Part F

Part E/SE_diff.m

@@ -1,5 +1,5 @@
 function [pw_se,w]=SE_diff(T,P,n)
-E = 1; %TPa Units may need to be changed
+E = 1e6; %TPa Units may need to be changed
 v = .31; %Poissons ratio
 t = .3; %nm
 h = 10/(n+1); %nm

Part F/bisect.m

@@ -0,0 +1,37 @@
+function [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,varargin)
+% bisect: root location zeroes
+% [root,fx,ea,iter]=bisect(func,xl,xu,es,maxit,p1,p2,...):
+% uses bisection method to find the root of func
+% input:
+% func = name of function
+% xl, xu = lower and upper guesses
+% es = desired relative error (default = 0.0001%)
+% maxit = maximum allowable iterations (default = 50)
+% p1,p2,... = additional parameters used by func
+% output:
+% root = real root
+% fx = function value at root
+% ea = approximate relative error (%)
+% iter = number of iterations
+if nargin<3,error('at least 3 input arguments required'),end
+test = func(xl,varargin{:})*func(xu,varargin{:});
+if test>0,error('no sign change'),end
+if nargin<4||isempty(es), es=0.0001;end
+if nargin<5||isempty(maxit), maxit=50;end
+iter = 0; xr = xl; ea = 100;
+while (1)
+  xrold = xr;
+  xr = (xl + xu)/2;
+  iter = iter + 1;
+  if xr ~= 0,ea = abs((xr - xrold)/xr) * 100;end
+  test = func(xl,varargin{:})*func(xr,varargin{:});
+  if test < 0
+    xu = xr;
+  elseif test > 0
+    xl = xr;
+  else
+    ea = 0;
+  end
+  if ea <= es || iter >= maxit,break,end
+end
+root = xr; fx = func(xr, varargin{:});

Part F/membrane_solution.m

@@ -0,0 +1,25 @@
+function [w] = membrane_solution(T,P,n)
+    % T = Tension (microNewton/micrometer)
+    % P = Pressure (MPa)
+    % n = # of 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;
+
+    % Solves for displacement (micrometers)
+    % Output w is a vector
+    % Solution represents a 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]);
+    surf(x,y,z)
+    title('Membrane Displacement')
+    zlabel('Displacement (micrometer)')
+
+    % Membrane displacement is shown on chart
+end

Part F/mod_secant.m

@@ -0,0 +1,30 @@
+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;

Part F/tension_sol.asv

@@ -0,0 +1,7 @@
+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);

Part F/tension_sol.m

@@ -0,0 +1,6 @@
+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