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membrane_solution3.m

@@ -0,0 +1,15 @@
+function [w] = membrane_solution3(T,P)
+    % Set up initial matrix
+    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);
+
+    % Solve for unknown matrix, w
+    y = -(10/4)^2*(P/T)*ones(9,1); %output vector 
+    w = k\y; %solves for w in microm
+
+    [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)
+end

membrane_solution31.m

@@ -0,0 +1,14 @@
+function [w] = membrane_solution31(T,P,n)% Set up initial matrix
+    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);
+
+    % Solve for unknown matrix, w
+    y = -(10/(n+1))^2*(P/T)*ones(n^2,1); %output vector 
+    w = k\y; %solves for w in microm
+
+    [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)
+end 

script1.m

@@ -0,0 +1,15 @@
+% Set up initial matrix
+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);
+
+% Solve for unknown matrix, w
+P = 0.001; %MPa
+T = 0.006; %microN/microm
+y = -(10/4)^2*(P/T)*ones(9,1); %output vector 
+w = k\y; %solves for w in microm
+
+[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)

script2.asv

@@ -0,0 +1,15 @@
+% Set up initial matrix
+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);
+
+% Solve for unknown matrix, w
+P = 0.001; %MPa
+T = 0.006; %microN/microm
+y = -(10/(n+1))^2*(P/T)*ones(n^2,1); %output vector 
+w = k\y; %solves for w in microm
+
+[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)

script2.m

@@ -0,0 +1,15 @@
+function [w] = membrane_solution31(T,P,n);% Set up initial matrix
+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);
+
+% Solve for unknown matrix, w
+P = 0.001; %MPa
+T = 0.006; %microN/microm
+y = -(10/(n+1))^2*(P/T)*ones(n^2,1); %output vector 
+w = k\y; %solves for w in microm
+
+[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)