README.md

ME3255_FInalProject

I noticed that I was never assigned to a group so I did this project solo

Part A

function [w] = membrane_solution3(T,P)


    od = ones(8,1);
    od(3:3:end) = 0;
    a = -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 = a\y;

grid on
    [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')
    xlabel('X (\muM)')
    ylabel('Y (\muM)')
    zlabel('Displacement (\muM)')
    colormap jet
    shading interp
    disp(w)

end

Part B

membrane_solution3(0.006,0.001)

Part C

function [w] = membrane_solution3(T,P)


    od = ones(8,1);
    od(3:3:end) = 0;
    a = -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 = a\y;

grid on
    [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')
    xlabel('X (\muM)')
    ylabel('Y (\muM)')
    zlabel('Displacement (\muM)')
    colormap jet
    shading interp
    disp(w)

end

Part D

membrane_solution(0.006,0.001,10)

Part E

function [pw_se,w]=SE_diff(T,P,n)

E = 1e6;
v = .31;
t = .0003;
h = 10/(n+1);
w = membrane_solution(T,P,n);
z = zeros(n+2);
z(2:end-1,2:end-1) = reshape(w,[n n]);
nt = n + 1;
wn = zeros(nt);
for i = 1:nt
    for j = 1:nt
        wn(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
    end
end
pw = sum(sum(wn.*h^2.*P));
dwdx = zeros(nt);
dwdy = zeros(nt);
for i = 1:nt
    for j = 1:nt
        dwdx(i,j) = mean([z(i+1,j)-z(i,j),z(i+1,j+1)-z(i,j+1)]);
        dwdy(i,j) = mean([z(i,j+1)-z(i,j),z(i+1,j+1)-z(i+1,j)]);
    end
end
se = E*t*h^2/(2*(1-v^2))*sum(sum(0.25.*dwdx.^4+.25.*dwdy.^4+0.5.*(dwdx.*dwdy).^2));
pw_se = pw-se;