How to modify the mesh generated from meshgrid to create a rectangular void in the middle of the mesh

Hi , I'm new to matlab and trying to create a void or remove the points within a rectangular area in the mesh grid. I have to use this meshgrid to generate structured mesh for FEA.

The mesh grid is ;

[x y] = meshgrid([0: 1: 15],[0: 0.5 :13])

The x & y coordinates for the four corner points of rectangular area ; p1= [5.6 3.8] ; p2= [9.4 3.8] ; p3 =[9.4 9.2] ; p4= [3.8 9.2]

How do I do this?If this is not possible, please provide advise how to select the points/element nodes witin the rectangular area. I appreciate if someone can provide some help on this.

Thanks

Answer 1

[Epsilon]

Hi Prasad,

To create a void set the values at the indices to 'NaN'.

[x, y] = meshgrid(0:1:15, 0:0.5:13);
voidIndices = (x >= 5.6 & x <= 9.4) & (y >= 3.8 & y <= 9.2);

% Remove points inside the rectangle by setting them to NaN
x(voidIndices) = NaN;
y(voidIndices) = NaN;

plot(x, y, 'b.');

To know more about 'NaN' refer to the link: https://www.mathworks.com/help/matlab/ref/nan.html?

[Prasad]

Hi Epsilon,

Thank you for your input. The codes worked. However,I'm finding issues with creatinng structured mesh using delaunayTriangulation. I want to create a mesh as shown below.

Thanks.

[Walter Roberson]

You cannot do this using delaunayTriangulation . delaunayTriangulation does not give the possibility of excluding an area. delaunayTriangulation() only accepts finite coordinates.

If you extract the non-nan values from x and y:

[x, y] = meshgrid(0:1:15, 0:0.5:13);
voidIndices = (x >= 5.6 & x <= 9.4) & (y >= 3.8 & y <= 9.2);
% Remove points inside the rectangle by setting them to NaN
x(voidIndices) = NaN;
y(voidIndices) = NaN;
XY = rmmissing([x(:), y(:)]);
DT = delaunayTriangulation(XY(:,1), XY(:,2))

DT = 
  delaunayTriangulation with properties:

              Points: [388x2 double]
    ConnectivityList: [692x3 double]
         Constraints: []

triplot(DT)

Notice that you get triangles crossing the void. The large space shown there is not void -- it is a pair of large triangles occupying the area enclosed.

[Prasad]

Thank you for your advise with the outputs. I appreciate your support. Now understand the issue. Any other suggetions to obtain triangluar element mesh with a void for Finite Element Analysis.

Thanks

Answer 2

[Walter Roberson]

You might be better off taking a different approach. You might be better off decomposing a geometry

If you follow the steps from the examples at https://www.mathworks.com/help/pde/ug/decsg.html you should be able to build a decomposed mesh. You might then fegeometry the result.

[Prasad]

Hi Walter,

Thank you for your advise. I'm struggling to get the mesh that I mentioned in the reply to Epsilon. I appreciate if you could provide your thoughts.

Thanks

[Walter Roberson]

You can follow the steps given at https://www.mathworks.com/help/pde/ug/create-geometry-at-the-command-line.html to create two rectangles, and then set the function to be R1-R2 and then [dl,bt] = decsg(gd,sf,ns); to get the decomposed geometry in a form suitable for use with the PDE toolbox.

You can construct a fegeometry from the description matrix; https://www.mathworks.com/help/pde/ug/fegeometry.html#mw_e77501a3-de38-4ca5-b632-cba2ad33ecb9 . If necessary you can generateMesh from that, https://www.mathworks.com/help/pde/ug/pde.pdemodel.generatemesh.html