From 6ffe9a33415e3a5238b80520ba7211a4aaedd58b Mon Sep 17 00:00:00 2001
From: mattmaliniak <31718098+mattmaliniak@users.noreply.github.com>
Date: Thu, 14 Dec 2017 14:53:27 -0500
Subject: [PATCH] .

---
 Part F/F_sol.asv       |  6 ++++++
 Part F/F_sol.m         |  7 +++++++
 Part F/SE_diff.m       | 26 ++++++++++++++++++++++++++
 Part F/mod_secant.m    | 30 ------------------------------
 Part F/tension_sol.asv | 11 +++++------
 Part F/tension_sol.m   |  9 +++------
 Part G/part_g.asv      |  5 +++++
 Part G/part_g.m        | 10 ++++++++++
 8 files changed, 62 insertions(+), 42 deletions(-)
 create mode 100644 Part F/F_sol.asv
 create mode 100644 Part F/F_sol.m
 create mode 100644 Part F/SE_diff.m
 delete mode 100644 Part F/mod_secant.m
 create mode 100644 Part G/part_g.asv
 create mode 100644 Part G/part_g.m

diff --git a/Part F/F_sol.asv b/Part F/F_sol.asv
new file mode 100644
index 0000000..764aed1
--- /dev/null
+++ b/Part F/F_sol.asv	
@@ -0,0 +1,6 @@
+ n=20:5:40;
+ P=0.001; %MPa
+ T = zeros(1,length(n));
+ for i = 1:length(n)
+     [T(i) ea(i)] = tension_sol(P,n(i));
+ end
\ No newline at end of file
diff --git a/Part F/F_sol.m b/Part F/F_sol.m
new file mode 100644
index 0000000..e7e8a13
--- /dev/null
+++ b/Part F/F_sol.m	
@@ -0,0 +1,7 @@
+ n=20:5:40;
+ P=0.001; %MPa
+ T = zeros(1,length(n));
+ ea = zeros(1,length(n));
+ for i = 1:length(n)
+     [T(i), ea(i)] = tension_sol(P,n(i));
+ end
\ No newline at end of file
diff --git a/Part F/SE_diff.m b/Part F/SE_diff.m
new file mode 100644
index 0000000..9338a84
--- /dev/null
+++ b/Part F/SE_diff.m	
@@ -0,0 +1,26 @@
+function [pw_se,w]=SE_diff(T,P,n)
+E = 1000000; %TPa Units may need to be changed
+v = .31; %Poissons ratio
+t = .0003; %um
+h = 10/(n+1); %nm
+w = membrane_solution(T,P,n);
+z = zeros(n+2);
+z(2:end-1,2:end-1) = reshape(w,[n n]);
+num = n + 1;
+wbar = zeros(num);
+for i = 1:num
+    for j = 1:num
+        wbar(i,j) = mean([z(i,j),z(i+1,j),z(i,j+1),z(i+1,j+1)]);
+    end
+end
+pw = sum(sum(wbar.*h^2.*P));
+dwdx = zeros(num);
+dwdy = zeros(num);
+for i = 1:num
+    for j = 1:num
+        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 = abs(pw-se);
\ No newline at end of file
diff --git a/Part F/mod_secant.m b/Part F/mod_secant.m
deleted file mode 100644
index b74f181..0000000
--- a/Part F/mod_secant.m	
+++ /dev/null
@@ -1,30 +0,0 @@
-function [root,ea,iter]=mod_secant(func,dx,xr,es,maxit,varargin)
-% newtraph: Modified secant root location zeroes
-% [root,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):
-%   uses modified secant method to find the root of func
-% input:
-%   func = name of function
-%   dx = perturbation fraction
-%   xr = initial guess
-%   es = desired relative error (default = 0.0001%)
-%   maxit = maximum allowable iterations (default = 50)
-%   p1,p2,... = additional parameters used by function
-% output:
-%   root = real root
-%   ea = approximate relative error (%)
-%   iter = number of iterations
-if nargin<3,error('at least 3 input arguments required'),end
-if nargin<4 || isempty(es),es=0.0001;end
-if nargin<5 || isempty(maxit),maxit=50;end
-iter = 0;
-while (1)
-  xrold = xr;
-  dfunc=(func(xr+dx)-func(xr))./dx;
-  xr = xr - func(xr)/dfunc;
-  iter = iter + 1;
-  if xr ~= 0 
-    ea = abs((xr - xrold)/xr) * 100;
-  end
-  if ea <= es || iter >= maxit, break, end
-end
-root = xr;
\ No newline at end of file
diff --git a/Part F/tension_sol.asv b/Part F/tension_sol.asv
index e513227..61dc9f5 100644
--- a/Part F/tension_sol.asv	
+++ b/Part F/tension_sol.asv	
@@ -1,7 +1,6 @@
 function T = tension_sol(P,n)
-num = length(n)
-for i = 1:nu
-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);
\ No newline at end of file
+num = length(n);
+for i = 1:num
+    y =@(T) SE_diff(
+    [root,fx,ea,iter]=bisect(y,0,.006)
+end
\ No newline at end of file
diff --git a/Part F/tension_sol.m b/Part F/tension_sol.m
index 0e95ee4..dd534c9 100644
--- a/Part F/tension_sol.m	
+++ b/Part F/tension_sol.m	
@@ -1,6 +1,3 @@
-function T = tension_sol(P,n)
-num = length(n);
-for i = 1:num
-    y =@(T) (P./T)+3.6534e+04;
-    [root,fx,ea,iter]=bisect(y,0,.006)
-end
\ No newline at end of file
+function [T,ea] = tension_sol(P,n)
+y =@(T) SE_diff(T,P,n);
+[T,fx,ea,iter]=bisect(y,.01,1);
diff --git a/Part G/part_g.asv b/Part G/part_g.asv
new file mode 100644
index 0000000..85a7561
--- /dev/null
+++ b/Part G/part_g.asv	
@@ -0,0 +1,5 @@
+P = linspace(.001,.01,10);
+n = 20;
+for i = 1:length(P)
+    T(i) = tension_sol(P(i),n);
+    
\ No newline at end of file
diff --git a/Part G/part_g.m b/Part G/part_g.m
new file mode 100644
index 0000000..c36bedf
--- /dev/null
+++ b/Part G/part_g.m	
@@ -0,0 +1,10 @@
+P = linspace(.001,.01,10);
+n = 20;
+T = zeros(1,length(P));
+wmax = zeros(1,length(P));
+for i = 1:length(P)
+    T(i) = tension_sol(P(i),n);
+    w = membrane_solution(T(i),P(i),n);
+    wmax(i) = max(w);
+end
+plot(wmax,P,'o')