Merge branch 'master' of https://github.uconn.edu/ltd13002/ME3255_Fin…

…al_Project

Part A/membrane_solution3.m

@@ -1,17 +1,14 @@
 function [w] = membrane_solution3(T,P)
-    % T = Tension (microNewton/micrometer)
-    % P = Pressure (MPa)
-
-    od = ones(8,1);
-    od(3:3:end) = 0;
-    k = -4*diag(ones(9,1))+diag(ones(9-3,1),3)+diag(ones(9-3,1),-3)+diag(od,1)+diag(od,-1);
-
-
-    y = -(10/4)^2*(P/T)*ones(9,1);
-    w = k\y; 
-    % Solves for displacement (micrometers)
-    % Solution represents a 2D data set w(x,y)
+% membrane_solution3: dispalacement of node for membrane with 3x3 interior
+% nodes
+% [w] = membrane_solution3(T,P)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% output:
+% w = vector of displacement of interior nodes
 
+<<<<<<< HEAD
     [x,y] = meshgrid(0:10/4:10,0:10/4:10);
     z = zeros(size(x));
     z(2:end-1,2:end-1) = reshape(w,[3 3]);
@@ -22,4 +19,27 @@ function [w] = membrane_solution3(T,P)
     xlabel('X Position (micron)')
     % Membrane displacement is shown on chart
 
-end 
+end 
+=======
+od = ones(8,1);
+od(3:3:end) = 0;
+k = -4*diag(ones(9,1))+diag(ones(9-3,1),3)+diag(ones(9-3,1),-3)+diag(od,1)+diag(od,-1);
+
+
+y = -(10/4)^2*(P/T)*ones(9,1);
+w = k\y;
+
+% Solves for displacement (micrometers)
+% Solution represents a 2D data set w(x,y)
+
+[x,y] = meshgrid(0:10/4:10,0:10/4:10);
+z = zeros(size(x));
+z(2:end-1,2:end-1) = reshape(w,[3 3]);
+surf(x,y,z)
+title('Membrane Displacement')
+zlabel('Displacement (micrometer)')
+
+% Membrane displacement is shown on chart
+
+end
+>>>>>>> 3217bec2baefdb9797b60fd7e29f12b838227cd0

Part C/membrane_solution.asv

@@ -0,0 +1,27 @@
+function [w] = membrane_solution(T,P,n)
+% membrane_solution: dispalacement of node for membrane with nxn interior nodes
+% [w] = membrane_solution(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% output:
+% w = vector of displacement 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 C/membrane_solution.m

@@ -1,23 +1,28 @@
 function [w] = membrane_solution(T,P,n)
-    % T = Tension (microNewton/micrometer)
-    % P = Pressure (MPa)
-    % n = # of interior nodes
+% membrane_solution: dispalacement of node for membrane with nxn interior nodes
+% [w] = membrane_solution(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% w = vector of displacement 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);
+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)
+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
+[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 E/SE_diff.m

@@ -1,4 +1,16 @@
 function [pw_se,w]=SE_diff(T,P,n)
+% SE_diff: difference between strain energy and work done by pressure in
+% membrane
+% [pw_se,w]=SE_diff(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% pw_se = difference between strain energy and work done by pressure in
+% membrane
+% w = vector of displacement of interior nodes
+
 E = 1e6; %TPa Units may need to be changed
 v = .31; %Poissons ratio
 t = .3; %nm

Part E/membrane_solution.m

@@ -1,23 +1,28 @@
 function [w] = membrane_solution(T,P,n)
-    % T = Tension (microNewton/micrometer)
-    % P = Pressure (MPa)
-    % n = # of interior nodes
+% membrane_solution: dispalacement of node for membrane with nxn interior nodes
+% [w] = membrane_solution(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% w = vector of displacement 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);
+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)
+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
+[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/Rel_error.asv

@@ -0,0 +1,14 @@
+function re = Rel_error (T)
+% Rel_error: calculates relative error of a vector
+% [w] = membrane_solution(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% w = vector of displacement of interior nodes
+
+re = zeros(1,length(T)-1);
+for i = 2:length(T)
+    re(i-1)= abs(T(i)-T(i-1))/T(i-1);
+end

Part F/Rel_error.m

@@ -1,4 +1,11 @@
 function re = Rel_error (T)
+% Rel_error: calculates relative error of a vector
+% re = Rel_error (T)
+% input:
+% T = vector of numbers
+% output:
+% re = relative error of vector
+
 re = zeros(1,length(T)-1);
 for i = 2:length(T)
     re(i-1)= abs(T(i)-T(i-1))/T(i-1);

Part F/SE_diff.m

@@ -1,4 +1,16 @@
 function [pw_se,w]=SE_diff(T,P,n)
+% SE_diff: difference between strain energy and work done by pressure in
+% membrane
+% [pw_se,w]=SE_diff(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% pw_se = difference between strain energy and work done by pressure in
+% membrane
+% w = vector of displacement of interior nodes
+
 E = 1000000; %TPa Units may need to be changed
 v = .31; %Poissons ratio
 t = .0003; %um

Part F/membrane_solution.m

@@ -1,25 +1,31 @@
 function [w] = membrane_solution(T,P,n)
-    % T = Tension (microNewton/micrometer)
-    % P = Pressure (MPa)
-    % n = # of interior nodes
+% membrane_solution: dispalacement of node for membrane with nxn interior nodes
+% [w] = membrane_solution(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% w = vector of displacement 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)
+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);
 
-    [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
+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/tension_sol.m

@@ -1,3 +1,13 @@
 function [T,ea] = tension_sol(P,n)
+% tension_sol: outputs tension of a membrane given the pressure and number
+% of nodes
+% [T,ea] = tension_sol(P,n)
+% input:
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% T = Tension (microNewton/micrometer)
+% ea = approximate relative error (%)
+
 y =@(T) SE_diff(T,P,n);
 [T,fx,ea,iter]=bisect(y,.01,1);

Part G/SE_diff.m

@@ -1,4 +1,16 @@
 function [pw_se,w]=SE_diff(T,P,n)
+% SE_diff: calculates difference between strain energy and work done by pressure in
+% membrane
+% [pw_se,w]=SE_diff(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% pw_se = difference between strain energy and work done by pressure in
+% membrane
+% w = vector of displacement of interior nodes
+
 E = 1000000; %TPa Units may need to be changed
 v = .31; %Poissons ratio
 t = .0003; %um

Part G/membrane_solution.m

@@ -1,25 +1,30 @@
 function [w] = membrane_solution(T,P,n)
-    % T = Tension (microNewton/micrometer)
-    % P = Pressure (MPa)
-    % n = # of interior nodes
+% membrane_solution: dispalacement of node for membrane with nxn interior nodes
+% [w] = membrane_solution(T,P,n)
+% input:
+% T = Tension (microNewton/micrometer)
+% P = Pressure (MPa)
+% n = number of rows and columns of interior nodes
+% output:
+% w = vector of displacement 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);
+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)
+y = -(10/(n+1))^2*(P/T)*ones(n^2,1);
+w = k\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
+% 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 G/part_g.m

@@ -9,12 +9,12 @@ for i = 1:length(P)
 end
 clf
 setDefaults
-x = wmax;
+x = wmax';
 y = P';
-Z = [x.^3]';
+Z = x.^3;
 a = Z\y;
 x_fcn = linspace(min(x),max(x));
-plot(x,y,'o',x_fcn,a.*x_fcn)
+plot(x,y,'o',x_fcn,a.*x_fcn.^3)
 title('Pressure vs. Maximum Deflection')
-xlabel('Max w')
-ylabel('Pressure vs.. Max Deflection')
+xlabel('Maximum Deflection (um)')
+ylabel('Pressure (MPa)')