From 96d48b1e3e8adc23f41ba2a66ede34f7ed07e73b Mon Sep 17 00:00:00 2001 From: Leahy Date: Sun, 10 Dec 2017 12:38:07 -0500 Subject: [PATCH] 1 --- README.md | 59 +++++++++++++++++++++++++++++++++++++++++++- figures/figure1.png | Bin 0 -> 22004 bytes figures/figure2.png | Bin 0 -> 33111 bytes 3 files changed, 58 insertions(+), 1 deletion(-) create mode 100644 figures/figure1.png create mode 100644 figures/figure2.png diff --git a/README.md b/README.md index bca93f3..c25bf87 100644 --- a/README.md +++ b/README.md @@ -1 +1,58 @@ -# 07_final_project \ No newline at end of file +# 07_final_project + +### Part A +``` matlab +function [w] = membrane_solution3(T,P) % Set up initial matrix + % T = given tension (microNewton/micrometer) + % P = given 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); + + % 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 +``` + +### Part B +``` matlab +[w] = membrane_solution3(0.006,0.001); +``` + +![3x3 Interior Nodes](./figures/figure1.png) + +### Part C +```matlab +function [w] = membrane_solution(T,P,n)% Set up initial matrix + % T = given tension (microNewton/micrometer) + % P = given pressure (MPa) + % n = number 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); + + % 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 +``` + +### Part D +``` matlab +[w] = membrane_solution(0.006,0.001,10) +``` + +![nxn Interior Nodes, n = 10](./figures/figure2.png) diff --git 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