How can I code Finite element discretization of 2D for rectangular object ? .... The sample is attached on the picture.

~ I took this picture from someones article. And now I need to do a similar FEM discretization with this one. But I couldn't generate a code for this picture using a matlab. how can I code for this problem 2D FEM plot?

Figure: Finite element discretization of bread and baking pan.

The nodes in the above figure labeled in black are nodes of baking pan, nodes written in red represent nodes of bread, and nodes in blue are interface nodes during baking.

Answer 1

[Mrutyunjaya Hiremath]

check this one

% Define problem parameters
Lx = 1; % Length of the rectangular domain in the x-direction
Ly = 1; % Length of the rectangular domain in the y-direction
numElementsX = 10; % Number of elements in the x-direction
numElementsY = 10; % Number of elements in the y-direction

% Step 1: Generate mesh
xNodes = linspace(0, Lx, numElementsX + 1);
yNodes = linspace(0, Ly, numElementsY + 1);
[X, Y] = meshgrid(xNodes, yNodes);

% Create element connectivity matrix
numNodesX = numElementsX + 1;
numNodesY = numElementsY + 1;
connectivity = zeros(numElementsX * numElementsY, 4);
elementIndex = 1;
for j = 1:numElementsY
    for i = 1:numElementsX
        connectivity(elementIndex, :) = [i, i+1, i+numNodesX+1, i+numNodesX];
        elementIndex = elementIndex + 1;
    end
end

% Step 2: Assign material properties to elements (e.g., conductivity, modulus)

% Step 3: Assemble global stiffness matrix and load vector

% Step 4: Apply boundary conditions

% Step 5: Solve the system of equations
% You can use the backslash operator (\) to solve the system of equations

% Step 6: Post-process results and plot
% For example, plot the nodal displacements using surf or contourf

% Example plot of nodal displacements
figure;
surf(X, Y, nodalDisplacements);
xlabel('X');
ylabel('Y');
zlabel('Nodal Displacements');
title('Nodal Displacements');