1

SE_diff.asv

@@ -0,0 +1,46 @@
+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);
+
+    % 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 
+    disp(dw_dx)
+
+    % 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 
+    disp(dw_dy)
+
+    pw_se = zeros(n,n);
+
+    for i = 1:16
+        se_e1(i) = (1000*10^3*0.3*10^-3*h^2)/(2*(1-0.31^2))*((dw_dx(i))^4/4+(dw_dy(i))^4/4+0.5*(dw_dx(i))^2+0.5*(dw_dy(i))^2);
+    end 
+    disp(pw_se)

SE_diff.m

@@ -6,23 +6,39 @@
     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
-    disp(m); % symmetric matrix 
+    % m = symmetric matrix 
 
      h = 10/(n+1);
+
     % Compute dw_dx
     dx = zeros(n+2,n+1);
     for i = 2:n+2
-        dx(:,i-1)= (m(:,i)-m(:,i-1))/h;
+        dx(:,i-1)= (m(:,i)-m(:,i-1))/(h);
     end
-    disp(dx)
+
     dw_dx = zeros(n+1,n+1);
-    for i = 1:n+1
-        %dw_dx((i:n+1),i) = (dx(i,i)+dx(i+1,i))/2;
-        %dw_dx((i-1:n+1),i+1) = (dx(i,2)+dx(i+1,2))/2;
-        %dw_dx(i,3) = (dx(i,3)+dx(i+1,3))/2;
-        %dw_dx(i,4) = (dx(i,4)+dx(i+1,4))/2;
-        %i = i+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 
-    disp(dw_dx)
 
-    % Compute dw_dy
+    % 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 
+
+    pw_se = zeros(n+1,n+1);
+
+    for i = 1:16
+        pw_se(i) = (1000*10^3*0.3*10^-3*h^2)/(2*(1-0.31^2))*((dw_dx(i))^4/4+(dw_dy(i))^4/4+0.5*(dw_dx(i))^2+0.5*(dw_dy(i))^2);
+    end 
+