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Computer Aided Design (CAD)
Covers the creation of geometry:
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2 approaches to create geometry:
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Bottom-up approach: from points to surfaces and volumes,
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Constructive Solid Geometry (CGS) approach: use boolean operation,
Examples are take from Gmsh screencasts.
1. Goals
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What we will learn?
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create geometry
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automate creation
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define tags or ids to "identify" volumes/surfaces and "boundaries"
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Practise with Gmsh and Salome
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use GUI and TUI/API mode
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2. CAD ecosystem
Gives an oveview of
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Software
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Commercial: Catia, Seimens Nx, SolidWorks, …
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OpenSource: FreeCad, Salome
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Main formats:
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STL
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Brep
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Xao
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3. Bottom-up approach
Use of Gmsh with builtin kernel
3.1. Basic Usage: a square
setFactory("Built-in"); (1)
h = 1; (2)
Point(1) = {0, 0, 0, h}; (3)
Point(2) = {10, 0, 0, h};
Point(3) = {10, 10, 0, h};
Point(4) = {0, 10, 0, h};
Line(1) = {1,2}; (4)
Line(2) = {2,3};
Line(3) = {3,4};
Line(4) = {4,1};
Curve Loop(1) = {1,2,3,4}; (5)
Plane Surface(1) = {1}; (6)
Physical Surface(1) = {1}; (7)| 1 | Use Built-in kernel, aka Bottom-up approach |
| 2 | Characteristic length of a mesh element |
| 3 | Point construction |
| 4 | Lines |
| 5 | A Boundary |
| 6 | A Surface |
| 7 | Setting a label to the Surface |
To view the geometry:
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In GMSH, go to
files→open (CTRL+o)`and open the file, or type gmsh square.geo in a terminal (warning: this open a new instance of GMSH (which is very light by the way!)). A square should have appear in GMSH’s windows. -
The camera can be adjusted using the mouse: rotating (left click), translating (right click) or zooming (wheel). At bottom left of GMSH’s windows, camera can be reseted using X,Y,Z and 1:1 (scale) buttons.
| The square can now be meshed by typing 2 on the keyboard (or maybe shift + 2) or using the menu: Mesh→2D |
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add parameters for GUI mode
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h =DefineNumber[ 0.1, Name "Parameters/MeshSize" ]; (1)
dx = DefineNumber[ 0.1, Name "Parameters/dx" ];
Point(1) = {0, 0, 0, h}; (2)
Point(2) = {dx, 0, 0, h};
...| 1 | define a 'MeshSize' parameter, |
| 2 | use 'dx' parameter in Point(2) definition |
For more infos on parameters, see this doc.
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"academic" cube
Comment out the last line in the geo file Perform an elevation of Surface 1 to get a cube.
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dz = DefineNumber[ 0.1, Name "Parameters/dz" ];
out[] = Extrude {0, 0, dz} {Surface{1};}; (1)
Physical Surface("Top") = {1};
Physical Surface("Bottom") = {out[0]};
Physical Surface("Other") = {out[2], out[3], out[4], out[5]};
Physical Volume("Cube") = {out[1]};| 1 | Note how we retrieve the volume number programatically
by using the return value (a list) of the Extrude command. This list contains:
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3.2. "academic" cube with hole
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r =DefineNumber[ 0.1, Name "Parameters/HoleRadius" ];
Point(5) = {dx/2.-r, 0, 0, h/4.}; (1)
Point(6) = {dx/2., dy/2.+r, 0, h/4.};
Point(7) = {-dx/2.-r, 0, 0, h/4.};
Point(8) = {-dx/2.-r, -dy/2.-r, 0, h/4.};
Point(10) = {dx/2., dy/2., 0, h/4.};
Circle(5) = {5,1O,6};
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Curve Loop(2) = {5, 6, 7, 8}; (2)
Plane Surface(1) = {1, -2}; (3)
...| 1 | Create a disk |
| 2 | Create a Curve Loop for the hole |
| 3 | Create the surface: square with a hole, Note the sign before curve loop 2 |
Exercise:
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Perform the elevation
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Assign the Physical ids
3.3. "academic" cube with holes
Create a function to define the hole with a radius r centered on (x0, y0, 0) Store the Line Loop in an array
Macro CHole
O=newp; Point(O) = {x0,y0,0,h};
p1=newp; Point(p1) = { x0+r, y0, 0, h_h};
p2=newp; Point(p2) = { x0+0, y0+r, -dz, h_h};
p3=newp; Point(p3) = { x0-r, y0, -dz, h_h};
p4=newp; Point(p4) = { x0+0, y0-r, -dz, h_h};
c1=newl; Circle(c1) = {p1,O,p2};
c2=newl; Circle(c2) = {p2,O,p3};
c3=newl; Circle(c3) = {p3,O,p4};
c4=newl; Circle(c4) = {p4,O,p1};
loop[t]=newl; Line Loop(loop[t]) = {c1, c2, c3, c4}; t += 1;
ReturnUse the macro to create the geometry
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nx =DefineNumber[ 1, Name "Parameters/HoleNumbersAlongOX" ];
ny =DefineNumber[ 1, Name "Parameters/HoleNumbersAlongOY" ];
t = 0; loop[] = {};
Macro CHole
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Return
For i In {1:nx}
x0 = -dx/(2*nx) + (i-1) * dx/nx;
For j In {1:ny}
y0 = -dy/(2*ny) + (j-1) * dy/ny;
Call CHole;
EndFor
EndFor
bord = newl; Plane Surface(bord) = {1, -loop[]};
...Exercise:
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Perform the elevation
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Assign the Physical ids
4. CGS approach
Use of Gmsh with OpenCascade kernel
setFactory("Built-in"); (1)
lc = DefineNumber[ 0.1, Name "Parameters/lc" ];
dx = DefineNumber[ 0.1, Name "Parameters/dx" ];
dy = DefineNumber[ 0.1, Name "Parameters/dy" ];
dz = DefineNumber[ 0.1, Name "Parameters/dz" ];
Box(1) = {0,0,0, dx,dy,dz}; (2)
// get boundary??
Physical Volume("Cube") = {1};| 1 | Switch from 'Built-In' to 'OpenCASCADE' kernel |
| 2 | Create a rectangular box
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