From 54a17ceab5f5390ef1fd17fcc38c8c7a948ab866 Mon Sep 17 00:00:00 2001
From: nin13001 <32068635+nin13001@users.noreply.github.com>
Date: Fri, 15 Dec 2017 18:33:40 -0500
Subject: [PATCH] Part E

---
 README.md   | 31 +++++++++++++++++++++++++++++++
 SE_diff.asv | 27 +++++++++++++++++++++++++++
 SE_diff.m   | 27 +++++++++++++++++++++++++++
 3 files changed, 85 insertions(+)
 create mode 100644 SE_diff.asv
 create mode 100644 SE_diff.m

diff --git a/README.md b/README.md
index 32e01fa..b8b040a 100644
--- a/README.md
+++ b/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;
+```
diff --git a/SE_diff.asv b/SE_diff.asv
new file mode 100644
index 0000000..9e4c550
--- /dev/null
+++ b/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;
\ No newline at end of file
diff --git a/SE_diff.m b/SE_diff.m
new file mode 100644
index 0000000..9e4c550
--- /dev/null
+++ b/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;
\ No newline at end of file