Merge branch 'master' of https://github.uconn.edu/cpl11001/07_final_p…

…roject

README.md

@@ -1,6 +1,9 @@
 # 07_final_project
 
-### Part A
+## Part A
+### Problem Statement
+Create a function called membrane_solution3 that uses the central finite difference approximation to solve for the displacements of a membrane with 3 x 3 interior nodes. The function should take the pressure (P) and tension (T) as inputs and output a column vector, w.
+
 ``` matlab
 function [w] = membrane_solution3(T,P) % Set up initial matrix
     % T = given tension (microNewton/micrometer)
@@ -21,14 +24,20 @@ function [w] = membrane_solution3(T,P) % Set up initial matrix
 end
 ```
 
-### Part B
+## Part B
+### Problem Statement
+Using the function from part A as well as a given tension of 0.006 uN/um and a given pressure of 0.001 MPa, solve for w and plot the result in 3 dimensions
+
 ``` matlab
 [w] = membrane_solution3(0.006,0.001);
 ```
 
 ![3x3 Interior Nodes](./figures/figure1.png)
 
-### Part C
+## Part C
+### Problem Statement
+Create a function called membrane_solution that uses the central finite difference approximation to solve for the displacements of a membrane with n x n interior nodes.  The function should take the pressure (P), tension (T), and number of interior nodes (n) as inputs and output the column vector, w.
+
 ```matlab
 function [w] = membrane_solution(T,P,n)% Set up initial matrix
     % T = given tension (microNewton/micrometer)
@@ -50,7 +59,8 @@ function [w] = membrane_solution(T,P,n)% Set up initial matrix
 end
 ```
 
-### Part D
+## Part D
+### Problem Statement
 ``` matlab
 [w] = membrane_solution(0.006,0.001,10)
 ```

SE_diff.m

@@ -1,91 +1,63 @@
-function [pw_se,w]=SE_diff(T,P,n)
-w = membrane_solution31(T,P,n);
-A = zeros(n,n);
-h = zeros(n,1);
-m = n+1; %Represents the number of nodes
-
-%Top Left Corner Interior Node
-for i = 2+m
-    A(i,i)=1;
-    A(i,i-1)=0;
-    A(i,i+m)=1;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end
-%Top Right Corner Interior Node
-for i = m*2-1
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-%Bottom Left Corner Interior Node
-for i = m*m-(2*m)+1
-    A(i,i)=1;
-    A(i,i-1)=0;
-    A(i,i+m)=0;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end
-%Bottom Right Corner Interior Node
-for i = (m*m)-m-1
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=0;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end 
-
-%The following represent the values for the interior nodes
-
-%Top Interior Row
-for i = 3+m:m*2-2
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-%Bottom Interior Row
-for i = m*m-(2*m)+2:(m*m)-m-2
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=0;
-    A(i,i+m-1)=0;
-    h(i) = 10;
-end
-%Left Interior Column
-for i = (2*m)+2,(2*m)+2:(m*m)-(2*m)+2
-    A(i,i)=1;
-    A(i,i-1)=0;
-    A(i,i+m)=1;
-    A(i,i+m-1)=0; 
-    h(i) = 10;
-end
-%Right Interior Column
-for i = (3*m)-1,(2*m)+2:(m*m)-(2*m)+2
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-%Inerior Nodes
-for i = (2*m)+3:(3*m)-2,(2*m)+3:(m*m)-(3*m)+3
-    A(i,i)=1;
-    A(i,i-1)=1;
-    A(i,i+m)=1;
-    A(i,i+m-1)=1;
-    h(i) = 10;
-end
-
-
-dw_dx = (A(i,i)-A(i-1)+A(i,i+m)-A(i,i+m-1))/(2.*h);
-dw_dx'
+function [pw_se,w] = SE_diff(T,P,n)
+
+    % Call function from part c to obtain vector w
+    w = membrane_solution(T,P,n);
+    % Create All Nodes Matrix (Interior & Exterior)
+    m = zeros(n+2);
+    c = vec2mat(w,n); % Vector w rearranged to n x n matrix.
+    m(2:n+1,2:n+1) = c; % insert matrix c into middle of m matrix
+    % m = symmetric matrix 
+
+    h = 10/(n+1); % h = delta_x = delta_y (micron)
+
+    % Compute w bar
+    w_bar = zeros(n+1,n+1);
+    for i = 1:n+1
+        for j = 1:n+1
+            w_bar(i,j) = (m(i,j)+m(i,j+1)+m(i+1,j)+m(i+1,j+1))/4;
+        end
+    end
+
+    % Left side of the equation
+    left_side = zeros(n+1,n+1);
+    for  i = 1:(n+1)^2
+        left_side(i) = P * h^2*w_bar(i);
+    end
+    L = sum(sum(left_side));
+
+    % Compute dw_dx
+    dx = zeros(n+2,n+1);
+    for i = 2:n+2
+        dx(:,i-1)= (m(:,i)-m(:,i-1))/(h);
+    end
+
+    dw_dx = zeros(n+1,n+1);
+    for i = 1:n+1 % rows
+        for j = 1:n+1 % columns
+        dw_dx(i,j) = (dx(i,j)+dx(i+1,j))/2;
+        end 
+    end 
 
-end 
+    % Compute dw_dy
+    dy = zeros(n+1,n+2);
+    for i = 2:n+2
+        dy(i-1,:)= (m(i-1,:)-m(i,:))/(h);
+    end
 
+    dw_dy = zeros(n+1,n+1);
+    for i = 1:n+1 % rows
+        for j = 1:n+1 % columns
+        dw_dy(i,j) = (dy(i,j)+dy(i,j+1))/2;
+        end 
+    end 
+
+    right_side = zeros(n+1,n+1);
 
+    for i = 1:(n+1)^2
+        right_side(i) = (0.25*(dw_dx(i))^4+0.25*(dw_dy(i))^4+0.5*(dw_dx(i)*dw_dy(i))^2);
+    end 
+    R = sum(sum(right_side));
+    R = (1000*10^3*0.3*10^-3*h^2)/(2*(1-0.31^2))*R;
 
-
+    pw_se = R - L;
+end 

membrane_solution.m

@@ -9,7 +9,7 @@
 
     % Solve for unknown matrix, w
     y = -(10/(n+1))^2*(P/T)*ones(n^2,1); %output vector 
-    w = k\y; %solves for w in microm
+    w = k\y; %solves for w in micron
 
     [x,y] = meshgrid(0:10/(n+1):10,0:10/(n+1):10);
     z = zeros(size(x));