Part E

README.md

@@ -73,3 +73,34 @@ end
 membrane_solution(0.006,0.001,10)
 ```
 ![](assets/README-579fb915.png)
+
+## Part E
+```
+function [pw_se,w]=SE_diff(T,P,n)
+
+E = 1e6;
+v = .31;
+t = .0003;
+h = 10/(n+1);
+w = membrane_solution(T,P,n);
+z = zeros(n+2);
+z(2:end-1,2:end-1) = reshape(w,[n n]);
+nt = n + 1;
+wn = zeros(nt);
+for i = 1:nt
+    for j = 1:nt
+        wn(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
+    end
+end
+pw = sum(sum(wn.*h^2.*P));
+dwdx = zeros(nt);
+dwdy = zeros(nt);
+for i = 1:nt
+    for j = 1:nt
+        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;
+```

SE_diff.asv

@@ -0,0 +1,27 @@
+function [pw_se,w]=SE_diff(T,P,n)
+
+E = 1e6;
+v = .31;
+t = .0003;
+h = 10/(n+1);
+w = membrane_solution(T,P,n);
+z = zeros(n+2);
+z(2:end-1,2:end-1) = reshape(w,[n n]);
+nt = n + 1;
+wn = zeros(nt);
+for i = 1:nt
+    for j = 1:nt
+        wn(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
+    end
+end
+pw = sum(sum(wn.*h^2.*P));
+dwdx = zeros(nt);
+dwdy = zeros(nt);
+for i = 1:nt
+    for j = 1:nt
+        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;

SE_diff.m

@@ -0,0 +1,27 @@
+function [pw_se,w]=SE_diff(T,P,n)
+
+E = 1e6;
+v = .31;
+t = .0003;
+h = 10/(n+1);
+w = membrane_solution(T,P,n);
+z = zeros(n+2);
+z(2:end-1,2:end-1) = reshape(w,[n n]);
+nt = n + 1;
+wn = zeros(nt);
+for i = 1:nt
+    for j = 1:nt
+        wn(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
+    end
+end
+pw = sum(sum(wn.*h^2.*P));
+dwdx = zeros(nt);
+dwdy = zeros(nt);
+for i = 1:nt
+    for j = 1:nt
+        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;