README.md

ME3255_Final_Project

Part A

function [w] = membrane_solution3(T,P)
    % T = Tension (microNewton/micrometer)
    % P = Pressure (MPa)
    
    od = ones(8,1);
    od(3:3:end) = 0;
    k = -4*diag(ones(9,1))+diag(ones(9-3,1),3)+diag(ones(9-3,1),-3)+diag(od,1)+diag(od,-1);
   
    
    y = -(10/4)^2*(P/T)*ones(9,1);
    w = k\y; 
    % Solves for displacement (micrometers)
    % Solution represents a 2D data set w(x,y)

    [x,y] = meshgrid(0:10/4:10,0:10/4:10);
    z = zeros(size(x));
    z(2:end-1,2:end-1) = reshape(w,[3 3]);
    surf(x,y,z)
    title('Membrane Displacement')
    zlabel('Displacement (micrometer)')
    % Membrane displacement is shown on chart
    
end 

Part B

% Part B Script
[w] = membrane_solution3(0.006,0.001);

Part C

function [w] = membrane_solution(T,P,n)
    % T = Tension (microNewton/micrometer)
    % P = Pressure (MPa)
    % n = # of interior nodes

    od = ones(n^2-1,1);
    od(n:n:end) = 0;
    k = -4*diag(ones(n^2,1))+diag(ones((n^2)-n,1),n)+diag(ones((n^2)-n,1),-n)+diag(od,1)+diag(od,-1);

    y = -(10/(n+1))^2*(P/T)*ones(n^2,1);
    w = k\y;
    % Solves for displacement (micrometers)
    % Output w is a vector
    % Solution represents a 2D data set w(x,y)

    [x,y] = meshgrid(0:10/(n+1):10,0:10/(n+1):10);
    z = zeros(size(x));
    z(2:end-1,2:end-1) = reshape(w,[n n]);
    surf(x,y,z)
    title('Membrane Displacement')
    zlabel('Displacement (micrometer)')
    % Membrane displacement is shown on chart
end

Part D

% Part D Script
[w] = membrane_solution(0.006,0.001,10)