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 # ME3255_Final_Project
-ME 3255 Final Project
+
+# Part A
+```matlab
+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
+```matlab
+% Part B Script
+[w] = membrane_solution3(0.006,0.001);
+```
+![](https://github.uconn.edu/ltd13002/ME3255_Final_Project/blob/master/Part%20B/PartBFigure.png)
+
+
+# Part C
+```matlab
+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
+```matlab
+% Part D Script
+[w] = membrane_solution(0.006,0.001,10)
+```
+![](https://github.uconn.edu/ltd13002/ME3255_Final_Project/blob/master/Part%20D/PartDFigure.png)