Computer Aided Design (CAD)

Covers the creation of geometry:

  • 2 approaches to create geometry:

    • Bottom-up approach: from points to surfaces and volumes,

  • Constructive Solid Geometry (CGS) approach: use boolean operation,

Examples are take from Gmsh screencasts.

1. Goals

  • What we will learn?

    • create geometry

    • automate creation

    • define tags or ids to "identify" volumes/surfaces and "boundaries"

  • Practise with Gmsh and Salome

    • use GUI and TUI/API mode

2. CAD ecosystem

Gives an oveview of

  • Software

    • Commercial: Catia, Seimens Nx, SolidWorks, …​

    • OpenSource: FreeCad, Salome

  • Main formats:

    • STL

    • STEP

    • Brep (Xao, aka Brep + xml)

3. Bottom-up approach

Use of Gmsh with builtin kernel image::orientation.png[fallback=orientation.png]

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:

  • 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

  • add parameters for GUI mode

...
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.

  • "academic" cube

Comment out the last line in the geo file Perform an elevation of Surface 1 to get a cube.

...
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:

  • the "top" of the extruded surface (in 'out[0]''),

  • the newly created volume (in 'out[1]'')

  • and the ids of the lateral surfaces (in 'out[2]'', 'out[3]', …​)

3.2. "academic" cube with hole

...
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};
...
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:

  • Perform the elevation

  • 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;
Return

Use the macro to create the geometry

...
nx =DefineNumber[ 1, Name "Parameters/HoleNumbersAlongOX" ];
ny =DefineNumber[ 1, Name "Parameters/HoleNumbersAlongOY" ];

t = 0; loop[] = {};
Macro CHole
    ...
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:

  • Perform the elevation

  • 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

  • previous examples using CSG

5. Use of python Gmsh API

5.1. Exercises

6. Use of Salome for more complex geometries