From a4b43a8ade6acefc32543428b5a585c4f1a18d06 Mon Sep 17 00:00:00 2001
From: Ayush Rathore <ayush.rathore@uconn.edu>
Date: Thu, 14 Dec 2017 22:59:03 -0500
Subject: [PATCH] Part C update

---
 README.md           | 44 +++++++++++++++++++++++++++++++++-----------
 membrane_solution.m | 18 +++++++++---------
 2 files changed, 42 insertions(+), 20 deletions(-)

diff --git a/README.md b/README.md
index 519854c..0976c82 100644
--- a/README.md
+++ b/README.md
@@ -43,7 +43,6 @@ Solve for w given a pressure, P=0.001 MPa and tension, T=0.006 uN/um. Plot the r
 `surf(X,Y,W)` where X, Y, and W are the x-, y-, and z-coordinates of each point on the
 membrane from 0-10um.
 #### Approach
-
 T = 0.006 uN/um
 P = 0.001 MPa
 ```matlab
@@ -56,23 +55,46 @@ P = 0.001 MPa
 #### Problem Statement
 Create a general central finite difference approximation of the gradient with
 n-by-n interior nodes of w
-for the given membrane solution in terms of P and T. `[w]=membrane_solution(T,P,n);` The
-output `w` should be a vector, but the solution represents a 2D data set w(x,y).
-#### Approach
+for the given membrane solution in terms of P and T. `[w]=membrane_solution(T,P,n);`
 
-General central finite difference approximation for gradient
-of nxn interior nodes of w.
+#### Approach
 ```matlab
-[w] = membrane_solution(T,P,n)
+function [w] = membrane_solution(T,P,n)
+  % General Central finite difference approximation of
+  % gradient with n-by-n interior nodes in terms of P & T.
+  % Input:
+  % T = tension per unit length (uN/um)
+  % P = pressure (MPa)
+  % n = # of interior node rows/columns
+  % Output:
+  % w = displacement vector for interior nodes
+
+  od = ones(n^2-1,1);
+  od(n:n:end) = 0;
+  k = -4 * diag(ones(n^2,1)) + diag(ones((n^2)-n,1),n) + diag(ones((n^2)-n,1),-n) + diag(od,1) + diag(od,-1);
+
+  y = -(10/(n+1))^2*(P/T)*ones(n^2,1);
+  w = k\y;
+
+  % Find displacement vector w
+  % which represents 2D data set w(x,y)
+  [x,y] = meshgrid(0:10/(n+1):10,0:10/(n+1):10);
+  z = zeros(size(x));
+  z(2:end-1,2:end-1) = reshape(w,[n n]);
+
+  % Plot gradient of membrane displacement
+  surf(x,y,z)
+  title('Gradient of Membrane Displacement')
+  zlabel('Displacement [um] (micrometers)')
+end
+
 ```
 
 ## Part D
 #### Problem Statement
-Solve for w given a pressure, P=0.001 MPa and tension, T=0.006 uN/um with 10 interior
-nodes. Plot the result with `surf(X,Y,W)` where X, Y, and W are the x-, y-, and
-z-coordinates of each point on the membrane from 0-10um.
-#### Approach
+Solve for w given a pressure, P=0.001 MPa and tension, T=0.006 uN/um with 10 interior nodes. Plot the result with `surf(X,Y,W)` where X, Y, and W are the x-, y-, and z-coordinates of each point on the membrane from 0-10um.
 
+#### Approach
 - T = 0.006 uN/um
 - P = 0.001 MPa
 - n = 10 nodes
diff --git a/membrane_solution.m b/membrane_solution.m
index 0f68771..4e12254 100644
--- a/membrane_solution.m
+++ b/membrane_solution.m
@@ -1,28 +1,28 @@
 function [w] = membrane_solution(T,P,n)
-  %
+  % General Central finite difference approximation of
+  % gradient with n-by-n interior nodes in terms of P & T.
+  % Input:
   % T = tension per unit length (uN/um)
   % P = pressure (MPa)
-  % n = # of interior nodes
+  % n = # of interior node rows/columns
+  % Output:
+  % w = displacement vector for interior nodes
 
   od = ones(n^2-1,1);
   od(n:n:end) = 0;
   k = -4 * diag(ones(n^2,1)) + diag(ones((n^2)-n,1),n) + diag(ones((n^2)-n,1),-n) + diag(od,1) + diag(od,-1);
 
-  %
   y = -(10/(n+1))^2*(P/T)*ones(n^2,1);
-
-  %
   w = k\y;
 
-  %
+  % Find displacement vector w
+  % which represents 2D data set w(x,y)
   [x,y] = meshgrid(0:10/(n+1):10,0:10/(n+1):10);
-  %
   z = zeros(size(x));
-
   z(2:end-1,2:end-1) = reshape(w,[n n]);
 
+  % Plot gradient of membrane displacement
   surf(x,y,z)
-
   title('Gradient of Membrane Displacement')
   zlabel('Displacement [um] (micrometers)')
 end