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
$$
\begin{align}
&\int_{R_\mathrm{min}}^{R_\mathrm{max}} \left(\int_{B_\mathrm{min}}^{B_\mathrm{max}} 2\pi R \sin B \times R dB \right) dR \\
&= \frac{2}{3}\pi \left( R_\mathrm{max}^3 - R_\mathrm{min}^3 \right) \left( -\cos B_\mathrm{max} + \cos B_\mathrm{min} \right)
\end{align}
$$
$$
\begin{align}
R_\mathrm{max}&: \mathrm{Max~radius~of~the~solid~sphere} \\
R_\mathrm{min}&: \mathrm{Min~radius~of~the~solid~sphere} \\
B_\mathrm{max}&: \mathrm{Max~angle~in~latitudinal~direction},~ 0 \leq B_\mathrm{min} < B_\mathrm{max} \leq \pi \\
B_\mathrm{min}&: \mathrm{Min~angle~in~latitudinal~direction},~ 0 \leq B_\mathrm{min} < B_\mathrm{max} \leq \pi
\end{align}
$$