Part E

Part E/SE_diff.asv

@@ -0,0 +1,34 @@
+function [pw_se,w]=SE_diff(T,P,n)
+E = 1e12; %Pa
+v = .31;
+t = .3; %nm
+h = 10/(n+1); %nm
+w = membrane_solution(T,P,n);
+z = zeros(n+2);
+z(2:end-1,2:end-1) = reshape(w,[n n]);
+num = n + 1;
+wbar = zeros(num);
+for i = 1:num
+    for j = 1:num
+        wbar(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
+    end
+end
+pw = sum(wbar.*h^2.*P);
+dwdx = zeros(num);
+dwdy = zeros(num);
+% for i = 1:num
+%     for j = 1:num
+%         dwdx(j,i) = z(i+1,j)-z(i,j);
+%         dwdy(j,i) = z(i,j+1)-z(i,j);
+%     end
+% end
+dwdx(:,1) = wbar(:,2)-wbar(:,1);
+for i = 2:n
+    dwdx(:,3) = wbar(:,n+1)-wbar(:,n-1);
+end
+% dwdx(:,4) = wbar(:,4)-wbar(:,3);
+dwdy(1,:) = wbar(2,:)-wbar(1,:);
+dwdy(2,:) = wbar(3,:)-wbar(1,:);
+dwdy(3,:) = wbar(4,:)-wbar(2,:);
+
+%se = E*t*h^2/(2*(1-v^2));

Part E/SE_diff.m

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+function [pw_se,w]=SE_diff(T,P,n)
+E = 1; %TPa Units may need to be changed
+v = .31; %Poissons ratio
+t = .3; %nm
+h = 10/(n+1); %nm
+w = membrane_solution(T,P,n);
+z = zeros(n+2);
+z(2:end-1,2:end-1) = reshape(w,[n n]);
+num = n + 1;
+wbar = zeros(num);
+for i = 1:num
+    for j = 1:num
+        wbar(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
+    end
+end
+pw = sum(sum(wbar.*h^2.*P));
+dwdx = zeros(num);
+dwdy = zeros(num);
+for i = 1:num
+    for j = 1:num
+        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;

Part E/membrane_solution.m

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+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