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.

Answer 2

[Tejas]

Hello Prasad,

To create a rectangular void in a mesh grid, follow these steps:

• First, create a mesh and add the vertices to a list.

    [x, y] = meshgrid(0:1:15, 0:0.5:13);
    polygon_x = [5.6, 9.4, 9.4, 3.8];
    polygon_y = [3.8, 3.8, 9.2, 9.2]; 

• Then, create a logical array to store the points that fall inside the rectangle.

    insidePolygon = false(size(x)); 

• Next, iterate over each point in the mesh grid and use the 'inpolygon' function to determine whether the points lie within the polygon or outside it. More details about this function can be found in this documentation: https://www.mathworks.com/help/releases/R2024a/matlab/ref/inpolygon.html .

    for i = 1:numel(x)
        insidePolygon(i) = inpolygon(x(i), y(i), polygon_x, polygon_y);
    end 

• Set the points inside the polygon to NaN.

    x(insidePolygon) = NaN;
    y(insidePolygon) = NaN;

To visualize the mesh, you can use the code snippet provided below:

figure;
plot(x, y, 'b.', 'MarkerSize', 10); 
hold on;
plot(polygon_x([1:end 1]), polygon_y([1:end 1]), 'r-', 'LineWidth', 2);

[Prasad]

Hi Tejas,

I appreciate your respone. I wan't to create a mesh as noted in the reply to Epsilon. Kindly provide your suggestions.

Thanks

Answer 3

[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