diff --git a/README.md b/README.md index 2ba5b42..32e01fa 100644 --- a/README.md +++ b/README.md @@ -8,11 +8,11 @@ function [w] = membrane_solution3(T,P) 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); + a = -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; + w = a\y; grid on [x,y] = meshgrid(0:10/4:10,0:10/4:10); @@ -36,3 +36,40 @@ end membrane_solution3(0.006,0.001) ``` ![](assets/README-20ed9cd0.png) + +## Part C + +``` +function [w] = membrane_solution3(T,P) + + + od = ones(8,1); + od(3:3:end) = 0; + a = -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 = a\y; + +grid on + [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') + xlabel('X (\muM)') + ylabel('Y (\muM)') + zlabel('Displacement (\muM)') + colormap jet + shading interp + disp(w) + +end +``` + +## Part D + +``` +membrane_solution(0.006,0.001,10) +``` +![](assets/README-579fb915.png) diff --git a/assets/PartD.png b/assets/PartD.png new file mode 100644 index 0000000..e0eeada Binary files /dev/null and b/assets/PartD.png differ diff --git a/assets/README-579fb915.png b/assets/README-579fb915.png new file mode 100644 index 0000000..1c50c90 Binary files /dev/null and b/assets/README-579fb915.png differ diff --git a/membrane_solution.m b/membrane_solution.m new file mode 100644 index 0000000..f705552 --- /dev/null +++ b/membrane_solution.m @@ -0,0 +1,21 @@ +function [w] = membrane_solution(T,P,n) + + od = ones(n^2-1,1); + od(n:n:end) = 0; + a = -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 = a\y; +grid on + [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') + xlabel('X (\muM)') + ylabel('Y (\muM)') + zlabel('Displacement (\muM)') + colormap jet + shading interp + disp(w) +end \ No newline at end of file diff --git a/membrane_solution3.asv b/membrane_solution3.asv new file mode 100644 index 0000000..b49dbfd --- /dev/null +++ b/membrane_solution3.asv @@ -0,0 +1,25 @@ +function [w] = membrane_solution3(T,P) + + + od = ones(8,1); + od(3:3:end) = 0; + a = -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 = a\y; + +grid on + [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') + xlabel('X (\muM)') + ylabel('Y (\muM)') + zlabel('Displacement (\muM)') + colormap jet + shading interp + disp(w) + +end \ No newline at end of file diff --git a/membrane_solution3.m b/membrane_solution3.m index e668403..b49dbfd 100644 --- a/membrane_solution3.m +++ b/membrane_solution3.m @@ -3,11 +3,11 @@ function [w] = membrane_solution3(T,P) 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); + a = -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; + w = a\y; grid on [x,y] = meshgrid(0:10/4:10,0:10/4:10);