.

Part A/membrane_solution3.m

@@ -16,8 +16,10 @@ function [w] = membrane_solution3(T,P)
     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)')
+    title('Membrane Displacement (3 x 3)')
+    zlabel('Z Position (micron)')
+    ylabel('Y Position (micron)')
+    xlabel('X Position (micron)')
     % Membrane displacement is shown on chart
 
 end 

Part B/membrane_solution3.m

@@ -0,0 +1,25 @@
+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 (3 x 3)')
+    zlabel('Z Position (micron)')
+    ylabel('Y Position (micron)')
+    xlabel('X Position (micron)')
+    % Membrane displacement is shown on chart
+
+end 

Part D/membrane_solution.m

@@ -0,0 +1,25 @@
+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 (10 x 10)')
+    zlabel('Z Position (micron)')
+    ylabel('Y Position (micron)')
+    xlabel('X Position (micron)')
+    % Membrane displacement is shown on chart
+end