From 9181783d18777aedc4f3c360f1233bf99fbb5806 Mon Sep 17 00:00:00 2001
From: Matthew Maliniak <matthew.maliniak@uconn.edu>
Date: Thu, 14 Dec 2017 20:38:36 -0500
Subject: [PATCH] Update README.md

---
 README.md | 43 ++++++++++++++++++++++++++++++++++++++-----
 1 file changed, 38 insertions(+), 5 deletions(-)

diff --git a/README.md b/README.md
index 1bd4f88..09f3690 100644
--- a/README.md
+++ b/README.md
@@ -32,11 +32,13 @@ w = k\y;
     zlabel('Z Position (micron)')
     ylabel('Y Position (micron)')
     xlabel('X Position (micron)')
+    % Membrane displacement is shown on chart
 
 % Membrane displacement is shown on chart
 
 end
-   
+    
+end 
 ```
 ### Approach
 - A matrix is set up using finite element analysis of the interior nodes of a 5x5 matrix
@@ -78,10 +80,8 @@ function [w] = membrane_solution(T,P,n)
     z = zeros(size(x));
     z(2:end-1,2:end-1) = reshape(w,[n n]);
     surf(x,y,z)
-    title('Membrane Displacement (10 x 10)')
-    zlabel('Z Position (micron)')
-    ylabel('Y Position (micron)')
-    xlabel('X Position (micron)')
+    title('Membrane Displacement')
+    zlabel('Displacement (micrometer)')
     % Membrane displacement is shown on chart
 end
 ```
@@ -267,3 +267,36 @@ print('Part g','-dpng')
 - Additionally, the max deflection for each pressure and tension is calculated at each iteration
 - From there, a general linear regression is calculated with the formula P(x) = A*w^3
 - The results are plotted
+
+# Part H
+```matlab
+P=0.001;
+n = 5:5:50;
+a = zeros(1,length(n));
+for i = 1:length(n)
+    T = tension_sol(P,n(i));
+    w = membrane_solution(T,P,n(i));
+    wmax = max(w);
+    x = wmax';
+    y = P';
+    Z = x.^3;
+    a(i) = Z\y;
+end
+Rel_error(a)
+```
+|number of nodes|vaalue of const. A| rel. error|
+|---|---|---|
+|5 |0.4423 |n/a|
+|10|0.5389|21.84%|
+|15|0.5349|0.73%|
+|20|0.5483|2.5%|
+|25|0.5454|0.52%|
+|30|0.5503|0.89%|
+|35|0.5485|0.31%|
+|40|0.5510|0.45%|
+|45|0.5499|0.2%|
+
+### Approach
+- Part H uses the same basis as Part G, but with varrying n (number of nodes) valeus instead
+- Additionally, the outputs and a few calculations were deleted to speed up the process since they were not needed here
+- In the chart, while there are some fluctuations, there is a clear decrease in the relative error of A, leading to the assumption that it is converging as the number of nodes increases