diff --git a/Part A/membrane_solution3.m b/Part A/membrane_solution3.m index ec29f9b..d495083 100644 --- a/Part A/membrane_solution3.m +++ b/Part A/membrane_solution3.m @@ -16,8 +16,10 @@ function [w] = membrane_solution3(T,P) 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)') + title('Membrane Displacement (3 x 3)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') % Membrane displacement is shown on chart end \ No newline at end of file diff --git a/Part B/PartBFigure.png b/Part B/PartBFigure.png index 4699760..32dd6f3 100644 Binary files a/Part B/PartBFigure.png and b/Part B/PartBFigure.png differ diff --git a/Part B/membrane_solution3.m b/Part B/membrane_solution3.m new file mode 100644 index 0000000..d495083 --- /dev/null +++ b/Part B/membrane_solution3.m @@ -0,0 +1,25 @@ +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) + + [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 (3 x 3)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') + % Membrane displacement is shown on chart + +end \ No newline at end of file diff --git a/Part D/PartDFigure.png b/Part D/PartDFigure.png index ca69c45..f367cda 100644 Binary files a/Part D/PartDFigure.png and b/Part D/PartDFigure.png differ diff --git a/Part D/membrane_solution.m b/Part D/membrane_solution.m new file mode 100644 index 0000000..f5a442a --- /dev/null +++ b/Part D/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 (10 x 10)') + zlabel('Z Position (micron)') + ylabel('Y Position (micron)') + xlabel('X Position (micron)') + % Membrane displacement is shown on chart +end \ No newline at end of file