Shap3d45.dat, 45th 'shape' file for CPO3D
Rectangular slot in rectangular plate, by users equation.
For information on the option for users equations, see users equations.
45th shape file -rectangular hole in a rectangular plate, by users equations.
The inner rectangle has sides 0.2 and 0.05 (sx and sy), while the outer has 1 and 0.5 (Sx and Sy).
Consider first the right hand sides of the electrode.
The equations, say g1(x,y,z), for the inner edge at x = sx are
x = sx, y = sy*tan(phi), z = 0, where phi = 0 to pi/4 (allowing for the symmetry planes).
The equations, say g2(x,y,z), for the outer edge at Sx = 0.5 are
x = Sx, y = Sy*tan(phi), z = 0.
In the usual fashion we can combine these by using the general equation
g(x,y,z) = (1 - f)*g1 + f*g2,
where f goes from 0 to 1.
This reproduces g1 when f = 0, and g2 when f = 1.
To concentrate the segments near the inner edge, we can use f^n instead of f and in the present example n = 1.5.
The x=0 symmetry plane reflects this shape to the left-hand side.
A second analogous electrode completes the simulation.
The data, as they appear in the data file, are:
For the 1st electrode:
f 0 1 name of variable number 1 and its limits
phi 0 0.785398 name of variable number 2 and its limits
sx 0.2 name of parameter number 1 and its fixed value
sy 0.05 name of parameter number 2 and its fixed value
Sx 1 name of parameter number 3 and its fixed value
Sy 0.5 name of parameter number 4 and its fixed value
sx*(1-f^1.5)+Sx*f^1.5
sy*tan(phi)*(1-f^1.5)+Sy*tan(phi)*f^1.5
0
1 numbers of 2 applied voltages (can be same)
10 5 numbers of subdivisions of variables 1 and 2
For the 2nd electrode:
f 0 1 name of variable number 1 and its limits
phi 0 0.785398 name of variable number 2 and its limits
sx 0.2 name of parameter number 1 and its fixed value
sy 0.05 name of parameter number 2 and its fixed value
Sx 1 name of parameter number 3 and its fixed value
Sy 0.5 name of parameter number 4 and its fixed value
sx*tan(phi)*(1-f^1.5)+Sx*tan(phi)*f^1.5
sy*(1-f^1.5)+Sy*f^1.5
0
1 1 numbers of 2 applied voltages (can be same)
10 5 numbers of subdivisions of variables 1 and 2
(The program has corrected the less accurate value that was entered for pi/4.)