Ytdyklly

I am trying to create a finite element code that describes the voltage along a coaxial cable. I have pasted an image of where the boundaries are located but I do not think you need to know much about the finite element method.

Here is the code:

function FEM2D

%

% This function demonstrates how the 2D Laplace equation with prescribed

% essential boundary conditions is solved by the finite element method.

%



clc, clear, close all;



% geometric parameters of a rectangule domain

% These are in cm



% *** SPLITTING IN QUARTER SIZE REDUCES # OF ELEMENTS ***

% *** WHEN LEFT AS FULL SIZE AND IN mm # OF ELEMENTS CREATES A PROPER

% MESH**

Length = 12.5e-3;

Height = 10e-3;





% Element Size



ElementSize = .001;



% Number Of Elements



NumberOfElementInX = 2*(floor(0.5*Length/ElementSize)+1);

NumberOfElementInY = ceil(Height/ElementSize);



display(NumberOfElementInX);

display(NumberOfElementInY);



ElementSizeInX = Length/NumberOfElementInX;

ElementSizeInY = Height/NumberOfElementInY;



display(ElementSizeInX);

display(ElementSizeInY);



% Node coordinates



NumberOfNode    = (NumberOfElementInX+1)*(NumberOfElementInY+1);

NumberOfElement = 2*NumberOfElementInX*NumberOfElementInY;



X = zeros(NumberOfNode,1);

Y = zeros(NumberOfNode,1);





for j = 1 : NumberOfElementInY+1

    for i = 1 : NumberOfElementInX+1

        n = (j-1)*(NumberOfElementInX+1)+i;

        X(n) = (i-1)*ElementSizeInX;

        Y(n) = (j-1)*ElementSizeInY;

    end

end







% element node connectivity



ElementNode = zeros(NumberOfElement,3);

for j = 1 : NumberOfElementInY

    for i = 1 : NumberOfElementInX

        n = (j-1)*NumberOfElementInX+i;

        if i <= NumberOfElementInX/2

            ElementNode(2*n-1, 1) = (j-1)*(NumberOfElementInX+1)+i;

            ElementNode(2*n-1, 2) = j*(NumberOfElementInX+1)+i+1;

            ElementNode(2*n-1, 3) = j*(NumberOfElementInX+1)+i;

            ElementNode(2*n, 1)   = (j-1)*(NumberOfElementInX+1)+i;

            ElementNode(2*n, 2)   = (j-1)*(NumberOfElementInX+1)+i+1;

            ElementNode(2*n, 3)   = j*(NumberOfElementInX+1)+i+1;

        else

            ElementNode(2*n-1, 1) = (j-1)*(NumberOfElementInX+1)+i;

            ElementNode(2*n-1, 2) = (j-1)*(NumberOfElementInX+1)+i+1;

            ElementNode(2*n-1, 3) = j*(NumberOfElementInX+1)+i;

            ElementNode(2*n, 1)   = (j-1)*(NumberOfElementInX+1)+i+1;

            ElementNode(2*n, 2)   = j*(NumberOfElementInX+1)+i+1;

            ElementNode(2*n, 3)   = j*(NumberOfElementInX+1)+i;

        end

    end

end



% ElementNode = delaunay(X,Y.*(1+0.001*ElementSize*sin(pi*X/Length)));

% %ElementNode = delaunay(X,Y);



% show mesh



trimesh(ElementNode,X,Y);

axis equal



end

So here is the mesh I get:

The problem is that I need to find a way to create a rectangular hole in my mesh. This problem would be applicable to a normal plate if the boundaries were on the outsides of my square but in this problem the boundaries are restricted. Basically, how can I remove the smaller rectangle in my problem? I have posted a screenshot of the dimensions of the problem I'm analyzing. Any tips would be appreciated.