I am modelling carbon nanotube (CNT) with hemispherical ends in ANSYS APDL. I don't know how to find coordinates of points lying on the surface of a hemisphere. That coordinates will be defined as a node so that I can create elements manually using command reference and form a hemispherical model.
Hello,
In analytic geometry, a sphere with center (x0, y0, z0) and radius r is the locus of all points (x, y, z) such that
(x - x0 )^2 + (y - y0 )^2 + ( z - z0 )^2 = r^2.
The points on the sphere with radius r can be parameterized via
x = x0 + r*cos(theta)*sin(arpha)
y = y0 + r*sin(theta)*sin(arpha)
z = z0 + r*cos(arpha)
with 0
The algebraic equation of a sphere with center h,j,k and a radius r is given as:
(x - h)^2 + (y - j)^2 + (z - k)^2 = r^2
If you want to simplify things for your numerical problem at hand, assume that your hemisphere's center is located at 0,0,0 and that its surface is located at the positive z axis. This means that all coordinate points on your surface must have a z=>0.
Then your equation will simplify to:
(x )^2 + (y )^2 + (z )^2 = r^2
Any x,y,z coordinate that satisfies the above equation is a point on your surface. Nevertheless, this method will be time consuming in comparison to using a 3D CAD software instead so as to solve the above problem.
I want them in terms of spherical coordinates. Also what is the range for angles theta and phi for hemisphere?
(x-x0)^2+(y-y0)^2+(z-z0)^2=R^2???
This is the equation of a sphere if you only take x>x0 or x
Its done by simply you just open a meshing and simply change the viewing mode in menu bar so you can able to find out the co-ordinates where you mover your mouse pointer.
This same thing is done by menu options so i suggest that try this or just use help menu and you easily able to do this.
Dependently on your data entry, if you choose any two coordinates x and y : you can find the third one with : (x-xc)^2+(y-yc)^2+(z-zc)^2=R^2 such that c is for sphere center coordinates. Also:
x=R*cos(Phi)*cos(Theta)
y=R*cos(Phi)*sin(Theta)
z=R*sin(Phi)
with: 0
You need also to satisfy the following constraints when selecting x and y:
(xc-R)
It is important that before applying any formula you must to define the range varying values.
Why you don't try to model an hemispere with (1/4)circle +generate a surface with 2Pi rotation after that mesh your area with the selected element types? Finally you can list your keypoints, nodes, elements from your menu.
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