surface |
GMAX optical |
str |
optical property name of the GMAX surface |
RMIN optical |
str |
optical property name of the RMIN surface |
RMAX optical |
str |
optical property name of the RMAX surface |
HMIN optical |
str |
optical property name of the HMIN surface |
HMAX optical |
str |
optical property name of the HMAX surface |
Material |
str |
name of the bulk material |
GMIN group |
str |
analysis group name of the GMIN surface |
GMAX group |
str |
analysis group name of the GMAX surface |
RMIN group |
str |
analysis group name of the RMIN surface |
RMAX group |
str |
analysis group name of the RMAX surface |
HMIN group |
str |
analysis group name of the HMIN surface |
HMAX group |
str |
analysis group name of the HMAX surface |
Color |
int |
color code |
Comment |
str |
unique comment within the submodel for specifying the element |
In 'data' (type: pandas.Series), the following parameters shall be specified.
keyword |
type |
description |
Submodel name |
str |
name of the submodel |
Start ID |
int |
starting node ID for this element |
Breakdown U |
int |
number of divisions in angular direction |
Breakdown V |
int |
number of divisions in radial direction |
Breakdown W |
int |
number of divisions in height direction |
Node positions |
str |
'EDGE' or 'CENTERED' |
Rmax [mm] |
float |
max radius of the solid cylinder |
Rmin [mm] |
float |
min radius of the solid cylinder |
Start angle [deg] |
float |
start angle of the sphere in the azimuth direction |
End angle [deg] |
float |
end angle of the sphere in the azimuth direction |
Bmin [deg] |
float |
start angle of the sphere in the elevation direction |
Bmax [deg] |
float |
end angle of the sphere in the elevation direction |
X [mm] |
float |
X coordinate of the element origin |
Y [mm] |
float |
Y coordinate of the element origin |
Z [mm] |
float |
Z coordinate of the element origin |
rot X [deg] |
float |
X roation angle of the ZYX Euler angles |
rot Y [deg] |
float |
Y roation angle of the ZYX Euler angles |
rot Z [deg] |
float |
Z roation angle of the ZYX Euler angles |
GMIN optical |
str |
optical property name of the GMIN surface |
GMAX optical |
str |
optical property name of the GMAX surface |
RMIN optical |
str |
optical property name of the RMIN surface |
RMAX optical |
str |
optical property name of the RMAX surface |
BMIN optical |
str |
optical property name of the HMIN surface |
BMAX optical |
str |
optical property name of the HMAX surface |
Material |
str |
name of the bulk material |
GMIN group |
str |
analysis group name of the GMIN surface |
GMAX group |
str |
analysis group name of the GMAX surface |
RMIN group |
str |
analysis group name of the RMIN surface |
RMAX group |
str |
analysis group name of the RMAX surface |
BMIN group |
str |
analysis group name of the HMIN surface |
BMAX group |
str |
analysis group name of the HMAX surface |
Color |
int |
color code |
Comment |
str |
unique comment within the submodel for specifying the element |
In 'data' (type: pandas.Series), the following parameters shall be specified.
keyword |
type |
description |
Submodel name |
str |
name of the submodel |
Start ID |
int |
starting node ID for this element |
Breakdown U |
int |
number of divisions in angular direction |
Breakdown V |
int |
number of divisions in radial direction |
Breakdown W |
int |
number of divisions in height direction |
Node positions |
str |
'EDGE' or 'CENTERED' |
Base Rmax [mm] |
float |
max radius of the cone base surface |
Base Rmin [mm] |
float |
min radius of the cone base surface |
Top Rmax [mm] |
float |
max radius of the cone top surface |
Top Rmin [mm] |
float |
min radius of the cone top surface |
Height [mm] |
float |
height of the cylinder |
Start angle [deg] |
float |
start angle of the cylinder |
End angle [deg] |
float |
end angle of the cylinder |
X [mm] |
float |
X coordinate of the element origin |
Y [mm] |
float |
Y coordinate of the element origin |
Z [mm] |
float |
Z coordinate of the element origin |
rot X [deg] |
float |
X roation angle of the ZYX Euler angles |
rot Y [deg] |
float |
Y roation angle of the ZYX Euler angles |
rot Z [deg] |
float |
Z roation angle of the ZYX Euler angles |
GMIN optical |
str |
optical property name of the GMIN surface |
GMAX optical |
str |
optical property name of the GMAX surface |
RMIN optical |
str |
optical property name of the RMIN surface |
RMAX optical |
str |
optical property name of the RMAX surface |
HMIN optical |
str |
optical property name of the HMIN surface |
HMAX optical |
str |
optical property name of the HMAX surface |
Material |
str |
name of the bulk material |
GMIN group |
str |
analysis group name of the GMIN surface |
GMAX group |
str |
analysis group name of the GMAX surface |
RMIN group |
str |
analysis group name of the RMIN surface |
RMAX group |
str |
analysis group name of the RMAX surface |
HMIN group |
str |
analysis group name of the HMIN surface |
HMAX group |
str |
analysis group name of the HMAX surface |
Color |
int |
color code |
Comment |
str |
unique comment within the submodel for specifying the element |
This function returns the volume of the given SolidCone element.
The volume of a SolidCone with Start angle = 0° and End angle = 360° can be calculated by
$$
\begin{align}
&\pi \int_{0}^{H} \left(R_\mathrm{base} - \frac{R_\mathrm{top} - R_\mathrm{base}}{H} x\right)^2 dx
- \pi \int_{0}^{H} \left(r_\mathrm{base} - \frac{r_\mathrm{top} - r_\mathrm{base}}{H} x\right)^2 dx \\
&= \pi \int_{0}^{H} \left\{ \left( \frac{R_\mathrm{top} - R_\mathrm{base}}{H} \right)^2 x^2 + 2 R_\mathrm{base} \left( \frac{R_\mathrm{top} - R_\mathrm{base}}{H} \right) x + R_\mathrm{base}^2 \right\} dx
- \pi \int_{0}^{H} \left\{ \left( \frac{r_\mathrm{top} - r_\mathrm{base}}{H} \right)^2 x^2 + 2 r_\mathrm{base} \left( \frac{r_\mathrm{top} - r_\mathrm{base}}{H} \right) x + r_\mathrm{base}^2 \right\} dx \\
&= \pi \left[ \left( \frac{R_\mathrm{top} - R_\mathrm{base}}{H} \right)^2 \frac{x^3}{3} + R_\mathrm{base} \left( \frac{R_\mathrm{top} - R_\mathrm{base}}{H} \right) x^2 + R_\mathrm{base}^2 x \right]^H_0
- \pi \left[ \left( \frac{r_\mathrm{top} - r_\mathrm{base}}{H} \right)^2 \frac{x^3}{3} + r_\mathrm{base} \left( \frac{r_\mathrm{top} - r_\mathrm{base}}{H} \right) x^2 + r_\mathrm{base}^2 x \right]^H_0 \\
&= \pi H \left\{ \frac{(R_\mathrm{top} - R_\mathrm{base})^2}{3} + R_\mathrm{base} (R_\mathrm{top} - R_\mathrm{base}) + R_\mathrm{base}^2 \right\}
- \pi H \left\{ \frac{(r_\mathrm{top} - r_\mathrm{base})^2}{3} + r_\mathrm{base} (r_\mathrm{top} - r_\mathrm{base}) + r_\mathrm{base}^2 \right\}
\end{align}
$$
$$
\begin{align}
H&: \mathrm{Height~of~the~cone} \\
R_\mathrm{top}&: \mathrm{Max~radius~of~the~top~surface} \\
R_\mathrm{base}&: \mathrm{Max~radius~of~the~base~surface} \\
r_\mathrm{top}&: \mathrm{Min~radius~of~the~top~surface} \\
r_\mathrm{base}&: \mathrm{Min~radius~of~the~base~surface}
\end{align}
$$
This function returns the volume of the given SolidCone element.
The volume of a SolidSphere with Start angle = 0° and End angle = 360° can be calculated by
$$
\begin{align}
&\int_{R_\mathrm{min}}^{R_\mathrm{max}} \left(\int_{B_\mathrm{min}}^{B_\mathrm{max}} 2\pi R \sin B \times R dB \right) dR \\
&= \frac{2}{3}\pi \left( R_\mathrm{max}^3 - R_\mathrm{min}^3 \right) \left( -\cos B_\mathrm{max} + \cos B_\mathrm{min} \right)
\end{align}
$$
$$
\begin{align}
R_\mathrm{max}&: \mathrm{Max~radius~of~the~solid~sphere} \\
R_\mathrm{min}&: \mathrm{Min~radius~of~the~solid~sphere} \\
B_\mathrm{max}&: \mathrm{Max~angle~in~latitudinal~direction},~ 0 \leq B_\mathrm{min} < B_\mathrm{max} \leq \pi \\
B_\mathrm{min}&: \mathrm{Min~angle~in~latitudinal~direction},~ 0 \leq B_\mathrm{min} < B_\mathrm{max} \leq \pi
\end{align}
$$